The amazing world of String Theory. Keshav Dasgupta
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- Josephine Richards
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1 The amazing world of String Theory Keshav Dasgupta Department of Physics McGill University Montréal, QC, CANADA Dasgupta (McGill) String Theory Homer / 92
2 String theory is an amazing branch of science that manages to unify all matter and interactions under one simple idea Dasgupta (McGill) String Theory Homer / 92
3 String theory is an amazing branch of science that manages to unify all matter and interactions under one simple idea The starting point is the so-called Nambu-Goto action S NG = T d 2 σ det X µ σ α X ν σ β η µν Dasgupta (McGill) String Theory Homer / 92
4 String theory is an amazing branch of science that manages to unify all matter and interactions under one simple idea The starting point is the so-called Nambu-Goto action S NG = T d 2 σ det X µ σ α X ν σ β η µν where T is the tension of the string, σ α are the world-sheet coordinates, X µ are the space-time coordinates and η µν is the flat spacetime metric. Dasgupta (McGill) String Theory Homer / 92
5 The more useful version is the so-called Polyakov action, that goes in the following way S = T d 2 σ hh αβ α X µ β X ν η µν Dasgupta (McGill) String Theory Homer / 92
6 The more useful version is the so-called Polyakov action, that goes in the following way S = T d 2 σ hh αβ α X µ β X ν η µν You really didn t come here to listen to this, did you? Dasgupta (McGill) String Theory Homer / 92
7 The more useful version is the so-called Polyakov action, that goes in the following way S = T d 2 σ hh αβ α X µ β X ν η µν You really didn t come here to listen to this, did you? I was just kidding! Dasgupta (McGill) String Theory Homer / 92
8 The more useful version is the so-called Polyakov action, that goes in the following way S = T d 2 σ hh αβ α X µ β X ν η µν You really didn t come here to listen to this, did you? I was just kidding! Lets start our talk now Dasgupta (McGill) String Theory Homer / 92
9 The more useful version is the so-called Polyakov action, that goes in the following way S = T d 2 σ hh αβ α X µ β X ν η µν You really didn t come here to listen to this, did you? I was just kidding! Lets start our talk now hopefully I ll manage to explain what on earth is string theory! Dasgupta (McGill) String Theory Homer / 92
10 The more useful version is the so-called Polyakov action, that goes in the following way S = T d 2 σ hh αβ α X µ β X ν η µν You really didn t come here to listen to this, did you? I was just kidding! Lets start our talk now hopefully I ll manage to explain what on earth is string theory! Its also a good time to open your can of draft beer! Dasgupta (McGill) String Theory Homer / 92
11 From very early on people have been thinking about this: Dasgupta (McGill) String Theory Homer / 92
12 From very early on people have been thinking about this: Dasgupta (McGill) String Theory Homer / 92
13 From very early on people have been thinking about this: In this talk I ll try aim for this Dasgupta (McGill) String Theory Homer / 92
14 From very early on people have been thinking about this: In this talk I ll try aim for this hopefully! Dasgupta (McGill) String Theory Homer / 92
15 But before we start discussing String Theory, some of you might be wondering: Dasgupta (McGill) String Theory Homer / 92
16 What is String Theory? Dasgupta (McGill) String Theory Homer / 92
17 What is String Theory? How does this fit in with what we already know? Dasgupta (McGill) String Theory Homer / 92
18 What is String Theory? How does this fit in with what we already know? Do we really need string theory to answer our fundamental questions? Dasgupta (McGill) String Theory Homer / 92
19 What is String Theory? How does this fit in with what we already know? Do we really need string theory to answer our fundamental questions? Where did those good old theories go wrong? Dasgupta (McGill) String Theory Homer / 92
20 Therefore let me start from the very beginning, way down in history, when Classical Mechanics ruled our ideas... Dasgupta (McGill) String Theory Homer / 92
21 It All Started With This Book Dasgupta (McGill) String Theory Homer / 92
22 And The Ideas Developed By Him Dasgupta (McGill) String Theory Homer / 92
23 And The Ideas Developed By Him The Year Was 1687 Dasgupta (McGill) String Theory Homer / 92
24 And The Ideas Developed By Him The Year Was 1687 For almost two centuries the theory developed by Newton (and others) ruled supreme. However towards the beginning of the 20th century people started finding cracks in the edifice... Dasgupta (McGill) String Theory Homer / 92
