Transcript Martin Schvellinger: Gauge/gravity duality and Non-Relativistic Quantum Field Theories

The gauge/gravity duality
and
Non-Relativistic Quantum Field Theories
Martín Schvellinger
Instituto de Física de La Plata - CONICET
Departamento de Física - UNLP
The two parts of this talk
• A very brief introduction to the gauge/gravity duality.
• The gauge/gravity duality and non-relativistic QFTs:
• Gravity dual models of Non-Relativistic Quantum Mechanical
theories at finite Temperature and finite Chemical Potential in
diverse number of space-like dimensions.
Introduction: Black holes and Holography
•
Black hole entropy: S=Area/4 (Bekenstein and Hawking)
•
Degrees of freedom are the same as if the BH were a bidimensional
system: the degrees of freedom are those on its horizon-> holography (´t
Hooft and Susskind)
•
String theory calculations of BH entropy give the proportionality between S
and A.
•
Question: is string theory holographic? Maldacena’s answer: yes
•
What does it mean for string theory? AdS/CFT correspondence.
• Witten (1998), and Gubser, Klebanov, Polyakov (1998), independently
proposed an ansatz for the generating functional of the QFT correlation
functions in terms of the gravity dual model.
• The best known example is the large N limit of SU(N) N=4 SYM theory in
4d, that is dual to type IIB supergravity on AdS5 x S5, with N units of F5
flux on S5, a constant dilaton.
There are extensions of this idea in several directions:
•
•
•
•
Gauge theories with less or no supersymmetry.
Non-conformal gauge field theories, i.e. RG flows.
Applications to BSM physics, cosmology, AdS/QCD, etc.
Transport and hydrodynamical properties of strongly coupled quarkgluon plasmas.
• Non-Relativistic QFTs.
Introduction to the AdS/CFT correspondence
Minkowski 10d = 0 1 2 3 4 5 6 7 8 9
D3-brane:
0123
Identifications
Small curvature
Large t´Hooft coupling= strongly coupled QFT
So, we have a powerful tool to calculate QFT properties at strong coupling!
Isometries :
AdS5 -> Conformal group of SCFT 4d SO(2,4)
S5
-> SO(6) ~ SU(4)R of N=4 SCFT
So, isometries have a dual realization in the FT side.
Non-Relativistic Conformal Quantum Mechanical Theories and
their gravity dual models
• Start from a Relativistic QM theory and consider its DLCQ
• This gives a Non-Relativistic QM theory.
• If the generators of the conformal group are included: NRCQM th.
AdS/CFT
Relativistic CQF Th
Poincaré Symm Gravity Dual Th
DLCQ
DLCQ
AdS/CFT
Non-Relativistic CQF Th
Schrödinger Symm Gravity Dual Th
• Particular interest in the DLCQ of CQFT theories with plane-wave
boundary conditions, and their gravity dual description.
• These NRCQM theories are defined on plane-wave backgrounds in
diverse dimensions.
• The boundary plane-wave structure can be shown by slicing the
AdS metric.
D5 brane in type I theory in S1 x R9
And 16 Wilson lines
S1
T-duality along S1
D4
D4 brane in type I’ theory in S1/Z2 x R9
And 16 D8-branes
Nf D8
Massive IIA supergravity
16-Nf D8
Holographic RG flows: example D4-brane wrapping a 2-cycle
5678
012
34
r
U.Gursoy, C.Nunez and M.Schvellinger, JHEP 0206, 015 (2002)
M.Schvellinger and T.Tran, JHEP 0106, 025 (2001)
C.Nunez, I.Park, M.Schvellinger and T.Tran, JHEP 0104, 025 (2001)
M theory 11d
IIA Sugra
H
Massive
IIA Sugra
F(4) 6d
AdS6 UV
AdS4 IR
A
B
BPS HRGF
N=2
5d SCFT
3d CFT
Conclusions:
We have seen how to obtain certain gravity backgrounds which
allow us to predict finite temperature and finite chemical potential
for NRCQM theories in diverse dimensions.
We suggested possible strings theory/M theory upliftings for them.
Future directions: for example
consider NRQM theories, with RG flows.