Generalised symmetries, anomalous magnetohydrodynamics and holography

Abstract

In this thesis we study the finite temperature physics of a system which is afflicted by the Adler-Bell-Jackiw anomaly or, the chiral anomaly. The universality class of such systems are commonly referred to as the . Its weakly coupled physics is described by a theory of massless Dirac fermions coupled to dynamical electromagnetism and hence the universal symmetry structure of the is that of dynamical Abelian gauge theory with charged matter. In this theory, the non-conservation of the axial current due to the chiral anomaly is given by a dynamical operator constructed from the field-strength tensor. We attempt to describe this physics in a universal manner by casting this operator in terms of the 2-form current for the 1-form symmetry associated with magnetic flux conservation. The precise symmetry structure in encoded by the anomaly equation which can be formulated as the intertwining of these two currents. The sense in which this is universal is that it is preserved along RG flows. Utilising this universal structure we first perform a holographic investigation of this system and then construct a hydrodynamic effective action for it. This effective action can be understood as ``an action" for , which is devoted to understanding the long-distance, late-time behavior of such a system suffering from an ABJ anomaly.

To perform the holographic study, we first construct a dual bulk theory with the aformentioned symmetry breaking pattern and study some aspects of finite temperature anomalous magnetohydrodynamics. We explicitly calculate the charge susceptibility and the axial charge relaxation rate as a function of temperature and magnetic field and compare to recent lattice results. At small magnetic fields we find agreement with elementary hydrodynamics weakly coupled to an electrodynamic sector, but we find deviations at larger fields.

Next we consider chiral magnetohydrodynamics. Using the universal symmetry structure encoded in the anomaly we write down ``effective actions" capturing the equilibrium physics and the physics of dissipation. We present Euclidean generating functional and dissipative action approaches to the dynamics and reproduce some aspects of known chiral MHD phenomenology from an effective theory viewpoint, including the chiral separation and magnetic effects. We also discuss the construction of the axial symmetry defect operators in our formalism in real time.

Finally, to study the axial charge relaxation rate in the limit of vanishing magnetic field, we undertake a study to see if hydrodynamic fluctuations affect this rate. We compute the finite-frequency real-time topological susceptibility arising from magnetohydrodynamic fluctuations. We find that it vanishes at zero frequency, indicating that the axial charge dissipation rate vanishes at zero background magnetic field. This is probably suggestive of the fact that the symmetry structure encoded in the anomaly is protected by the non-invertible defect operators as 1-loop effects do not spoil it.