Collisions of Cosmic F- and D- Strings p.1

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1 Collisions of Cosmic F- and D- Strings Nicholas Jones Cornell University with Jackson & Polchinski [th/ ] (NJ, Stoica, Tye [th/ ], [th/ ] ) Collisions of Cosmic F- and D- Strings p1

2 Field Theory Cosmic String Interactions Cosmic Strings from vortices formed at some phase transition (eg some hybrid inflation models) Collisions of Cosmic F- and D- Strings p2

3 Field Theory Cosmic String Interactions Cosmic Strings from vortices formed at some phase transition (eg some hybrid inflation models) Inter-vortex reconnection probability is essentially 1 (numerically; Matzner) Collisions of Cosmic F- and D- Strings p2

4 String Pair Interactions and the Network Naively, cosmic string network density scales like Radiation: ; Dust: Collisions of Cosmic F- and D- Strings p3

5 String Pair Interactions and the Network Naively, cosmic string network density scales like Radiation: ; Dust: String interactions force network to lock onto scaling of dominant species Collisions of Cosmic F- and D- Strings p3

6 String Pair Interactions and the Network Naively, cosmic string network density scales like Radiation: ; Dust: String interactions force network to lock onto scaling of dominant species For a probability of interaction network density scales like losses to loop formation), the interacting (simulations; Collisions of Cosmic F- and D- Strings p3

7 String Pair Interactions and the Network Naively, cosmic string network density scales like Radiation: ; Dust: String interactions force network to lock onto scaling of dominant species For a probability of interaction network density scales like losses to loop formation), the interacting (simulations;, enhancement of cosmic string effects & observables Collisions of Cosmic F- and D- Strings p3

8 The End of Brane Inflation String theory inflationary models involving movement of branes and anti-branes (& variants) Collisions of Cosmic F- and D- Strings p4

9 The End of Brane Inflation String theory inflationary models involving movement of branes and anti-branes (& variants) Irrespective of details (warping, compactification ), the brane collision ending inflation is hybrid inflation Collisions of Cosmic F- and D- Strings p4

10 The End of Brane Inflation String theory inflationary models involving movement of branes and anti-branes (& variants) Irrespective of details (warping, compactification ), the brane collision ending inflation is hybrid inflation Inflation ends when the complex tachyon rolls Collisions of Cosmic F- and D- Strings p4

11 The End of Brane Inflation String theory inflationary models involving movement of branes and anti-branes (& variants) Irrespective of details (warping, compactification ), the brane collision ending inflation is hybrid inflation Inflation ends when the complex tachyon rolls Post inflation, string-like defects (only) are formed; no monopoles or domain walls (NJ, Stoica, Tye; Sarangi, Tye) Collisions of Cosmic F- and D- Strings p4

12 String Types and Stability Different string types are (meta)-stable in different models (Copeland, Myers, Polchinski) Collisions of Cosmic F- and D- Strings p5

13 String Types and Stability Different string types are (meta)-stable in different models (Copeland, Myers, Polchinski) Possibility of having F-, D- and -strings Collisions of Cosmic F- and D- Strings p5

14 String Types and Stability Different string types are (meta)-stable in different models (Copeland, Myers, Polchinski) Possibility of having F-, D- and -strings -strings stable in KKLMMT when no branes are in the inflationary throat ( relatively prime, ) Collisions of Cosmic F- and D- Strings p5

15 String Types and Stability Different string types are (meta)-stable in different models (Copeland, Myers, Polchinski) Possibility of having F-, D- and -strings -strings stable in KKLMMT when no branes are in the inflationary throat ( relatively prime, ) General brane inflation (non-stabilised) models can have long-lived F-, D- and -strings Collisions of Cosmic F- and D- Strings p5

16 Field Theory vs String Theory Strings distinguishes string theory from field theory cosmic strings Collisions of Cosmic F- and D- Strings p6

17 Field Theory vs String Theory Strings distinguishes string theory from field theory cosmic strings -string networks distinguish (simple) FT from string theory cosmic strings Collisions of Cosmic F- and D- Strings p6

18 Field Theory vs String Theory Strings distinguishes string theory from field theory cosmic strings -string networks distinguish (simple) FT from string theory cosmic strings Spectrum of tensions distinguish FT from string theory cosmic strings Collisions of Cosmic F- and D- Strings p6

