1. Martín Schvellinger Instituto de Física de La Plata - CONICET Departamento de Física - UNLP The gauge/gravity duality and Non-Relativistic Quantum Field Theories

2. 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.

3. 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.

4. 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 AdS 5 x S 5, with N units of F 5 flux on S 5, 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.

5. Introduction to the AdS/CFT correspondence D3-brane: 0 1 2 3 Minkowski 10d = 0 1 2 3 4 5 6 7 8 9

7. Isometries : AdS 5 -> Conformal group of SCFT 4d SO(2,4) S 5 -> 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 curvature Large t´Hooft coupling= strongly coupled QFT

9. 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 Non-Relativistic CQF ThSchrödinger Symm Gravity Dual Th Poincaré Symm Gravity Dual Th AdS/CFT

10. 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.

32. D5 brane in type I theory in S 1 x R 9 And 16 Wilson lines S1S1 T-duality along S 1 D4 brane in type I’ theory in S 1 /Z 2 x R 9 And 16 D8-branes N f D8 16-N f D8 D4 Massive IIA supergravity

37. Holographic RG flows: example D4-brane wrapping a 2-cycle 34 012 r 5678 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)

40. 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.