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Bum-Hoon Lee Sogang University, Seoul, Korea

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. References. Center for Quantum Spacetime. Based on the works: 1. J. Kim, BHL, & H.S. Yang

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Bum-Hoon Lee Sogang University, Seoul, Korea

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  1. Bum-Hoon LeeSogang University, Seoul, Korea D-branes in Type IIBPlane Wave Background 15th Mini-Workshop on Particle Physics May 14-15, 2006, Seoul National University

  2. References Center for Quantum Spacetime 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

  3. * 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

  4. 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.

  5. Some relation * Strings on pp-waves Choose light-cone gauge ; ( is the worldsheet time.) The light-cone action

  6. Center for Quantum Spacetime

  7. Center for Quantum Spacetime

  8. pp-wave background metric

  9. - the light-cone Hamiltonian : From the point of view, is given by

  10. * 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

  11. * 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

  12. - 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

  13. * 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.

  14. In the light-cone gauge , the Green-Schwarz action is : Equations of motion for string

  15. 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

  16. BulkClosed string Center for Quantum Spacetime Boundary Open string D3 + Open string sector D5-D5 + D3-D5 string D5 SUGRA Solution Intersecting D-branes ½ BPS (# 16 SUSY) # N Near Horizon limit Conformal limit Ads_5 X S^5 N=4 d=3+1 SYM

  17. Penrose limit BMN limit Center for Quantum Spacetime N=4 d=3+1 SYM (λ=g YM ^2 , N<<1) Ads_5 X S^5 (gs N >> 1) Max. SUSY # 32 Intersecting 2+1 dim defect CFT Ads_4 X S^2 , D brane (J , Δ>>1) Sector of SYM λ’ = g YM ^2 N / J^2 G. Semenoff … Constable… Max. SUSY # 32 Symmetric Plane Wave Geometry Blau, … Metsaev … Intersecting D-branes : Open string sector Corresponding dCFT

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

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  23. The allowed choices for Solutions for bosonic coordinates

  24. for fermions The boundary conditions

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

  38. Thank You !

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