25 These cracks came from two regions Dasgupta (McGill) String Theory Homer / 92
26 These cracks came from two regions Exploring very high speeds Dasgupta (McGill) String Theory Homer / 92
27 These cracks came from two regions Exploring very high speeds Exploring very short distances Dasgupta (McGill) String Theory Homer / 92
28 So First: What happens when we explore short distances? Dasgupta (McGill) String Theory Homer / 92
29 It is now known that the theory there should be Quantum Mechanics whose main result can be summarised by one line Dasgupta (McGill) String Theory Homer / 92
30 Nature is probabilistic i.e Uncertainity rules supreme Dasgupta (McGill) String Theory Homer / 92
31 Nature is probabilistic i.e Uncertainity rules supreme or, more appropriately, just like coin toss! Before you toss the coin you ll never know the outcome! Dasgupta (McGill) String Theory Homer / 92
32 The former idea was proposed by Erwin Schrodinger Dasgupta (McGill) String Theory Homer / 92
33 The former idea was proposed by Erwin Schrodinger Dasgupta (McGill) String Theory Homer / 92
34 And the latter idea was presented by Werner Heisenberg Dasgupta (McGill) String Theory Homer / 92
35 And the latter idea was presented by Werner Heisenberg Dasgupta (McGill) String Theory Homer / 92
36 Quantum mechanics is a strange theory which, fortunately, is visible only at very short distances! If it was visible at large distances, then we would see the following: Dasgupta (McGill) String Theory Homer / 92
37 Quantum mechanics is a strange theory which, fortunately, is visible only at very short distances! If it was visible at large distances, then we would see the following: Dasgupta (McGill) String Theory Homer / 92
38 Quantum mechanics is a strange theory which, fortunately, is visible only at very short distances! If it was visible at large distances, then we would see the following: Dasgupta (McGill) String Theory Homer / 92
39 Which means we would never be sure if the cat is dead or alive, unless we make a measurement! Dasgupta (McGill) String Theory Homer / 92
40 Which means we would never be sure if the cat is dead or alive, unless we make a measurement! Much like: Dasgupta (McGill) String Theory Homer / 92
41 Which means we would never be sure if the cat is dead or alive, unless we make a measurement! Much like: Dasgupta (McGill) String Theory Homer / 92
42 The previous observation is generically represented in the following way that distinguishes Newtonian theory from Quantum mechanics Dasgupta (McGill) String Theory Homer / 92
43 The previous observation is generically represented in the following way that distinguishes Newtonian theory from Quantum mechanics Dasgupta (McGill) String Theory Homer / 92
44 These were all developed around 1927 Dasgupta (McGill) String Theory Homer / 92
45 These were all developed around 1927 It was the best of times and it was the worst of times! Dasgupta (McGill) String Theory Homer / 92
46 These ideas were very beautiful, and very very revolutionary. At that time the key person who really understood both these ideas was Dasgupta (McGill) String Theory Homer / 92
47 These ideas were very beautiful, and very very revolutionary. At that time the key person who really understood both these ideas was Neils Bohr Dasgupta (McGill) String Theory Homer / 92
48 In fact he understood the subject so well that he made the following comment Dasgupta (McGill) String Theory Homer / 92
49 In fact he understood the subject so well that he made the following comment If Quantum Mechanics hasn t profoundly shocked you, you haven t understood it yet! Dasgupta (McGill) String Theory Homer / 92
50 Although relatively not well publicised, it seem he also made the following comments: Dasgupta (McGill) String Theory Homer / 92
51 Although relatively not well publicised, it seem he also made the following comments: If you don t understand Quantum Mechanics Dasgupta (McGill) String Theory Homer / 92
52 Although relatively not well publicised, it seem he also made the following comments: If you don t understand Quantum Mechanics Dasgupta (McGill) String Theory Homer / 92
53 But then there was one person who was really disturbed by Quantum Mechanics Dasgupta (McGill) String Theory Homer / 92
54 But then there was one person who was really disturbed by Quantum Mechanics Dasgupta (McGill) String Theory Homer / 92
55 Einstein said Dasgupta (McGill) String Theory Homer / 92
56 Einstein said Quantum Mechanics cannot be the right theory of nature, because it is hard to believe that God plays with dice! Dasgupta (McGill) String Theory Homer / 92
57 To which Bohr replied Dasgupta (McGill) String Theory Homer / 92
