Download presentation

Presentation is loading. Please wait.

Published byZander Sherfield Modified about 1 year ago

1
Open String Tachyon in Supergravity Solution Shinpei Kobayashi ( Research Center for the Early Universe, The University of Tokyo ) 2005/01/18 at KEK Based on hep-th/ in collaboration with Tsuguhiko Asakawa and So Matsuura ( RIKEN )

2
Motivation We would like to apply the string theory to the analyses of the gravitational systems. We would like to apply the string theory to the analyses of the gravitational systems. We have to know We have to know how we should apply string theory to realistic gravitational systems, how we should apply string theory to realistic gravitational systems, or what stringy (non-perturbative) effects are, or what stringy (non-perturbative) effects are, or what stringy counterparts of the BHs or Universe in the general relativity are. or what stringy counterparts of the BHs or Universe in the general relativity are. → D-branes may be a clue to tackle such problems (BH entropy, D-brane inflation, etc.) → D-branes may be a clue to tackle such problems (BH entropy, D-brane inflation, etc.)

3
Contents 1. D-branes and Classical Descriptions 2. D/anti D-brane system 3. Three-parameter solution 4. Conclusions 5. Discussions and Future Works

4
String Field Theory D-brane ( Boundary State ) Supergravity low energy limit α ’ → 0 classical description ( Black p-brane ) low energy limit 1. D-branes and Classical descriptions

5
D-brane ( BPS case ) Open string endpoints stick to a D-brane Open string endpoints stick to a D-brane Properties Properties SO(1,p)×SO(9-p) ( BPS case ), RR-charged SO(1,p)×SO(9-p) ( BPS case ), RR-charged (mass) 1/(string coupling) (mass) 1/(string coupling) X0X0 XμXμ XiXi open string Dp-brane

6
BPS black p-brane solution Symmetry : SO(1,p)×SO(9-p), RR-charged Symmetry : SO(1,p)×SO(9-p), RR-charged setup : SUGRA action setup : SUGRA action ansatz : ansatz :

7
BPS black p-brane solution (D=10) Di Vecchia et al. suggested more direct method to check the correspondence between a Dp-brane and a black p-brane solution using the boundary state. it must be large for the validity of SUGRA ・ SO(1,p)×SO(9-p), ・ (mass)=(RR-charge), which are the same as D-branes

8
asymptotic behavior of the black p-brane = difference from the flat background = graviton, dilaton, RR-potential in SUGRA asymptotic behavior of the black p-brane = difference from the flat background = graviton, dilaton, RR-potential in SUGRA massless modes of the closed strings from the boundary state ( D-brane in closed string channel ) = graviton, dilaton, RR-potential in string theory massless modes of the closed strings from the boundary state ( D-brane in closed string channel ) = graviton, dilaton, RR-potential in string theory ( string field theory ) ( string field theory ) coincide Relation between the D-brane ( the boundary state) and the black p-brane solution (Di Vecchia et al. (1997))

9
Boundary State ( = D-brane) Boundary states are defined as sources of closed strings ( = D-branes in closed string channel ). Boundary states are defined as sources of closed strings ( = D-branes in closed string channel ). As closed strings include gravitons, the boundary state directly relates to a black p-brane solution. As closed strings include gravitons, the boundary state directly relates to a black p-brane solution.

10

11
We can reproduce the leading term of a black p-brane solution ( asymptotic behavior ) via the boundary state. leading term at infinity e.g. ) asymptotic behavior of Φ of black p-brane coincident ** |φ>
**

12
String Field Theory Supergravity classical solution ( Black p-brane ) D-brane ( Boundary State ) low energy limit α ’ → 0 low energy limit eom BPS case → OK (Di Vecchia et al. (1997)) We study non-BPS systems ( e.g. D/anti D-brane system ). non-BPS case → ? non-BPS cases are more realistic in GR sense

13
BPS case BPS case Dp-brane black p-brane Dp-brane black p-brane Non-BPS case Non-BPS case D/anti D-brane system with a constant tachyon vev Three-parameter solution ? ( guessed by Brax-Mandal-Oz (2000)) D/anti D-brane system with a constant tachyon vev Three-parameter solution ? ( guessed by Brax-Mandal-Oz (2000)) ( other non-BPS system corresponding classical solution ?) ( other non-BPS system corresponding classical solution ?) We verify their claim using the boundary state.

