Martín Schvellinger Instituto de Física de La Plata - CONICET Departamento de Física - UNLP

1. Martín SchvellingerInstituto de Física de La Plata - CONICETDepartamento 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 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.

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

7. 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.

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. AdS/CFT Relativistic CQF Th Poincaré Symm Gravity Dual Th DLCQ DLCQ AdS/CFT Non-Relativistic CQF Th Schrödinger Symm Gravity Dual Th

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 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 16-Nf D8 Nf D8 Massive IIA supergravity

37. 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)

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.