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D3 branes and • N charged D3-brane
•Extreme limit
•Near horizon
0 rr
0r
25
222
222
2
22 dRdr
r
Rdxdt
R
rds i
55 SAdS
Open/Closed strings duality•Open strings
•Closed strings
spacehorizon near on StringsSG Free SSS
braneSG Free SSS
AdS/CFT in Type IIB•AdS/CFT conjecture (1997)
•N=4 SYM in 3+1 IIB on
•The precise relationship (1998) xzxZe
xxxd
0StringCFT
0,04
55 SAdS
Strong/Weak duality
•Effective coupling:
•Small curvature for SG:
•Small coupling in SG:
RNgs
11 Ngs
1R
Gravity/Gauge duality
String theory Gauge theory
IIB Strings on N=4 SYM
Strings on deformed AdS strong coupling theory?
55 SAdS
AdS/CMT(Superconductor)
•Einstein-Maxwell-charged scalar
•Backreaction and probe•Instability and symmetry breaking
22222
4
4
16 miqAFL
RxdS
Conductivity•Fluctuations of gauge field
•At boundary
•AdS/CFT dictionary
•Ohm’s law
tixx erArtA )(),(
r
AArA x
xx
)1()0()(
)1()0( , xxxx AJAA
)0(
)1(
)(x
x
x
x
x
x
x
x
A
iA
A
Ji
A
J
E
J
Magnetic Field•Meissner effect
•Type I superconductor
•Type II superconductor
)()(8
)(TFTF
VTBsn
c
u
uur
at constant
0at 0 ),(
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