58 To which Bohr replied Einstein, stop telling God what to do! Dasgupta (McGill) String Theory Homer / 92
59 But then why was Einstein so disturbed? Dasgupta (McGill) String Theory Homer / 92
60 But then why was Einstein so disturbed? Because he had, towards the beginning of the 20th century, developed two theories that modifies classical mechanics at high speeds Dasgupta (McGill) String Theory Homer / 92
61 But then why was Einstein so disturbed? Special Theory of Relativity: at uniform speeds Because he had, towards the beginning of the 20th century, developed two theories that modifies classical mechanics at high speeds Dasgupta (McGill) String Theory Homer / 92
62 But then why was Einstein so disturbed? Because he had, towards the beginning of the 20th century, developed two theories that modifies classical mechanics at high speeds Special Theory of Relativity: at uniform speeds General Theory of Relativity: at non-uniform speeds Dasgupta (McGill) String Theory Homer / 92
63 The GTR views the spacetime as rubber sheets on which masses form dents Dasgupta (McGill) String Theory Homer / 92
64 The GTR views the spacetime as rubber sheets on which masses form dents Dasgupta (McGill) String Theory Homer / 92
65 So gravity is simply a distortion of geometry! Dasgupta (McGill) String Theory Homer / 92
66 So gravity is simply a distortion of geometry! Dasgupta (McGill) String Theory Homer / 92
67 For Einstein this was nice and elegant because everything was precise and there was no ambiguity or uncertainity... Dasgupta (McGill) String Theory Homer / 92
68 For Einstein this was nice and elegant because everything was precise and there was no ambiguity or uncertainity... Yet Quantum Mechanics was right, so was General Theory of Relativity! Dasgupta (McGill) String Theory Homer / 92
69 So whats going on? Does nature behave differently as we explore different limits? Dasgupta (McGill) String Theory Homer / 92
70 To investigate this first let us go to the limit where we can have Dasgupta (McGill) String Theory Homer / 92
71 To investigate this first let us go to the limit where we can have Short Distances + High Speeds Dasgupta (McGill) String Theory Homer / 92
72 To investigate this first let us go to the limit where we can have Quantum Mechanics + High Speeds Dasgupta (McGill) String Theory Homer / 92
73 To investigate this first let us go to the limit where we can have Quantum Mechanics + Special Theory of Relativity Dasgupta (McGill) String Theory Homer / 92
74 To investigate this first let us go to the limit where we can have Quantum Mechanics + Special Theory of Relativity = QUANTUM FIELD THEORY Dasgupta (McGill) String Theory Homer / 92
75 The special theory of relativity is based on the fact that the speed of light is the highest speed and is a constant. This leads to: Dasgupta (McGill) String Theory Homer / 92
76 The special theory of relativity is based on the fact that the speed of light is the highest speed and is a constant. This leads to: Time dilation Dasgupta (McGill) String Theory Homer / 92
77 The special theory of relativity is based on the fact that the speed of light is the highest speed and is a constant. This leads to: Time dilation Dasgupta (McGill) String Theory Homer / 92
78 And length contraction Dasgupta (McGill) String Theory Homer / 92
79 And length contraction Dasgupta (McGill) String Theory Homer / 92
80 Take 1: Lets mix QM with STR Dasgupta (McGill) String Theory Homer / 92
81 Take 1: Lets mix QM with STR Dasgupta (McGill) String Theory Homer / 92
82 Take 1: Lets mix QM with STR What do we really get? Dasgupta (McGill) String Theory Homer / 92
83 Well... Dasgupta (McGill) String Theory Homer / 92
84 Well... Dasgupta (McGill) String Theory Homer / 92
85 Well... More appropriately: disaster! Dasgupta (McGill) String Theory Homer / 92
86 What did we miss? Dasgupta (McGill) String Theory Homer / 92
87 What did we miss? After much confusion Dasgupta (McGill) String Theory Homer / 92
88 What did we miss? After much confusion Dasgupta (McGill) String Theory Homer / 92
89 What did we miss? After much confusion and anger.. Dasgupta (McGill) String Theory Homer / 92
90 What did we miss? After much confusion and anger.. Dasgupta (McGill) String Theory Homer / 92
91 It was eventually suggested by Feynman Dasgupta (McGill) String Theory Homer / 92
92 It was eventually suggested by Feynman and others... Dasgupta (McGill) String Theory Homer / 92
93 Quantum Mechanics + STR + Renormalisation Dasgupta (McGill) String Theory Homer / 92
94 Quantum Mechanics + STR + Renormalisation = Something really nice and consistent Dasgupta (McGill) String Theory Homer / 92
