Bum-Hoon Lee Sogang University, Seoul, Korea
description
Transcript of Bum-Hoon Lee Sogang University, Seoul, Korea
![Page 1: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/1.jpg)
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
![Page 2: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/2.jpg)
www.themegallery.com
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
![Page 3: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/3.jpg)
www.themegallery.com
* 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
![Page 4: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/4.jpg)
www.themegallery.com
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.
![Page 5: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/5.jpg)
www.themegallery.com
![Page 6: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/6.jpg)
www.themegallery.com
Some relation
* Strings on pp-waves
Choose light-cone gauge ; ( is the worldsheet time.)
The light-cone action
![Page 7: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/7.jpg)
www.themegallery.comCenter for Quantum SpacetimeCenter for Quantum Spacetime
![Page 8: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/8.jpg)
www.themegallery.comCenter for Quantum SpacetimeCenter for Quantum Spacetime
![Page 9: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/9.jpg)
www.themegallery.com
pp-wave background metric
![Page 10: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/10.jpg)
www.themegallery.com
- the light-cone Hamiltonian
:
From the point of view,
is given by
![Page 11: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/11.jpg)
www.themegallery.com
* 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
![Page 12: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/12.jpg)
www.themegallery.com
* 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
![Page 13: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/13.jpg)
www.themegallery.com
- 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
![Page 14: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/14.jpg)
www.themegallery.com
* 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.
![Page 15: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/15.jpg)
www.themegallery.com
In the light-cone gauge , the Green-Schwarz action is
:
Equations of motion for string
![Page 16: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/16.jpg)
www.themegallery.com
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
![Page 17: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/17.jpg)
www.themegallery.comCenter for Quantum SpacetimeCenter for Quantum Spacetime
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
![Page 18: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/18.jpg)
www.themegallery.comCenter for Quantum SpacetimeCenter 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. 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
![Page 19: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/19.jpg)
www.themegallery.comCenter for Quantum SpacetimeCenter for Quantum Spacetime
![Page 20: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/20.jpg)
www.themegallery.com
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 :
![Page 21: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/21.jpg)
www.themegallery.comCenter for Quantum SpacetimeCenter for Quantum Spacetime
![Page 22: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/22.jpg)
www.themegallery.comCenter for Quantum SpacetimeCenter for Quantum Spacetime
![Page 23: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/23.jpg)
www.themegallery.comCenter for Quantum SpacetimeCenter for Quantum Spacetime
![Page 24: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/24.jpg)
www.themegallery.com
The allowed choices for
Solutions
for bosonic coordinates
![Page 25: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/25.jpg)
www.themegallery.com
for fermions
The boundary conditions
![Page 26: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/26.jpg)
www.themegallery.comCenter for Quantum SpacetimeCenter for Quantum Spacetime
![Page 27: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/27.jpg)
www.themegallery.comCenter for Quantum SpacetimeCenter for Quantum Spacetime
![Page 28: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/28.jpg)
www.themegallery.comCenter for Quantum SpacetimeCenter for Quantum Spacetime
![Page 29: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/29.jpg)
www.themegallery.comCenter for Quantum SpacetimeCenter for Quantum Spacetime
![Page 30: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/30.jpg)
www.themegallery.comCenter for Quantum SpacetimeCenter for Quantum Spacetime
![Page 31: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/31.jpg)
www.themegallery.comCenter for Quantum SpacetimeCenter for Quantum Spacetime
![Page 32: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/32.jpg)
www.themegallery.comCenter for Quantum SpacetimeCenter for Quantum Spacetime
![Page 33: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/33.jpg)
www.themegallery.comCenter for Quantum SpacetimeCenter for Quantum Spacetime
![Page 34: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/34.jpg)
www.themegallery.comCenter for Quantum SpacetimeCenter for Quantum Spacetime
![Page 35: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/35.jpg)
www.themegallery.comCenter for Quantum SpacetimeCenter for Quantum Spacetime
![Page 36: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/36.jpg)
www.themegallery.comCenter for Quantum SpacetimeCenter for Quantum Spacetime
![Page 37: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/37.jpg)
www.themegallery.comCenter for Quantum SpacetimeCenter for Quantum Spacetime
![Page 38: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/38.jpg)
www.themegallery.com
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
Center for Quantum SpacetimeCenter for Quantum Spacetime
![Page 39: Bum-Hoon Lee Sogang University, Seoul, Korea](https://reader036.fdocuments.in/reader036/viewer/2022062309/56815966550346895dc6a44a/html5/thumbnails/39.jpg)