Martín SchvellingerInstituto de Física de La Plata - CONICET

Departamento de Física - UNLP

The gauge/gravity duality and

Non-Relativistic Quantum Field Theories

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 quark-

gluon plasmas.• Non-Relativistic QFTs.

Introduction to the AdS/CFT correspondence

D3-brane: 0 1 2 3

Minkowski 10d = 0 1 2 3 4 5 6 7 8 9

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.

Identifications

So, we have a powerful tool to calculate QFT properties at strong coupling!

Small curvatureLarge t´Hooft coupling= strongly coupled QFT

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.

Relativistic CQF Th

DLCQ DLCQ

Non-Relativistic CQF Th Schrödinger Symm Gravity Dual Th

Poincaré Symm Gravity Dual Th

AdS/CFT

AdS/CFT

• 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 linesS1

T-duality along S1

D4 brane in type I’ theory in S1/Z2 x R9 And 16 D8-branes

Nf D8 16-Nf D8

D4

Massive IIA supergravity

Holographic RG flows: example D4-brane wrapping a 2-cycle

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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 3d CFT 5d SCFT

Conclusions:

We have seen how to obtain certain gravity backgrounds which allow us to predict finite temperature and finite chemical potentialfor 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.