Transcript D-branes

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
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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
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* 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
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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 Rcharge of a state of the field theory on
where the
has unit
radius.
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Some relation
* Strings on pp-waves
Choose light-cone gauge ;
The light-cone action
(
is the worldsheet time.)
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pp-wave background metric
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- the light-cone Hamiltonian
:
From the
point of view,
is given by
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* Strings from N=4 Super Yang-Mills
In the limit
find the spectrum of states with finite
of the Yang-Mills theory on
(single trace states
- 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
on the light-cone vacuum
and
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* 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
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- 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
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* 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.
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In the light-cone gauge
:
Equations of motion for string
, the Green-Schwarz action is
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Boundary conditions for boson
Neunmann :
Dirichlet :
for fermion
For BPS objects that preserve 16 supersymmetries,
satisfy two conditions
- 1st condition -> allows only odd p branes
have to
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Bulk
Closed string
Boundary
Open string
D3
+ Open string sector
D5-D5
+ D3-D5 string
D5
SUGRA
Intersecting
D-branes
Solution
½ BPS (# 16 SUSY)
Near Horizon
limit
Ads_5 X S^5
#N
Conformal limit
N=4 d=3+1 SYM
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Ads_5 X S^5
Max. SUSY
# 32
(gs N >> 1)
Intersecting
Ads_4 X S^2 , D brane
Penrose limit
Max. SUSY
# 32
N=4 d=3+1 SYM
(λ=g YM ^2 , N<<1)
2+1 dim defect CFT
BMN limit
Symmetric Plane Wave
Geometry
Intersecting
D-branes : Open string sector
(J , Δ>>1) Sector of SYM
Blau, …
G. Semenoff …
Metsaev …
Constable …
λ’ = g YM ^2 N / J^2
Corresponding dCFT
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Ex) Flat Minkowski
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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)
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The allowed choices for
Solutions
for bosonic coordinates
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for fermions
The boundary conditions
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Summary
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 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