Anomalous chiral transport with vorticity and torsion: Cancellation of two mixed gravitational anomaly currents in rotating chiral <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi><mml:mo>+</mml:mo><mml:mi>i</mml:mi><mml:mi>p</mml:mi></mml:math> Weyl condensates

Relativistic gravitational anomalies lead to anomalous transport coefficients that can be activated at finite temperature in condensed matter systems with gapless fermions. The chiral vortical effect (CVE) is an current along a rotation axis, expressed terms of gravimagnetic field and anomaly. Another one, the torsional (CTE), arises from hydrodynamically independent frame fields connection. We discuss relation CVE, CTE for relativistic fermions perspective torsion Nieh-Yan DC two are found closely related depending whether or not non-zero hydrodynamics. anomaly well defined if instead ultraviolet divergent term, chemical potential enter. term 2nd order gradients contributes linear response CTE, implying also same CVE. As example, we consider $p+ip$ Weyl superfluids/conductors. At low-energies, system effectively special anisotropy axis. hydrodynamics governed by velocities, normal velocity $\boldsymbol{v}_n$ superfluid $\boldsymbol{v}_s$. follow component dependence momentum density on (order parameter). In CVE produced solid body (angular) $\boldsymbol{v}_n= \boldsymbol\Omega \times \boldsymbol{r}$. vorticity $\nabla \boldsymbol{v}_s$, which low-energy effective theory torsion. equilibrium, $\langle\langle \nabla \boldsymbol{v_s}\rangle\rangle= 2\boldsymbol\Omega$ average currents cancel.