Relationship between marginal deformation parameters

in OSFT and boundary CFT

村田　仁樹 (Masaki Murata)with Matej Kudrna and Martin Schnabl

Institute of Physics AS CR(Czech Republic)

11.March @Osaka Univ.

SFT reproduces Boundary States

holds within

KnownWe computed

Outline

1. Motivation2. CFT Boundary State3. KMS Boundary State4. Cos X Solution5. Compare Boundary States

Background Independence

General Relativity

1. Independent of choice of g

2. Solutions backgrounds g can be … flat, Schwarzschild, etc

Background Independence

String Theory is Background Dependent

S-matrix on a fixed background

(Open) String Field Theory (SFT)

2. Solutions other backgrounds 1. Formulation depends on background

Solutions Backgrounds

Find solutionsTachyon condensationMarginal deformationLumpMultiplebrane Ghost brane

Schnabl, 2005Kiermaier-Okawa-Rastelli-Zwiebach, 2007Schnabl, 2007, Kiermaier-Okawa, 2007

Bonora-Maccaferri-Tolla, 2010

MM-Schnabl, 2011

Masuda-Noumi-Takahashi, 2012

CFT Boundary State Background

CFT Boundary State = label of vacua

KMS Boundary State is Simpler

KOZ boundary state : Non-polynomial

CFT boundary state

Compare

Kiermaier-Okawa-Zwiebach, 2008

Ellwood, 2008Kudrna-Maccaferri-Schnabl, 2012

KMS boundary state : Linear

Outline1. Motivation

2. CFT Boundary State3. KMS Boundary State4. Cos X Solution5. Compare Boundary States

Compare

Boundary Condition gives CFT Boundary State

open string boundary conditions

DN

Two aspects ofD-brane

Emit (absorb)closed string

CFT Boundary state

Cos X deformation

deformation parameter

Neumann

Dirichlet D25 D24

Outline

1. Background independence2. CFT Boundary state

3. KMS Boundary State4. Cos X Solution5. Compare Boundary States

Compare

KMS Boundary StateEllwood, 2008Kawano-Kishimoto-Takahashi, 2008Kudrna-Maccaferri-Schnabl, 2012

Sample computation of

For Fock states

Outline

1. Background Independence2. CFT Boundary States3. KMS Boundary State

4. Cos X Solution5. Compare Boundary States

Compare

Cos X deformation

deformation parameter

Neumann

Dirichlet D25 D24

Cos X solution

SFT solution in quasi Schnabl gauge

Q : Related to Cos X deformation?

Kiermaier-Okawa-Rastelli-Zwiebach, 2008

vs

?

Outline

1. Background Independence2. CFT Boundary States3. KMS Boundary State4. Cos X Solution5. Compare Boundary States

?

Comparing Boundary States

SFT : CFT :

?

?

Results

Consistency : holds within

?up to

Summary and Future works

• Systematic way for higher order• Higher level in Siegel gauge

quasi Schnabl

SiegelKudrna-Masuda-Okawa-Schnabl-Yoshida, 2012

Thank you!!

App : CFT Boundary sate

boundary conditions backgrounds of open string

CFT Boundary state

Neumann:

Dirichlet:

App : Gauge dependence

Gauge invariant

Gauge dependent

depends on gauge

App: Siegel gauge

based on data with L<13

Integrate out

Kudrna-Masuda-Okawa-Schnabl-Yoshida, 2012

Boundary state