19 Field Theory vs String Theory Strings distinguishes string theory from field theory cosmic strings -string networks distinguish (simple) FT from string theory cosmic strings Spectrum of tensions distinguish FT from string theory cosmic strings Calculate & interactions for scaling estimates and network simulations; detectable differences Collisions of Cosmic F- and D- Strings p6

20 " " Field Theory vs String Theory Strings distinguishes string theory from field theory cosmic strings -string networks distinguish (simple) FT from string theory cosmic strings Spectrum of tensions distinguish FT from string theory cosmic strings Calculate & interactions for scaling estimates and network simulations; detectable differences Results: ; # # %$ Collisions of Cosmic F- and D- Strings p6

21 & String Interaction Types F+F or D+D reconnection Collisions of Cosmic F- and D- Strings p7

22 & ' String Interaction Types ' connection Collisions of Cosmic F- and D- Strings p7

23 & ' String Interaction Types ' disconnection Collisions of Cosmic F- and D- Strings p7

24 Flat-Space Cosmic String Interactions Perform calculations in flat 10D spacetime on torii Collisions of Cosmic F- and D- Strings p8

25 Flat-Space Cosmic String Interactions Perform calculations in flat 10D spacetime on torii Account for warping by effective confining potential Collisions of Cosmic F- and D- Strings p8

26 Flat-Space Cosmic String Interactions Perform calculations in flat 10D spacetime on torii Account for warping by effective confining potential Quantum fluctuations of string position give an effective volume of compactification Collisions of Cosmic F- and D- Strings p8

27 Flat-Space Cosmic String Interactions Perform calculations in flat 10D spacetime on torii Account for warping by effective confining potential Quantum fluctuations of string position give an effective volume of compactification Valid if geometry varying slowly on string scale Collisions of Cosmic F- and D- Strings p8

28 F-F Interaction Compactify 2D of 4D spacetime directions on torus and use wound closed strings (Polchinski, 1988) Collisions of Cosmic F- and D- Strings p9

29 F-F Interaction Use unitarity to sum over all final states and macroscopic string limit (Polchinksi 1988) Collisions of Cosmic F- and D- Strings p9

30 F-F Interaction ( ) *+-, + / ) *+-, + ) * /, / ) * /, / * ' ;: / : < >= E AC F 6E AC F G H ' I K I K I L K I K I K I L K M N 8 O 0 9 ' J RQP S T K R UBV S T T $ Collisions of Cosmic F- and D- Strings p10

31 \ [ F- WYX>Z Interaction Interaction of a wound closed string with a boundary; add Dirichlet boundary conditions, Chan-Paton factors & constant electric flux Collisions of Cosmic F- and D- Strings p11

32 \ [ 6 b c n _ D? j 6 6 c b ^ _ D D, 6 y od + w D vu w D D + D vu D w w x + + Interaction WYX>Z F- Unitarity etc j c_ gh *edf` * ` ]n, df` *a` gih *edf` *a` ]^ df` ` D u 6 v u t vu zqzrzq{ v u t u 6 pqprpqs _ch j vu (Callan, Lovelace, Nappi, Yost; Seiberg, Witten; ) Collisions of Cosmic F- and D- Strings p11

33 \ [ * + ) ( ) / /?? / + I I M S T RQP T 9 $ M 8 T O Interaction WYX>Z F- / /, *+-, 6 4~} } 8 10 N MN ' 10 M N N T S U V R Collisions of Cosmic F- and D- Strings p12

34 D-D Interaction: Pair Production Add a second boundary for interaction of two D-strings Collisions of Cosmic F- and D- Strings p13

35 ' 9 D-D Interaction: Pair Production Add a second boundary for interaction of two D-strings Open string spectrum for branes at an angle; Tachyon ( ), 4 massless fermions, (at 0 impact parameter; Berkooz, Douglas, Leigh) 10 S Collisions of Cosmic F- and D- Strings p13

36 ' 9 ' D-D Interaction: Pair Production Add a second boundary for interaction of two D-strings Open string spectrum for branes at an angle; Tachyon ( ), 4 massless fermions, (at 0 impact parameter; Berkooz, Douglas, Leigh) 10 S Similar for - ' interaction Collisions of Cosmic F- and D- Strings p13

37 / ˆ K Š Ž / / 0 + K K $ 0 h D-D Interaction: Pair Production S ˆ J K ˆ J ˆ 6 ƒœ S ˆ J K ˆ J ˆ ˆ J / Collisions of Cosmic F- and D- Strings p14