14
2. D/anti D-brane system 2. D/anti D-brane system D-branes and anti D-branes attracts together Unstable multiple branes Open string tachyon represents its instability Stable D-branes are left case D/anti D-brane system tachyon condensation closed string emission

15
Boundary State with boundary interaction

16
open string

17
Boundary state for D/anti D-brane with a constant tachyon vev mass RR-charge constant tachyon

18
Change of the Mass during the tachyon condensation Change of the Mass during the tachyon condensation 1. D-branes, anti D-branes coincide with each other. ( t = 0 ) 1. D-branes, anti D-branes coincide with each other. ( t = 0 ) 2. During the tachyon condensation ( t = t 0 ) tachyon vev is included in the mass. 3. Final state ( t = ∞ ) The mass will decrease through the closed string emission, and the value of the mass will coincide with that of the RR-charge (BPS).

19
Boundary state for D/anti D-brane mass RR-charge constant tachyon

20
3. Three-parameter solution ( Zhou & Zhu (1999) ) SUGRA action SUGRA action ansatz : SO(1, p)×SO(9-p) ( D=10 ) ansatz : SO(1, p)×SO(9-p) ( D=10 ) same symmetry as the D/anti D-brane system

21
charge ? mass ? tachyon vev ?

22
Property of the three-parameter solution ADM mass ADM mass RR charge RR charge We can extend it to an arbitrary dimensionality. We can extend it to an arbitrary dimensionality. ~?~? From the form of the boundary state, Brax-Mandal-Oz claimed that c_1 corresponds to the tachyon vev. ~?~? We re-examine the correspondence between the D/anti D-brane system and the three-parameter solution using the boundary state.

23
New parametrization → During the tachyon condensation, the RR-charge does not change its value. → We need a new parametrization suitable for t.c. → During the tachyon condensation, the RR-charge does not change its value. → We need a new parametrization suitable for t.c.

24
Asymptotic behavior of the three-parameter solution (= graviton, dilaton, RR-potential in SUGRA )

25
graviton, dilaton, RR-potential in string theory **
**

26
Using the boundary state, we obtain

27
asymptotic behavior of the three-parameter solution massless modes via the boundary state Results and Comparison

28

29
asymptotic behavior of the three-parameter solution massless modes via the boundary state Results and Comparison

30
We find that they coincide with each other under the following identification, We find that they coincide with each other under the following identification, RR-charge, constant during the tachyon condensation v ^2 ~ M^2 – Q^2 : non-extremality → tachyon vev can be seen as a part of the ADM mass c_1 does not corresponds to the vev of the open string tachyon. The three-parameter solution with c_1=0 does correspond to the D/anti D-brane system.

31
Conclusions Using the boundary state, we find that the three- parameter solution with c_1=0 corresponds to the D/anti D-brane system with a constant tachyon vev. Using the boundary state, we find that the three- parameter solution with c_1=0 corresponds to the D/anti D-brane system with a constant tachyon vev. New parametrization is needed to keep the RR-charge constant during the tachyon condensation. New parametrization is needed to keep the RR-charge constant during the tachyon condensation. The vev of the open string tachyon is only seen as a part of the ADM mass. The vev of the open string tachyon is only seen as a part of the ADM mass. c_1 does not corresponds to the tachyon vev as opposed to the proposal made so far. c_1 does not corresponds to the tachyon vev as opposed to the proposal made so far. We find that we can extend the correspondence between D-branes and classical solutions to non-BPS case. We find that we can extend the correspondence between D-branes and classical solutions to non-BPS case. First discovery of the correspondence in non-BPS case. First discovery of the correspondence in non-BPS case. It may be a clue to describe “ realistic ” gravitational systems which are generally non-BPS. It may be a clue to describe “ realistic ” gravitational systems which are generally non-BPS.

