Stringtheorie Was ist das und wozu ist es nützlich?
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1 Stringtheorie Was ist das und wozu ist es nützlich? Martin Ammon Friedrich-Schiller Universität Jena Perlen der theoretischen Physik 2014 M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
2 Stringtheorie - Was ist das? String theory - a very short introduction The fundamental objects of string theory are one-dimensional spatial extended objects called strings. σ τ A string sweeps out a 1+1-dimensional worldsheet Σ in spacetime embedding into target spacetime: X M (τ,σ) closed versus open strings S = 1 2πα Σ dτdσ det( αx M β X N η MN ), M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
3 Stringtheorie - Was ist das? String theory - a very short introduction The vibrational modes correspond to particles There is a sector of massless states: m 2 = 0 graviton, dilaton, gauge bosons, gaugino,... in addition infinite tower of massive string states with masses m 2 n n α (super)string theory only consistent in D = 10 dimensions in curved spacetimes ds 2 = g MN dx M dx N string theory can be quantised consistently provided that Einstein equations are satisfied M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
4 Stringtheorie - Was ist das? String theory - a very short introduction So far we considered only non-interacting strings To consider interacting strings, we have to allow for worldsheets with holes in it (i.e. non-trivial genus) The left string diagram is of order g 0 s, while the right one is of order g s where g s is the string coupling constant. M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
5 Stringtheorie - Was ist das? String theory - a very short introduction Besides strings other extended objects exist in string theory such as Dp-branes. The tension/mass of D-branes scales as 1/g s. We may view Dp-branes in two different ways Dp-branes as a (p+1)-dimensional hypersurface, Dp-branes as a gravity source curving the surrounding spacetime. M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
6 Why string theory String phenomenology How to reproduce the standard model? A lot of dificulties, vacua or one string compatification Impact on mathematics (geometric Langlands program) surprising dualities between quantum gravity and field theories M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
7 The two sides of a coin What are dualities? Dualities relate two seemingly different quantum theories to each other by stating that the theories are in fact equivalent. In particular, the Hilbert spaces and the dynamics of both theories agree. Why are dualities interesting? It is always good to have to different perspectives on the same object. In this talk, we discuss dualities between a field theory (without gravity) and a gravity theory (which arises from string theory). Is it possible to have a duality between a quantum field theory and a theory of quantum gravity? M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
8 Holographic principle Is it possible to have a duality between a quantum field theory and a theory of quantum gravity? Entropy In a gravitational theory, the number of degrees of freedom in a given spatial volume V scales as the surface area A = V of that volume: S A In a quantum field theory, the number of degrees of freedom scales like the spatial volume V: S V M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
9 Holographic principle Is it possible to have a duality between a quantum field theory and a theory of quantum gravity? Entropy In a gravitational theory, the number of degrees of freedom in a given spatial volume V scales as the surface area A = V of that volume: S A In a quantum field theory, the number of degrees of freedom scales like the spatial volume V: S V Therefore the only possible mapping is... Quantum gravity Quantum field theory in d + 1 spacetime dimensions in d spacetime dimensions M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
10 Holograms in optics M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
11 Gauge/Gravity Duality What is the interpretation of the additional dimension in the gravity theory? AdS d+1 d 1,1 R minkowski... IR z UV IR z UV Gauge/Gravity Duality as Geometrising RG-flows RG-flow equations in gauge theory correspond to Einstein s equations of gravity z dg(z) dz = β(g(z)) Add to the field theory dimensions another dimension: energy scale z Gauge/Gravity Duality makes locality in the energy scale geometrically manifest M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
12 Gauge/Gravity Duality What is the interpretation of the additional dimension in the gravity theory? AdS d+1 d 1,1 R minkowski... IR z UV IR z UV In particular: AdS/CFT correspondence A strongly coupled d-dimensional conformal field theory is dual to a gravity theory in asymptotically AdS d+1 spacetime M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