38 , Š, D-D Interaction: Pair Production Total inelastic probability (Schwinger; Bachas), or the probability of producing at least one pair of F-strings is š Im 6 œž lÿ l Collisions of Cosmic F- and D- Strings p15

39 , Š, D-D Interaction: Pair Production Total inelastic probability (Schwinger; Bachas), or the probability of producing at least one pair of F-strings is š Im 6 œž lÿ l Since, a single pair of F-strings will not cause connection # M N Collisions of Cosmic F- and D- Strings p15

40 D-D Interaction: Connection If few F pairs are produced, the D-strings continue but kink, stretching the F s F s eventually annihilate Collisions of Cosmic F- and D- Strings p16

41 D-D Interaction: Connection If few F pairs are produced, the D-strings continue but kink, stretching the F s F s eventually annihilate If many F pairs are produced, their total tension is sufficient to stick the D-strings together; tachyon rolls and D s reconnect (Hashimoto, Taylor; Hashimoto, Nagaoka) Collisions of Cosmic F- and D- Strings p16

42 0 / L D-D Interaction: Connection Precise condition for reconnection ( V ) 4ª UBV / R «Collisions of Cosmic F- and D- Strings p17

43 0 / L ± M N D-D Interaction: Connection Precise condition for reconnection ( V ) 4ª UBV / R «Impact parameter is generally small, Collisions of Cosmic F- and D- Strings p17

44 0 / L ± M N D-D Interaction: Connection Precise condition for reconnection ( V ) 4ª UBV / R «Impact parameter is generally small, At most cosmic velocities, only tachyon and massless fermions are important Collisions of Cosmic F- and D- Strings p17

45 0 / L ± M N H 0 ² D-D Interaction: Connection Precise condition for reconnection ( V ) 4ª UBV / R «Impact parameter is generally small, At most cosmic velocities, only tachyon and massless fermions are important Then, 4 fermionic strings always are produced, so need at least tachyonic strings U V / R «³ Collisions of Cosmic F- and D- Strings p17

46 0 / L ± M N H 0 ² µ H ² Š 0 $ D-D Interaction: Connection Precise condition for reconnection ( V ) 4ª UBV / R «Impact parameter is generally small, At most cosmic velocities, only tachyon and massless fermions are important Then, 4 fermionic strings always are produced, so need at least tachyonic strings Probability is U V / R «³ UBV R M N š Collisions of Cosmic F- and D- Strings p17

47 Compactification Effects Metric and dilaton depend on compact coords, : D 6 Ž¹ º»» º D 6 M Collisions of Cosmic F- and D- Strings p18

48 Compactification Effects Metric and dilaton depend on compact coords, : D 6 Ž¹ º»» º D 6 M Defines a worldsheet potential for : 8 A, ¼ 0 9 ' D 6 $ Collisions of Cosmic F- and D- Strings p18

49 D 6 6 D M 8 $ 6 D ' 9 ' 9 ½ $ 6 D ' 9 Compactification Effects : Metric and dilaton depend on compact coords, º»» Ž¹ º : Defines a worldsheet potential for ¼ A, 0 Fluctuations of position about a minimum are ¼ A, ¾ V 8, 10 ¼ A, Collisions of Cosmic F- and D- Strings p18

50 D 6 D ' 9 8 O / Fluctuations: F-Strings F-F wavefunction overlap: 6 $ ¼ A, V 8, 10 h Collisions of Cosmic F- and D- Strings p19

51 Fluctuations: F- & D-Strings F-D can have separated minima if dilaton depends on Collisions of Cosmic F- and D- Strings p20

52 Fluctuations: F- & D-Strings F-D can have separated minima if dilaton depends on & supression of wavefunction overlap volume: 8 O # À 8 O š # # 9 ' V ² $ $ $ $ Collisions of Cosmic F- and D- Strings p20

53 Â Á Fluctuations: D-Strings Localised to first order M N Collisions of Cosmic F- and D- Strings p21

54 Â Á ' 9 $ $ $ ' 9 Fluctuations: D-Strings Localised to first order M N Fluctuations induce effective impact parameter; open string masses increase by: ² V $ 0 ¼ A, Collisions of Cosmic F- and D- Strings p21

55 Â Á ' 9 $ $ $ ' 9 $ $ $ $ Fluctuations: D-Strings Localised to first order M N Fluctuations induce effective impact parameter; open string masses increase by: ² V $ 0 ¼ A, Reconnection probability supressed by ² V š ¼ A, 10 Collisions of Cosmic F- and D- Strings p21

