Holographic flavor transport in Schrödinger spacetime

Abstract

We use gauge-gravity duality to study the transport properties of a finite density of charge carriers in a strongly-coupled theory with non-relativistic symmetry. The field theory is \( \mathcal{N} = 4 \) supersymmetric SU(N c ) Yang-Mills theory in the limit of large N c and with large ’t Hooft coupling, deformed by an irrelevant operator, coupled to a number N f of massive \( \mathcal{N}{ = 4} \) supersymmetric hypermultiplets in the fundamental representation of the gauge group, i.e. flavor fields. The irrelevant deformation breaks the relativistic conformal group down to the Schrödinger group, which has non-relativistic scale invariance with dynamical exponent z = 2. Introducing a finite baryon number density of the flavor fields provides us with charge carriers. We compute the associated DC and AC conductivities using the dual gravitational description of probe D7-branes in an asymptotically Schrödinger spacetime. We generically find that in the infrared the conductivity exhibits scaling with temperature or frequency that is relativistic, while in the ultraviolet the scalings appear to be non-relativistic with dynamical exponent z = 2, as expected in the presence of the irrelevant deformation.

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Correspondence to Andy O’Bannon.

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ArXiv ePrint: 1003.5913

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Ammon, M., Hoyos, C., O’Bannon, A. et al. Holographic flavor transport in Schrödinger spacetime. J. High Energ. Phys. 2010, 12 (2010). https://doi.org/10.1007/JHEP06(2010)012

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Keywords

  • Gauge-gravity correspondence
  • AdS-CFT Correspondence
  • Brane Dynamics in Gauge Theories