95 Quantum Mechanics + STR + Renormalisation = Something really nice and consistent For example QED: Quantum Electrodynamics Dasgupta (McGill) String Theory Homer / 92
96 For those who don t know anything about renormalisation, the idea is very simple! Dasgupta (McGill) String Theory Homer / 92
97 For those who don t know anything about renormalisation, the idea is very simple! You do a calculation, and say you get an infinite answer. Dasgupta (McGill) String Theory Homer / 92
98 For those who don t know anything about renormalisation, the idea is very simple! You do a calculation, and say you get an infinite answer. Then you bring another infinity and do the following: Dasgupta (McGill) String Theory Homer / 92
99 For those who don t know anything about renormalisation, the idea is very simple! You do a calculation, and say you get an infinite answer. Then you bring another infinity and do the following: Infinity Infinity = finite Dasgupta (McGill) String Theory Homer / 92
100 For those who don t know anything about renormalisation, the idea is very simple! You do a calculation, and say you get an infinite answer. Then you bring another infinity and do the following: Infinity Infinity = finite Dasgupta (McGill) String Theory Homer / 92
101 Well it works, thats what matters, right? Dasgupta (McGill) String Theory Homer / 92
102 Well it works, thats what matters, right? After you have understood renormalisation i.e if you are in the following state: Dasgupta (McGill) String Theory Homer / 92
103 Well it works, thats what matters, right? After you have understood renormalisation i.e if you are in the following state: Dasgupta (McGill) String Theory Homer / 92
104 This would make life very simple! Dasgupta (McGill) String Theory Homer / 92
105 This would make life very simple! Dasgupta (McGill) String Theory Homer / 92
106 So simple that we bring the cook again and mix QM + General Theory of Relativity + Renormalisation Dasgupta (McGill) String Theory Homer / 92
107 This should give us the ultimate nice theory that explains everything! Dasgupta (McGill) String Theory Homer / 92
108 This should give us the ultimate nice theory that explains everything! So what do we get? Dasgupta (McGill) String Theory Homer / 92
109 Unfortunately Dasgupta (McGill) String Theory Homer / 92
110 Unfortunately What went wrong now?? Dasgupta (McGill) String Theory Homer / 92
111 After much thinking Dasgupta (McGill) String Theory Homer / 92
112 After much thinking And this time it required a lot of thinking! Dasgupta (McGill) String Theory Homer / 92
113 After much thinking And this time it required a lot of thinking! Dasgupta (McGill) String Theory Homer / 92
114 It was realised that the problem was created by point particles Dasgupta (McGill) String Theory Homer / 92
115 It was realised that the problem was created by point particles Thus point particles have to be replaced by vibrating strings! Dasgupta (McGill) String Theory Homer / 92
116 To understand how string theory changes the interaction diagrams, let us first draw a space-time picture Dasgupta (McGill) String Theory Homer / 92
117 To understand how string theory changes the interaction diagrams, let us first draw a space-time picture Dasgupta (McGill) String Theory Homer / 92
118 This means that the Feynman diagram would be the following Dasgupta (McGill) String Theory Homer / 92
119 This means that the Feynman diagram would be the following Dasgupta (McGill) String Theory Homer / 92
120 The corresponding string diagrams would be Dasgupta (McGill) String Theory Homer / 92
121 The corresponding string diagrams would be Dasgupta (McGill) String Theory Homer / 92
122 The corresponding string diagrams would be Dasgupta (McGill) String Theory Homer / 92
123 Such a situation should get rid of all the problems and nothing should blow up again! Dasgupta (McGill) String Theory Homer / 92
124 Such a situation should get rid of all the problems and nothing should blow up again! Thus string theory was born. Dasgupta (McGill) String Theory Homer / 92
125 Such a situation should get rid of all the problems and nothing should blow up again! Thus string theory was born. This was around 1970 Dasgupta (McGill) String Theory Homer / 92
126 Soon with the effort of many physicists the first concrete string model was built Dasgupta (McGill) String Theory Homer / 92
127 Soon with the effort of many physicists the first concrete string model was built Dasgupta (McGill) String Theory Homer / 92
128 Soon with the effort of many physicists the first concrete string model was built John Schwarz Dasgupta (McGill) String Theory Homer / 92
129 Soon with the effort of many physicists the first concrete string model was built John Schwarz Dasgupta (McGill) String Theory Homer / 92
