We analyze the breakdown of causality for the perfect fluid limit in a medium with polarizeability. We show that to restore causality a relaxation term linking vorticity and polarization, analogous to the Israel-Stewart term linking viscous forces and gradients,is required. This term provides a minimum amount of dissipation a locally thermalized relativistic medium with polarizeability must have, independently of its underlying degrees of freedom. For ferromagnetic materials an infrared acausal mode remains, which we interpret as a Banks-Casher mode signaling spontaneous magnetization. With these ingredients, we propose a candidate for a fully causal Lagrangian of a relativistic polarizeable system near the perfect fluid limit.The question of weather there exists a universal limit to viscosity and/or dissipation (parameterized, in relativistic systems by the viscosity over entropy ratio η/s) is both profound and difficult to handle. On a fundamental level, it is plausible to argue that quantum uncertainty gives rise to fluctuations which dissipate information. However, the unitarity of quantum theory is difficult to reconcile rigorously with dissipation. The usual procedure, given a microscopic theory, is to assume thermal equilibrium and then use correlators obtained from finite-temperature field theory to calculate viscosity [1]. This allows us in principle to calculate transport coefficients given a thermally equilibrated microscopic theory which is also tractable. However, since relativistic systems with low viscosity are usually strongly coupled, this is a very blunt instrument for claiming "universal" limits.Thus, a fundamental limit has been claimed decades ago by combining the uncertainty principle with Boltzmann's derivation of viscosity [2], η/s ∼ O (0.1). While this is a plausible order-of-magnitude estimate, it was always clear that Boltzmann's derivation should not generally apply to strongly coupled quantum fields. More recently, Gauge-gravity correspondence allowed us to conclude [3] that theories with a classical gravity dual have η/s = (4π) −1 in their strong-coupling limit. The universality of this limit is a consequence of the black-hole no-hair theorem, and hence it critically depends on the existence of a classical gravity dual, namely a planar limit and a conformal strongly coupled fixed point. Counter examples have been argued for beyond this limit [4].These difficulties illustrate that most likely one cannot get a lower limit from top-down arguments, where hydrodynamics appears as a limit of a known microscopic theory. A bottom-up constraint, based on effective field theory constraints such as low-energy unitarity, causality, and convergence of the gradient expansion are necessary. Attempts in this direction can be formulated in terms of a basic ambiguity within hydrodynamics: The fact that in the low viscosity limit thermal fluctuations will propagate as hydrodynamic modes, and the Kubo formula will need to be "renormalized" to take this into account [5]. In [5] the renormalization happen...

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We use Lagrangian effective field theory techniques to construct the equations of motion for an ideal relativistic fluid whose constituent degrees of freedom have microscopic polarization. We discuss the meaning of such a system, and argue that it is the first term in the EFT appropriate for describing polarization observables in heavy ion collisions, such as final state particle polarization and chiral magnetic and vortaic effects. We show that this system will generally require non-dissipative dynamics at higher order in gradient than second order, leading to potential stability issues known with such systems. We comment on the significance of this in the light of conjectured lower limits on viscosity.

We extend the effective theory approach to the ideal fluid limit where the polarization of the fluid is non-zero. After describing and motivating the equations of motion, we expand them around the hydrostatic limit, obtaining the sound wave and vortex degrees of freedom. We discuss how the presence of polarization affects the stability and causality of the ideal fluid limit.Comment: Version accepted for publication, Phys.Rev.

We rederive relativistic hydrodynamics as a Lagrangian effective theory using the doubled coordinates technique, allowing us to include dissipative terms. We include Navier-Stokes shear and bulk terms, as well as Israel-Stewart relaxation time terms, within this formalism. We show how the inclusion of shear dissipation forces the inclusion of the Israel-Stewart term into the theory, thereby providing an additional justification for the form of this term. PACS numbers: 25.75.-q,25.75.Dw,25.75.Nq arXiv:1604.05291v3 [hep-th] 1 Nov 2016