The Effective Field Theory for Hydrodynamics and its Analytic Properties

Hydrodynamics provides an effective description for many-body systems near thermal equilibrium. The success of the paradigm rests on the idea that the dynamics of such near-equilibrium systems can be captured by a very small number of parameters, such as the temperature and fluid velocity, and their derivatives. For instance, relativistic hydrodynamics, which is applicable to systems which respect the Lorentz symmetry, has been immensely successful in understanding the properties of the Quark-Gluon plasma that is produced in heavy-ion collisions at RHIC and CERN. In this talk, I will start by reviewing the construction of hydrodynamics in terms of a derivative expansion, followed by a discussion of the equilibrium generating functional and its properties. Interestingly, though the standard formulation of hydrodynamics captures the dissipative aspects of the system quite well, it does not take into account the effects of the underlying thermal fluctuations efficiently. One can remedy the situation to some extent by using the stochastic approach, where one can introduce random Gaussian fluctuations and derive an effective action. However, this approach has its limitations, as the structure of the interaction terms in the effective action is quite restricted. Recently, an effective field theory (EFT) approach based on the Schwinger-Keldysh (SK) formalism has been proposed, which systematically captures the effects of the underlying fluctuations, making use of symmetries. In the second part of the talk, I will discuss the construction of the stochastic as well as the SK effective actions for a theory of charge diffusion. I will then discuss a simplifying limit of the SK diffusive EFT, where the sound modes effectively decouple from the dynamics. I will discuss one-loop corrections to the retarded and symmetric correlators in this model, with special emphasis on the role played by the KMS symmetry in ensuring the correct analytic structure for the theory as required by the limit of thermal equilibrium, providing a strong consistency check on the EFT framework.