130 Soon with the effort of many physicists the first concrete string model was built John Schwarz Michael Green Dasgupta (McGill) String Theory Homer / 92
131 Soon with the effort of many physicists the first concrete string model was built John Schwarz Michael Green Dasgupta (McGill) String Theory Homer / 92
132 Soon with the effort of many physicists the first concrete string model was built John Schwarz Michael Green Edward Witten Dasgupta (McGill) String Theory Homer / 92
133 This was called the bosonic string theory because the interacting particles were all bosons. Dasgupta (McGill) String Theory Homer / 92
134 This was called the bosonic string theory because the interacting particles were all bosons. Bosons are particles that look the same no matter from what direction you are looking at! Dasgupta (McGill) String Theory Homer / 92
135 This was called the bosonic string theory because the interacting particles were all bosons. Bosons are particles that look the same no matter from what direction you are looking at! They were developed mainly by Dasgupta (McGill) String Theory Homer / 92
136 This was called the bosonic string theory because the interacting particles were all bosons. Bosons are particles that look the same no matter from what direction you are looking at! They were developed mainly by Satyendranath Bose Dasgupta (McGill) String Theory Homer / 92
137 This was called the bosonic string theory because the interacting particles were all bosons. Bosons are particles that look the same no matter from what direction you are looking at! They were developed mainly by Satyendranath Bose Dasgupta (McGill) String Theory Homer / 92
138 This was called the bosonic string theory because the interacting particles were all bosons. Bosons are particles that look the same no matter from what direction you are looking at! They were developed mainly by Satyendranath Bose and Albert Einstein Dasgupta (McGill) String Theory Homer / 92
139 This was called the bosonic string theory because the interacting particles were all bosons. Bosons are particles that look the same no matter from what direction you are looking at! They were developed mainly by Satyendranath Bose and Albert Einstein Dasgupta (McGill) String Theory Homer / 92
140 On the other hand there are particles that look different when you rotate them! They are called fermions. They were developed by Paul Dirac and Enrico Fermi Dasgupta (McGill) String Theory Homer / 92
141 On the other hand there are particles that look different when you rotate them! They are called fermions. They were developed by Paul Dirac and Enrico Fermi Dasgupta (McGill) String Theory Homer / 92
142 On the other hand there are particles that look different when you rotate them! They are called fermions. They were developed by Paul Dirac and Enrico Fermi Dasgupta (McGill) String Theory Homer / 92
143 The fermions also satisfy the Pauli Exclusion Principle, developed by Wolfgang Pauli Dasgupta (McGill) String Theory Homer / 92
144 The PEP says that no two fermions like each other! Dasgupta (McGill) String Theory Homer / 92
145 The PEP says that no two fermions like each other! Dasgupta (McGill) String Theory Homer / 92
146 The PEP says that no two fermions like each other! Dasgupta (McGill) String Theory Homer / 92
147 However the string theory that we developed had three sides: Dasgupta (McGill) String Theory Homer / 92
148 However the string theory that we developed had three sides: The Good, The Bad and The Ugly! Dasgupta (McGill) String Theory Homer / 92
149 The Good Dasgupta (McGill) String Theory Homer / 92
150 The Good Dasgupta (McGill) String Theory Homer / 92
151 The Good Theory reproduces Einsten General Theory of Relativity Dasgupta (McGill) String Theory Homer / 92
152 The Good Theory reproduces Einsten General Theory of Relativity Theory doesn t blow up Dasgupta (McGill) String Theory Homer / 92
153 The Good Theory reproduces Einsten General Theory of Relativity Theory doesn t blow up Seemed perfectly consistent with Quantum Mechanics Dasgupta (McGill) String Theory Homer / 92
154 The Good Theory reproduces Einsten General Theory of Relativity Theory doesn t blow up Seemed perfectly consistent with Quantum Mechanics Predicts the existence of gravity particles called graviton, much like the bosons that we discussed Dasgupta (McGill) String Theory Homer / 92
155 The Bad Dasgupta (McGill) String Theory Homer / 92
156 The Bad Dasgupta (McGill) String Theory Homer / 92
157 The Bad Predicts the existence of twenty-six space-time dimensions Dasgupta (McGill) String Theory Homer / 92
