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Quantum critical transport, duality, and M-theory

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arxiv hep-th/0701036 v2 pith:7SYP7QUF submitted 2007-01-05 hep-th cond-mat.str-el

Christopher P. Herzog , Pavel Kovtun , Subir Sachdev , Dam Thanh Son This is my paper · ORCID
classification hep-thcond-mat.str-el
keywords dimensionaldualitytheoriestheoryabelianconformalcrossoverfluctuating
verification ladder T0 review T1 audit T2 compute T3 formal
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We consider charge transport properties of 2+1 dimensional conformal field theories at non-zero temperature. For theories with only Abelian U(1) charges, we describe the action of particle-vortex duality on the hydrodynamic-to-collisionless crossover function: this leads to powerful functional constraints for self-dual theories. For the n=8 supersymmetric, SU(N) Yang-Mills theory at the conformal fixed point, exact hydrodynamic-to-collisionless crossover functions of the SO(8) R-currents can be obtained in the large N limit by applying the AdS/CFT correspondence to M-theory. In the gravity theory, fluctuating currents are mapped to fluctuating gauge fields in the background of a black hole in 3+1 dimensional anti-de Sitter space. The electromagnetic self-duality of the 3+1 dimensional theory implies that the correlators of the R-currents obey a functional constraint similar to that found from particle-vortex duality in 2+1 dimensional Abelian theories. Thus the 2+1 dimensional, superconformal Yang Mills theory obeys a "holographic self duality" in the large N limit, and perhaps more generally.

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Cited by 5 Pith papers

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