Magneto-thermal transport implies an incoherent Hall conductivity
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Springer
Received: May 28, Revised: July 8, Accepted: July 26, Published: August 20,
2020 2020 2020 2020
Andrea Amoretti,a,b Daniel K. Brattan,b Nicodemo Magnolia,b and Marcello Scanavinoa,b a
Dipartimento di Fisica, Universit` a di Genova, via Dodecaneso 33, I-16146, Genova, Italy b I.N.F.N. — Sezione di Genova, via Dodecaneso 33, I-16146, Genova, Italy
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: We consider magnetohydrodynamics with an external magnetic field. We find that in general one must allow for a non-zero incoherent Hall conductivity to correctly describe the DC longitudinal and Hall thermal conductivities beyond order zero in the magnetic field expansion. We apply our result to the dyonic black hole, determining the incoherent Hall conductivity in that case, and additionally prove that the existence of this transport coefficient leads to a significantly better match between the hydrodynamic and AC thermo-electric correlators. Keywords: AdS-CFT Correspondence, Gauge-gravity correspondence, Holography and condensed matter physics (AdS/CMT), Gauge Symmetry ArXiv ePrint: 2005.09662
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP08(2020)097
JHEP08(2020)097
Magneto-thermal transport implies an incoherent Hall conductivity
Contents 1
2 Magnetohydrodynamics 2.1 The diffeomorphism and U(1) gauge symmetry Ward identities 2.2 Equilibrium magnetohydrodynamics 2.3 AC diffusivities in magnetohydrodynamics 2.4 Constraining hydrodynamic correlators with the Ward identities
3 4 5 6 9
3 Revisiting the dyonic black hole 3.1 An incoherent conductivity 3.2 Matching the correlators
11 13 14
4 Discussion
17
A Standard formulation of relativistic magnetohydrodynamics
18
B Miscellaneous additional results
19
1
Introduction
Magnetohydrodynamics is a collective theory of hydrodynamic modes coupled to electromagnetic degrees of freedom. It is an effective field theory which describes the long-range correlations of near-equilibrium systems, when the microscopic theory is coupled to a U(1) gauge field. The electromagnetic field can be dynamical, where the evolution of the gauge field is governed by the Maxwell equations from a given initial configuration, or external where the profile is arbitrary up to satisfying the Bianchi identity. We are interested in the latter. In recent times magnetohydrodynamics has been intensively studied. New breakthroughs in the theoretical study of magnetohydrodynamics include, among others things, understanding the deeper underlying symmetries and structures that constrain the transport coefficients and subsequently formulating classification schemes [1, 2]. There have also been applications to the generalized global symmetry reformulation of hydrodynamics [3–6]. At a more practical level the formalism has been used to analyze the physics of relativistic plasmas [7], as well as to understand the behavior of strongly coupled condensed matter systems [8–13]. In
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