158 The Bad Predicts the existence of twenty-six space-time dimensions Any other lower/higher dimensions we face inconsistency Dasgupta (McGill) String Theory Homer / 92
159 The Bad Predicts the existence of twenty-six space-time dimensions Any other lower/higher dimensions we face inconsistency Our observable universe is 3+1 dimensions, so we need to account for 22 extra dimensions Dasgupta (McGill) String Theory Homer / 92
160 The Ugly Dasgupta (McGill) String Theory Homer / 92
161 The Ugly Dasgupta (McGill) String Theory Homer / 92
162 The Ugly The theory has an imaginary mass particle, also known as the Tachyon that moves faster then light, violating STR Dasgupta (McGill) String Theory Homer / 92
163 The Ugly The theory has an imaginary mass particle, also known as the Tachyon that moves faster then light, violating STR So at best the theory is not well defined in the present form, but could be ok if certain modifications are made Dasgupta (McGill) String Theory Homer / 92
164 The Ugly The theory has an imaginary mass particle, also known as the Tachyon that moves faster then light, violating STR So at best the theory is not well defined in the present form, but could be ok if certain modifications are made At worst, we have got the wrong theory Dasgupta (McGill) String Theory Homer / 92
165 What did we miss now? Dasgupta (McGill) String Theory Homer / 92
166 What did we miss now? Well, we haven t exploited one possible property of the particles Dasgupta (McGill) String Theory Homer / 92
167 What did we miss now? Well, we haven t exploited one possible property of the particles The existence of supersymmetry as a possible new symm! Dasgupta (McGill) String Theory Homer / 92
168 Supersymmetry is based on the following idea Dasgupta (McGill) String Theory Homer / 92
169 Supersymmetry is based on the following idea Dasgupta (McGill) String Theory Homer / 92
170 This is of course a conjecture and can only be proved experimentally Dasgupta (McGill) String Theory Homer / 92
171 This is of course a conjecture and can only be proved experimentally But let us assume that it is true... Dasgupta (McGill) String Theory Homer / 92
172 So we bring our cook back and add all the ingredients Dasgupta (McGill) String Theory Homer / 92
173 So we bring our cook back and add all the ingredients Strings + Supersymmetry Dasgupta (McGill) String Theory Homer / 92
174 So we bring our cook back and add all the ingredients Strings + Supersymmetry What do we get now? Dasgupta (McGill) String Theory Homer / 92
175 We get this Dasgupta (McGill) String Theory Homer / 92
176 We get this Dasgupta (McGill) String Theory Homer / 92
177 We get this or this.. Dasgupta (McGill) String Theory Homer / 92
178 We get this or this.. Dasgupta (McGill) String Theory Homer / 92
179 .. Or more completely, this Dasgupta (McGill) String Theory Homer / 92
180 .. Or more completely, this Dasgupta (McGill) String Theory Homer / 92
181 Good thing is that nothing seems to blow up now Dasgupta (McGill) String Theory Homer / 92
182 Good thing is that nothing seems to blow up now But then, what is it? Dasgupta (McGill) String Theory Homer / 92
183 To understand the last picture, let us take a simpler model: Dasgupta (McGill) String Theory Homer / 92
184 To understand the last picture, let us take a simpler model: Dasgupta (McGill) String Theory Homer / 92
185 To understand the last picture, let us take a simpler model: The picture represents a sphere at every point on a base. Dasgupta (McGill) String Theory Homer / 92
186 To understand the last picture, let us take a simpler model: The picture represents a sphere at every point on a base. Now identify the base with our four dimensional universe Dasgupta (McGill) String Theory Homer / 92
187 This is therefore a representation of a six-dimensional space Dasgupta (McGill) String Theory Homer / 92
188 This is therefore a representation of a six-dimensional space where the compact sphere is two-dimensional and the base is four dimensional. In other words: Dasgupta (McGill) String Theory Homer / 92
189 This is therefore a representation of a six-dimensional space where the compact sphere is two-dimensional and the base is four dimensional. In other words: 6 = Dasgupta (McGill) String Theory Homer / 92
190 For those who are still thinking about whats going on, here it is again Dasgupta (McGill) String Theory Homer / 92
191 For those who are still thinking about whats going on, here it is again Dasgupta (McGill) String Theory Homer / 92
192 For those who are still thinking about whats going on, here it is again Dasgupta (McGill) String Theory Homer / 92
193 The above set of ideas were in fact developed much before string theory by Theodor Kaluza and Oskar Klein, around 1919, that even Einstein tried to implement in his theory! Dasgupta (McGill) String Theory Homer / 92
