Bum-Hoon Lee Sogang University, Seoul, Korea D-branes in Type IIB Plane Wave Background 15th Mini-Workshop on Particle Physics May 14-15, 2006, Seoul National University

Based on the works: 1. J. Kim, BHL, & H.S. Yang Superstrings and D-branes in A Plane Wave Phys. Rev. D68 (2003) , hep-th/ K.-S. Cha, BHL, & H.S. Yang Intersecting D-branes in IIB PP Background Phys. Rev.D68 (2003) , hep-th/ K.-S. Cha, BHL, & H.S.Yang Supersymmetric D-branes in IIB PP Background JHEP03 (2004) 058, hep-th/ 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/ References Center 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 - 1 st condition -> allows only odd p branes

Center for Quantum Spacetime Boundary Open string Bulk Closed string + Open string sector D5-D5 + D3-D5 string D3 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

Center for Quantum Spacetime BMN limit N=4 d=3+1 SYM (λ=g YM ^2, N<<1) 2+1 dim defect CFT Penrose limit Max. SUSY # 32 Ads_5 X S^5 (g s 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. SUSY # 32 Symmetric Plane Wave Geometry Blau, … Metsaev … D-branes : Open string sector Intersecting

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Ex) Flat Minkowski Center for Quantum Spacetime IIB ½ BPS : D1 D3 D5 D7 D9 Dp-braneIntersectin D-branes Dp-Dp’ # ND, DN = 0, 4, 8 : SUSY If Not, NO SUSY D1 D3 Dp-DpD(p+4) Dp ¼BPS :

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The allowed choices for Solutions for bosonic coordinates

for fermions The boundary conditions

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Summary  Supersymmetric intersecting D-brane configurations intersecting D-brane configurations in pp-wave background in pp-wave background are systematically classified are systematically classified  Dual field theories and Application to the Phenomenological Model buildings to be Phenomenological Model buildings to be studied studied Center for Quantum Spacetime