56 Fluctuations in KKLMMT Model Vol à M N Collisions of Cosmic F- and D- Strings p22

57 6 D ± Fluctuations in KKLMMT Model Assume CY curvature has effect geometry on the throat Collisions of Cosmic F- and D- Strings p22

58 Ã ' ¾ ½ 9 $ Fluctuations in KKLMMT Model Two cases: Fluctuations are localised on : V M N Ä H Collisions of Cosmic F- and D- Strings p23

59 Ã ' ¾ ½ 9 $ Ã ' ¾ ½ 9 $ Fluctuations in KKLMMT Model Two cases: Fluctuations are localised on : V M N Ä H Fluctuations fill the : M N Collisions of Cosmic F- and D- Strings p23

60 M Å M N $ $ N Results: KKLMMT / M N V Collisions of Cosmic F- and D- Strings p24 FF reconnection: N M V Max

61 / M N M Å $ $ M N ª M Results: KKLMMT FF reconnection: N Max M N V V Require GUT value, N can range between 1 and the Collisions of Cosmic F- and D- Strings p24

62 M Å M N $ $ N ª M Æ Æ Results: KKLMMT FF reconnection: / N M N V M V Max N can range between 1 and the, Require GUT value Å %$,, $, Collisions of Cosmic F- and D- Strings p24

63 M Å M N $ $ N ª M Æ Æ M Results: KKLMMT FF reconnection: / N M N V M V Max N can range between 1 and the, Require GUT value Å %$,, $, F- connection probability increased by localised at same ) N (if Collisions of Cosmic F- and D- Strings p24

64 6 Ç µ Š R Å M Results: KKLMMT DD U V 0 š Æ # # M N Å ² M N $ N Min ' 9 0 Collisions of Cosmic F- and D- Strings p25

65 6 Ç µ Š R Å M ' S 9 Results: KKLMMT DD U V 0 š Æ # # M N Å ² M N $ N Min ' 9 0 Supression is angle dependent; tachyon production is limited when 10 Collisions of Cosmic F- and D- Strings p25

66 6 Ç µ Š R Å M ' S 9 " Results: KKLMMT DD U V 0 š Æ # # M N Å ² M N $ N Min ' 9 0 Supression is angle dependent; tachyon production is limited when 10 %$ # # Collisions of Cosmic F- and D- Strings p25

67 È Ê É +/ É / / Detection and Bounds: & Model Tensions: (KKLMMT) (General Brane Inflation) Collisions of Cosmic F- and D- Strings p26

68 È Ê É +/ É / / Ì Ë É Detection and Bounds: & Model Tensions: (KKLMMT) (General Brane Inflation) Cosmic Microwave Background: sensitive to Collisions of Cosmic F- and D- Strings p26

69 È Ê É +/ É / / Ì Ë É / / É / É Detection and Bounds: & Model Tensions: (KKLMMT) (General Brane Inflation) Cosmic Microwave Background: sensitive to Gravitational wave bursts: sensitive only to frequency sensitive to LIGO II: LISA: Burst Collisions of Cosmic F- and D- Strings p26

70 È Ê É +/ É / / Ì Ë É / / É / É É Detection and Bounds: & Model Tensions: (KKLMMT) (General Brane Inflation) Cosmic Microwave Background: sensitive to Gravitational wave bursts: sensitive only to frequency sensitive to LIGO II: LISA: Pulsar timing (stocastic GW background, Burst & ): Collisions of Cosmic F- and D- Strings p26

71 È Ê É +/ É / / Ì Ë É / / É / É É Detection and Bounds: & Model Tensions: (KKLMMT) (General Brane Inflation) Cosmic Microwave Background: sensitive to Gravitational wave bursts: sensitive only to frequency sensitive to LIGO II: LISA: Pulsar timing (stocastic GW background, Lensing: sensitive to Burst & ): Collisions of Cosmic F- and D- Strings p26

72 " " Summary # # %$ In most cases distinguishable from gauge theory strings; enhanced densities at a given tension -string networks can be very different from scaling solutions; interesting or disasterous? Collisions of Cosmic F- and D- Strings p27

73 Observation: Gravitational Waves GW burst sensitive to (Damour, Vilenkin [gr-qc/ ]) only, to first order Burst frequency sensitive to network density & therefore Collisions of Cosmic F- and D- Strings p28

74 Observation: CMB (Winstein) Collisions of Cosmic F- and D- Strings p29