13 Where does AdS/CFT come from? AdS/CFT can be motivated within string theory! There are two types of strings: open strings: gluons + additional stuff closed strings: graviton + additional stuff as well as higher dimensional objects in string theory AdS/CFT can be derived from the dynamics of such D-branes. M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
14 Black holes play an important role in AdS/CFT duality thermal states in QFT black hole in AdS M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
15 Applying AdS/CFT duality to real-world systems Which real-world systems do we have in mind? Quark-Gluon-Plasma High T c superconductors In this talk I want to concentrate on the Quark-Gluon Plasma M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
16 Applying AdS/CFT duality to real-world systems Which real-world systems do we have in mind? Quark-Gluon-Plasma High T c superconductors In this talk I want to concentrate on the Quark-Gluon Plasma But keep always in mind we are talking about spherical cows... M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
17 Applying AdS/CFT duality to real-world systems Quark-Gluon Plasma BNL press release 2005: The degree of collective interaction, rapid thermalization, and extremely low [shear] viscosity of the matter being formed at LHC makes this the most nearly perfect liquid ever observed observed at RHIC and LHC M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
![Shear viscosity the definition boundary plate (2D, moving) y dimension velocity, u F A = η u y units of shear viscosity η : [η] = 1cp = 0.](/docs-images/84/91046787/images/18-0.jpg "001Pa s typical values for η: boundary plate (2D, stationary) water: air: honey: pitch: 1cp 0.02cp 2000 10000cp 2.3 10 11 cp M.")
18 Shear viscosity the definition boundary plate (2D, moving) y dimension velocity, u F A = η u y units of shear viscosity η : [η] = 1cp = 0.001Pa s typical values for η: boundary plate (2D, stationary) water: air: honey: pitch: 1cp 0.02cp cp cp M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
19 Shear viscosity a world record The Pitch drop experiment Started in 1930 so far 8 drops fell but no one has ever witnessed a drop fall 2005: IG nobel prize for physics η cp M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
20 Applying AdS/CFT duality to real-world systems measurement of η at RHIC (confirmed by LHC) η = cp Why should it be the most perfect fluid ever observed? Holographic setup Results from gauge/gravity duality: Any strongly coupled (large N) gauge theory η/s = 4π 0.08 value for QGP: η/s 0.15 ± 0.1 smallest ratio ever observed M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
21 Applying AdS/CFT duality to real-world systems measurement of η at RHIC (confirmed by LHC) η = cp Why should it be the most perfect fluid ever observed? Holographic setup Results from gauge/gravity duality: Any strongly coupled (large N) gauge theory η/s = 4π 0.08 value for QGP: η/s 0.15 ± 0.1 smallest ratio ever observed For weakly coupled theories: η and η/s diverge for g 0. M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
22 Applying AdS/CFT duality to real-world systems measurement of η at RHIC (confirmed by LHC) η = cp Why should it be the most perfect fluid ever observed? Holographic setup Results from gauge/gravity duality: Any strongly coupled (large N) gauge theory η/s = 4π 0.08 value for QGP: η/s 0.15 ± 0.1 smallest ratio ever observed An interesting question: Is there a lower bound on η/s? M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
23 Summary Stringtheorie - wozu ist es nützlich? Strings are one-dimensional extended objects String theory unifies gravity and the other fundamental forces of the standard model. String theory as a candidate for a theory of everything. But: It is very difficult to obtain precisely the standard model! M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
24 Summary Stringtheorie - wozu ist es nützlich? Strings are one-dimensional extended objects String theory unifies gravity and the other fundamental forces of the standard model. String theory as a candidate for a theory of everything. But: It is very difficult to obtain precisely the standard model! Gravity and field theories are two sides of the same coin! A very powerful application of String theory! M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
25 Summary Stringtheorie - wozu ist es nützlich? Strings are one-dimensional extended objects String theory unifies gravity and the other fundamental forces of the standard model. String theory as a candidate for a theory of everything. But: It is very difficult to obtain precisely the standard model! Gravity and field theories are two sides of the same coin! A very powerful application of String theory! We can use string theory to study phenomena in quantum field theory and quantum gravity! gauge/gravity duality [String theory gr., Uppsala Universitet] [RHIC] M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
26 A last provocative question at the end Is the universe a hologram? Is gravity an illusion? M. Ammon (FSU Jena) Ist Stringtheorie nützlich? March 28th, / 19
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