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We study topological gapless modes in relativistic hydrodynamics by weakly breaking the conservation of energy momentum tensor. Several systems have been found to have topologically nontrivial crossing nodes in the spectrum of hydrodynamic modes and some of them are only topologically nontrivial with the protection of certain spacetime symmetries. The nontrivial topology for all these systems is further confirmed from the existence of undetermined Berry phases. Associated transport properties and second order effects have also been studied for these systems. The non-conservation terms of the energy momentum tensor could come from an external effective symmetric tensor matter field or a gravitational field which could be generated by a specific coordinate transformation from the flat spacetime. Finally we introduce a possible holographic realization of one of these systems. We propose a new method to calculate the holographic Ward identities for the energy momentum tensor without calculating out all components of the Green functions and match the Ward identities of both sides.
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We study the mechanisms setting the radius of convergence of hydrodynamic dispersion relations in kinetic theory in the relaxation time approximation. This introduces a qualitatively new feature with respect to holography: a nonhydrodynamic sector represented by a branch cut in the retarded Greens function. In contrast with existing holographic examples, we find that the radius of convergence in the shear channel is set by a collision of the hydrodynamic pole with a branch point. In the sound channel it is set by a pole-pole collision on a non-principal sheet of the Greens function. More generally, we examine the consequences of the Implicit Function Theorem in hydrodynamics and give a prescription to determine a set of points that necessarily includes all complex singularities of the dispersion relation. This may be used as a practical tool to assist in determining the radius of convergence of hydrodynamic dispersion relations.
We show that gapless modes in relativistic hydrodynamics could become topologically nontrivial by weakly breaking the conservation of energy momentum tensor in a specific way. This system has topological semimetal-like crossing nodes in the spectrum of hydrodynamic modes that require the protection of a special combination of translational and boost symmetries in two spatial directions. We confirm the nontrivial topology from the existence of an undetermined Berry phase. These energy momentum non-conservation terms could naturally be produced by an external gravitational field that comes from a reference frame change from the original inertial frame, i.e. by fictitious forces in a non-inertial reference frame. This non-inertial frame is the rest frame of an accelerating observer moving along a trajectory of a helix. This suggests that topologically trivial modes could become nontrivial by being observed in a special non-inertial reference frame, and this fact could be verified in laboratories, in principle. Finally, we propose a holographic realization of this system.
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We study the phenomenon of additional light waves (ALWs), observed in crystal optics: two or more electromagnetic waves with the same polarization, but different refractive index, propagate simultaneously in a isotropic medium. We show that ALWs are common in relativistic hydrodynamics, and in particular in strongly coupled systems that admit a dual gravitational description, where the ALWs are dual to quasi normal modes in the AdS gravity. We study both the transverse and the longitudinal light wave propagation. In the longitudinal channel we find a transition between regimes with different number of excitonic resonances which resembles the transition to standard optics observed in crystals.
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