194 The above set of ideas were in fact developed much before string theory by Theodor Kaluza and Oskar Klein, around 1919, that even Einstein tried to implement in his theory! Dasgupta (McGill) String Theory Homer / 92
195 Now comes the most important equation of string theory: Dasgupta (McGill) String Theory Homer / 92
196 Now comes the most important equation of string theory: 10 = Dasgupta (McGill) String Theory Homer / 92
197 Now comes the most important equation of string theory: 10 = where 6 is now the compact internal space fibered over our 3+1 dimensional universe Dasgupta (McGill) String Theory Homer / 92
198 Now comes the most important equation of string theory: 10 = where 6 is now the compact internal space fibered over our 3+1 dimensional universe Dasgupta (McGill) String Theory Homer / 92
199 Therefore string theory + supersymmetry predicts Dasgupta (McGill) String Theory Homer / 92
200 Therefore string theory + supersymmetry predicts 26 spacetime dimensions 10 spacetime dimensions. Dasgupta (McGill) String Theory Homer / 92
201 Therefore string theory + supersymmetry predicts 26 spacetime dimensions 10 spacetime dimensions. Cannot be lower than 10, but could be increased to 11, and not more! Dasgupta (McGill) String Theory Homer / 92
202 Therefore string theory + supersymmetry predicts 26 spacetime dimensions 10 spacetime dimensions. Cannot be lower than 10, but could be increased to 11, and not more! Therefore a 10 dim supersymm universe without tachyon with 3+1 dimensional non-compact space (where we live) and a six-dimensional internal space called a Dasgupta (McGill) String Theory Homer / 92
203 Therefore string theory + supersymmetry predicts 26 spacetime dimensions 10 spacetime dimensions. Cannot be lower than 10, but could be increased to 11, and not more! Therefore a 10 dim supersymm universe without tachyon with 3+1 dimensional non-compact space (where we live) and a six-dimensional internal space called a Calabi-Yau manifold Dasgupta (McGill) String Theory Homer / 92
204 The mathematical structures of these manifolds were developed by Dasgupta (McGill) String Theory Homer / 92
205 The mathematical structures of these manifolds were developed by Dasgupta (McGill) String Theory Homer / 92
206 The mathematical structures of these manifolds were developed by Eugenio Calabi Dasgupta (McGill) String Theory Homer / 92
207 The mathematical structures of these manifolds are developed by Dasgupta (McGill) String Theory Homer / 92
208 The mathematical structures of these manifolds are developed by Dasgupta (McGill) String Theory Homer / 92
209 The mathematical structures of these manifolds are developed by Shing-Tung Yau Dasgupta (McGill) String Theory Homer / 92
210 However with all the heavy mathematical machinery one might be feeling a bit Dasgupta (McGill) String Theory Homer / 92
211 However with all the heavy mathematical machinery one might be feeling a bit confused Dasgupta (McGill) String Theory Homer / 92
212 However with all the heavy mathematical machinery one might be feeling a bit confused Dasgupta (McGill) String Theory Homer / 92
213 and depressed However with all the heavy mathematical machinery one might be feeling a bit confused Dasgupta (McGill) String Theory Homer / 92
214 and depressed However with all the heavy mathematical machinery one might be feeling a bit confused Dasgupta (McGill) String Theory Homer / 92
215 Help was on the way! Dasgupta (McGill) String Theory Homer / 92
216 Help was on the way! Because far in the west Joe Polchinski at UCSB was thinking of an alternative scenario Dasgupta (McGill) String Theory Homer / 92
217 Help was on the way! Because far in the west Joe Polchinski at UCSB was thinking of an alternative scenario Dasgupta (McGill) String Theory Homer / 92
218 He asked: What if there could be slices of spacetime embedded in our ten-dimensional space? Dasgupta (McGill) String Theory Homer / 92
219 He asked: What if there could be slices of spacetime embedded in our ten-dimensional space? In other words we could be on a 3+1 dim slice floating in a ten dimensional space! Dasgupta (McGill) String Theory Homer / 92
220 He asked: What if there could be slices of spacetime embedded in our ten-dimensional space? In other words we could be on a 3+1 dim slice floating in a ten dimensional space! Dasgupta (McGill) String Theory Homer / 92
221 These slices could move and could have any dimensions Dasgupta (McGill) String Theory Homer / 92
222 These slices could move and could have any dimensions These slices were called D-Branes Dasgupta (McGill) String Theory Homer / 92
