Heat Kernel, Spectral Functions and Anomalies in Weyl Semimetals

Abstract

Being motivated by applications to the physics of Weyl semimetals we study spectral geometry of Dirac operator with an abelian gauge field and an axial vector field. We impose chiral bag boundary conditions with variable chiral phase $\theta$ on the fermions. We establish main properties of the spectral functions which ensure applicability of the $\zeta$ function regularization and of the usual heat kernel formulae for chiral and parity anomalies. We develop computational methods, including a perturbation expansion for the heat kernel. We show that the terms in both anomalies which include electromagnetic potential are independent of $\theta$.

19 pages

References in corpus (4)

• The Chiral Magnetic Effect
• Topological response in Weyl semimetals and the chiral anomaly
• Weyl Anomaly induced Fermi Condensation and Holography
• Spectral asymmetry on the ball and asymptotics of the asymmetry kernel

Cited by in corpus (3)

• Worldline approach for spinor fields in manifolds with boundaries
• Anomaly inflow for local boundary conditions
• Edge states and the $\eta$ invariant