32
1. Parametrization → during the t.c., the RR-charge does not change its value. → 2. The relation between the mass and the scalar charge → cf. Wyman solution in D=4 case c_1 corresponds to the dilaton charge. Discussion : Why was c_1 thought to be the open string tachyon vev ?

33
Wyman solution in Schwarzschild gauge Static, spherically symmetric, with a free scalar Static, spherically symmetric, with a free scalar

34
Wyman solution in isotropic gauge r → R r → R In this gauge, we can compare it with the 3-para. sln.

35
Three-parameter solution case Three-parameter solution case corresponds to the dilaton charge.

36
Discussion : Stringy counterpart of c_1 ? has something to do with the -brane. has something to do with the -brane. We can not relate these parts with an ordinary boundary state counterpart of the D/anti D-brane system

37
We can not relate these parts with an ordinary boundary state counterpart of the D/anti D-brane system

38
Deformation of the boundary state Deformation of the boundary state We can reproduce the 3-para. sln with non-zero by adjusting α ・ β Do we have such a deformation in string theory ? → with open string tachyon

39
Construction of (Asakawa-Sugimoto-Terashima, JHEP 0302 (2003) 011) Construction of (Asakawa-Sugimoto-Terashima, JHEP 0302 (2003) 011) boundary interaction

40
δ-function with ｔ → ∞ →ordinary boundary state

41
From Gaussian Boundary State to BPS Dp-brane tachyon has some configuration t → ∞ lower-dimensional BPS D-brane

42
extend to -direction infinitely localized atGaussian in -direction

43
So far, we treat So far, we treat Consider that each or is made from Consider that each or is made from boundary state is deformed as follows: boundary state is deformed as follows: origin Gaussian brane origin ordinary Deformed

44
Gaussian boundary state D9-tachyon Mixture of Neumann b.c. and Dirichlet b.c. → smeared boundary condition

45
Oscillator picture boundary condition in the oscillator picture boundary condition in the oscillator picture

46
cf. ordinary boundary state D-brane σ τ closed string closed tree graph σ τ open string open 1-loop graph boundary state

47
boundary conditions boundary conditions Longitudinal to the D-brane Transverse to the D-brane

48
・ Longitudinal to the Dp-brane ・ Transverse to the Dp-brane Gaussian boundary state case

49
Oscillator part 0-mode part combine them to ordinary boundary state with ｔ →∞

50
From ato one tension part via SFT thus, in the limit （ D9-tachyon vanishes ） （ Kraus-Larsen, PRD63 (2001) ）

51
integrate with finite finally, we obtain origin Gaussian brane origin

52

53
tachyon origin tachyon origin

54
graviton, dilaton via Gaussian boundary state graviton, dilaton via Gaussian boundary state

55
graviton, dilaton via three-parameter solution graviton, dilaton via three-parameter solution

56
constant criterion : RR charge Q keeps its value

57
Thus, we compare them as → The effect of can be interpreted as D9-tachyon t. D9-tachyon t.

58
Future Work c_1 and a Gaussian brane (SK, Asakawa & Matsuura, hep-th/0502XXX ) c_1 and a Gaussian brane (SK, Asakawa & Matsuura, hep-th/0502XXX ) Entropy counting via non-BPS boundary state Entropy counting via non-BPS boundary state Construction of a time-dependent solution Construction of a time-dependent solution feedback to SFT feedback to SFT Solving δ B |B>=0 ( E-M conservation law in SFT ) (Asakawa, SK & Matsuura, JHEP 0310 (2003) 023) Solving δ B |B>=0 ( E-M conservation law in SFT ) (Asakawa, SK & Matsuura, JHEP 0310 (2003) 023) Application to cosmology (SK, K. Takahashi & Himemoto) Application to cosmology (SK, K. Takahashi & Himemoto) Stability analysis ( K. Takahashi & SK) Stability analysis ( K. Takahashi & SK)

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google