Hall viscosity in a strongly coupled magnetized plasma

Abstract

We show how a Hall viscosity induced by a magnetic field can be generated in strongly coupled theories with a holographic dual. This is achieved by considering paritybreaking higher derivative terms in the gravity dual. These terms couple the Riemann curvature tensor to the field strength of a gauge field dual to the charge current, and have an analog in the field theory side as a coupling between the "Euler current" and the electromagnetic field. As a concrete example, we study the effect of the new terms in the thermodynamic and transport properties of a strongly coupled magnetized plasma dual to a dyonic black hole in AdS 4 . As a new property of the holographic model, we find that for a state that is initially neutral at zero magnetic field, a charge density and non-dissipative Hall transport are present when the magnetic field is turned on. Remarkably, we also observe that the results from the holographic model are consistent with hydrodynamics even at magnetic fields much larger than temperature.

On the hydrodynamics of (2 + 1)-dimensional strongly coupled relativistic theories in an external magnetic field

“…[10,36] for reviews). In the context of strongly coupled theories described by gauge-gravity dualities one finds the Hall conductivity is an integral part of the description of systems with a magnetic field; for example in probe brane models [5,6,8,37], bulk theories with Chern-Simon's like terms [7,[38][39][40] and/or systems with broken translation invariance [41,42]. There has also been related theoretical work examining constraints on the Hall viscosity [9,43].…”

Novel semi-circle law and Hall sliding in a strongly interacting electron liquid

“…Having obtained surprisingly good results using a hydrodynamical description, it would be an interesting exercise to understand it better in the probe brane case as studied here. 16 The underlying momentum sink of the adjoints makes hydrodynamic effective modeling JHEP05(2022)144 untrustworthy at late times, unless the finite-N c corrections that are behind the longtime power law tails [55] are considered. To this vein, a less arduous approach would be to consider constructing a stationary state by forming an appropriate combination of a temperature gradient and an electric field [56].…”

“…In particular, observables such as charge transport can be reliably computed, and there has been a strong focus on magneto-transport of holographic models in recent years. An early holographic-inspired hydrodynamical model of magneto-transport was constructed in [7], followed by a number of other holographic models [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], with attempts made to match the characteristic strange metallic behavior.…”

Novel semi-circle law and Hall sliding in a strongly interacting electron liquid

“…7 and (A.38), however, do not appear to be obviously the same. 12 This situation is like the near equality of the longitudinal conductivities σ DC xx and σ DC yy despite the clear asymmetry of the striped phase between the x and y directions. In the Hall case, however, the equality between − σ DC yx and σ DC xy is exact, at least up to the precision of our numerics.…”

“…In particular, observables such as charge transport can be reliably computed, and there has been a strong focus on magneto-transport of holographic models in recent years. An early holographic-inspired hydrodynamical model of magneto-transport was constructed in [7], followed by several other holographic models [8][9][10][11][12][13][14][15], with attempts made to match the characteristic strange metallic behavior.…”