Bum-Hoon Lee Sogang University, Seoul, Korea

Bum-Hoon LeeSogang University, Seoul, Korea

D-branes in Type IIBD-branes in Type IIBPlane Wave BackgroundPlane Wave Background

15th Mini-Workshop on Particle PhysicsMay 14-15, 2006, Seoul National University

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Based on the works:

1. J. Kim, BHL, & H.S. Yang Superstrings and D-branes in A Plane Wave Phys. Rev. D68 (2003) 026004, hep-th/0302060

2. K.-S. Cha, BHL, & H.S. Yang Intersecting D-branes in IIB PP Background Phys. Rev.D68 (2003) 106004, hep-th/0307146

3. K.-S. Cha, BHL, & H.S.Yang Supersymmetric D-branes in IIB PP Background JHEP03 (2004) 058, hep-th/0310177

4. BHL,Jong-won Lee, Chanyong Park, HyunSeok Yang More on supersymmetric D-branes in type IIB plane wave background JHEP 01 (2006) 015, hep-th/0506091

ReferencesCenter for Quantum SpacetimeCenter for Quantum Spacetime


* pp waves as limits of

the metric of

Consider the geometry near the trajectory of a particle that is moving along the direction and sitting at and

- introducing new coordinates

- performing the following rescaling

then, we obtain


Rewrite this as the form of pp wave metric

The mass parameter is introduced by rescaling

In global coordinates in

energy : angular momentum :

In terms of the dual CFT, these are the conformal dimension and R-charge of a state of the field theory on where the has unit radius.


Some relation

* Strings on pp-waves

Choose light-cone gauge ; ( is the worldsheet time.)

The light-cone action

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pp-wave background metric


- the light-cone Hamiltonian

:

From the point of view,

is given by


* Strings from N=4 Super Yang-Mills

In the limit

find the spectrum of states with finite (single trace states

of the Yang-Mills theory on

- Taking to be the generator rotating the plane 56,

the vacuum state in light-cone gauge (corresponding to a

unique single trace operator with ) is

- 8 bosonic and 8 fermionic modes with

On the string theory side, we construct all these states by

applying the zero momentum oscillators to and

on the light-cone vacuum


* Strings from N=4 Super Yang-Mills

In the limit

find the spectrum of states with finite (single trace states

of the Yang-Mills theory on

- Taking to be the generator rotating the plane 56,

the vacuum state in light-cone gauge (corresponding to a

unique single trace operator with ) is


- 8 bosonic and 8 fermionic modes with

On the string theory side, we construct all these states by

applying the zero momentum oscillators to and

on the light-cone vacuum

These string states correspond to the following operators in the Super Yang-Mills theory


* Dp-brane in the pp wave background

Start with the pp wave metric and 5-form flux

This background is maximally supersymmetric and thus preserve

32 supersymmetries.


In the light-cone gauge , the Green-Schwarz action is

:

Equations of motion for string


Boundary conditions for boson

Neunmann :

Dirichlet :

for fermion

For BPS objects that preserve 16 supersymmetries, have to

satisfy two conditions

- 1st condition -> allows only odd p branes


Boundary

Open string

BulkClosed string

+ Open string sector D5-D5

+ D3-D5 stringD3

½ BPS (# 16 SUSY)

D5

D-branes

Intersecting

# N

SUGRA

Solution

Ads_5 X S^5 N=4 d=3+1 SYM

Near Horizon

limit

Conformal limit


BMN limit

N=4 d=3+1 SYM(λ=g YM ^2 ,

N<<1)

2+1 dim defect CFT

Penrose limit

Max. Max. SUSY # SUSY #

3232

Ads_5 X S^5

(gs N >> 1)

Ads_4 X S^2 , D brane

Intersecting

(J , Δ>>1) Sector of SYM

λ’ = g YM ^2 N / J^2

G. Semenoff …

Constable …

Corresponding dCFT

Max. Max. SUSY # SUSY #

3232

Symmetric Plane Wave Geometry

Blau, …

Metsaev …

D-branes : Open string sector

Intersecting


Ex) Flat MinkowskiCenter for Quantum SpacetimeCenter for Quantum Spacetime

IIB ½ BPS : D1 D3 D5 D7 D9

Dp-braneIntersectin D-branes Dp-Dp’

# ND, DN = 0, 4, 8 : # ND, DN = 0, 4, 8 : SUSYSUSY

If Not, NO SUSYIf Not, NO SUSY

D1

D3

Dp-Dp D(p+4)

Dp

¼BPS :


The allowed choices for

Solutions

for bosonic coordinates


for fermions

The boundary conditions


Summary

Supersymmetric Supersymmetric intersecting D-brane configurations intersecting D-brane configurations in pp-wave backgroundin pp-wave background are systematically classifiedare systematically classified

Dual field theories and Application to the Dual field theories and Application to the Phenomenological Model buildings to bePhenomenological Model buildings to be studiedstudied

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Bum-Hoon Lee Sogang University, Seoul, Korea

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