Abstract
We study the long wavelength excitations in rotating QCD fluid in presence of an external magnetic field at finite vector and axial charge densities. We consider the fluctuations of vector and axial charge currents coupled to energy and momentum fluctuations and compute the $SO(3)$ covariant dispersion relations of the six corresponding hydrodynamic modes. Among them, there are always two scalar Chiral Magnetic-Vortical-Heat (CMVH) waves; In the absence of magnetic field (vorticity) these waves reduce to CVH (CMH) waves. While CMVH waves are the mixed of CMH and CVH waves, they have generally different velocities compared to the sum of velocities of the latter waves. The other four modes, which are made out of scalar-vector fluctuations, are mixed Sound-Alfv\'en waves. We show that in the direction parallel to both magnetic field and vorticity, these four modes are the two ordinary sound modes together with two Chiral Alfv\'en waves (CAW).
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