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Over the past years, considerable effort has been made to study the novel phenomena displayed by chiral systems arising from the interplay between quantum anomalies and the electromagnetic and vortical fields in a hydrodynamic framework [1]. Such novel theory is often referred to as chiral hydrodynamics. It is possible to derive the equations of motion of chiral hydrodynamics from a kinetic theory formulation, the so-called chiral kinetic theory [2]. While this approach has provided great insight into the physics of chiral matter, very little is known about the properties of the chiral hydrodynamic equations of motion and their solutions, especially in the nonlinear regime. Such knowledge is crucial when studying the consequences of the chiral anomaly in hydrodynamic simulations of the quark-gluon plasma formed in heavy-ion collisions. In this work [3] we prove that ideal chiral hydrodynamics, as derived from chiral kinetic theory, is acausal and its initial-value problem is ill-posed. Therefore, such theory cannot be used to determine how the chiral anomaly affects the hydrodynamic evolution. We show that these fundamental issues can be cured by using different definitions (frames) for the hydrodynamic fields. Finally, a new causal and stable first-order theory of viscous chiral hydrodynamics is presented.
[1] D. E. Kharzeev, J. Liao, S. A. Voloshin and G. Wang, Prog. Part. Nucl. Phys. 88, 1-28 (2016)
[2] J-Y Chen, D. T. Son and M. A. Stephanov, Phys. Rev. Lett. 115, 021601 (2015)
[3] E. Speranza, F. S. Bemfica, M. M. Disconzi and J. Noronha, 2104.02110 (2021)