223 These slices could move and could have any dimensions These slices were called D-Branes Dasgupta (McGill) String Theory Homer / 92
224 These slices could move and could have any dimensions These slices were called D-Branes In this language, we could be living on a three brane! Dasgupta (McGill) String Theory Homer / 92
225 This idea was so popular that Lisa Randall and Raman Sundrum almost immediately proposed a model for an alternative to compactification Dasgupta (McGill) String Theory Homer / 92
226 This idea was so popular that Lisa Randall and Raman Sundrum almost immediately proposed a model for an alternative to compactification Lisa Randall Dasgupta (McGill) String Theory Homer / 92
227 This idea was so popular that Lisa Randall and Raman Sundrum almost immediately proposed a model for an alternative to compactification Lisa Randall Raman Sundrum Dasgupta (McGill) String Theory Homer / 92
228 They toyed with the idea that maybe we don t need any Calabi-Yau manifolds to understand our universe. A simple three-brane would be enough because we would live on this surface! Dasgupta (McGill) String Theory Homer / 92
229 They toyed with the idea that maybe we don t need any Calabi-Yau manifolds to understand our universe. A simple three-brane would be enough because we would live on this surface! Dasgupta (McGill) String Theory Homer / 92
230 This picture led to numerous works in our field Dasgupta (McGill) String Theory Homer / 92
231 This picture led to numerous works in our field but Dasgupta (McGill) String Theory Homer / 92
232 This picture led to numerous works in our field but Unfortunately (or fortunately) such a simple idea doesn t quite work... Dasgupta (McGill) String Theory Homer / 92
233 What seems to work well is when D-branes are mixed with Calabi-Yau manifolds Dasgupta (McGill) String Theory Homer / 92
234 What seems to work well is when D-branes are mixed with Calabi-Yau manifolds Dasgupta (McGill) String Theory Homer / 92
235 In fact miraculous results can come out by this mixing as shown by these people Dasgupta (McGill) String Theory Homer / 92
236 In fact miraculous results can come out by this mixing as shown by these people Juan Maldacena Dasgupta (McGill) String Theory Homer / 92
237 In fact miraculous results can come out by this mixing as shown by these people Juan Maldacena Matt Strassler Dasgupta (McGill) String Theory Homer / 92
238 In fact miraculous results can come out by this mixing as shown by these people Juan Maldacena Matt Strassler Igor Klebanov Dasgupta (McGill) String Theory Homer / 92
239 Conclusion Dasgupta (McGill) String Theory Homer / 92
240 Conclusion I conclude by showing the following figures that capture the essence of my talk It all started with this book Dasgupta (McGill) String Theory Homer / 92
241 Conclusion I conclude by showing the following figures that capture the essence of my talk It all started with this book Dasgupta (McGill) String Theory Homer / 92
242 Conclusion I conclude by showing the following figures that capture the essence of my talk It all started with this book which eventually led to Dasgupta (McGill) String Theory Homer / 92
243 Conclusion I conclude by showing the following figures that capture the essence of my talk It all started with this book which eventually led to Dasgupta (McGill) String Theory Homer / 92
244 Therefore in the second phase it all started with the following books Dasgupta (McGill) String Theory Homer / 92
245 Therefore in the second phase it all started with the following books Dasgupta (McGill) String Theory Homer / 92
246 Therefore in the second phase it all started with the following books Dasgupta (McGill) String Theory Homer / 92
247 Which eventually led us to this Dasgupta (McGill) String Theory Homer / 92
248 Which eventually led us to this Dasgupta (McGill) String Theory Homer / 92
249 Till last year there weren t any positive identification of strings, supersymmetry or extra dimension! Dasgupta (McGill) String Theory Homer / 92
250 Till last year there weren t any positive identification of strings, supersymmetry or extra dimension! Dasgupta (McGill) String Theory Homer / 92
251 Till last year there weren t any positive identification of strings, supersymmetry or extra dimension! But recently some subtle hints of supersymmetry has emerged..! Dasgupta (McGill) String Theory Homer / 92
252 Thank You! Dasgupta (McGill) String Theory Homer / 92
253 Thank You! And hopefully it wasn t too confusing! Dasgupta (McGill) String Theory Homer / 92
254 Thank You! And hopefully it wasn t too confusing! FIN! Dasgupta (McGill) String Theory Homer / 92
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