Conformal anomalies for higher derivative free critical p-forms on even spheres

Abstract

The conformal anomaly is computed on even d-spheres for a p-form propagating according to the Branson-Gover higher derivative, conformally covariant operators. The system is set up on a q-deformed sphere and the conformal anomaly is computed as a rational function of the derivative order, 2k, and of q. The anomaly is shown to be an extremum at the round sphere (q = 1) only for k < d/2. At these integer values, therefore, the entanglement entropy is minus the conformal anomaly, as usual. The unconstrained p-form conformal anomaly on the full sphere is shown to be given by an integral over the Plancherel measure for a coexact form on hyperbolic space in one dimension higher. A natural ghost sum is constructed and leads to quantities which, for critical forms, i.e. when 2k = d − 2p, are, remarkably, a simple combination of standard quantities, for usual second order, k = 1, propagation, when these are available. Our values coincide with a recent hyperbolic computation of David and Mukherjee. Values are suggested for the Casimir energy on the Einstein cylinder from the behaviour of the conformal anomaly as q → 0 and compared with known results written as alternating sums over scalar values.

Entanglement entropy and the boundary action of edge modes

“…We show that the bulk entanglement entropy of p-forms evaluated in [25] together with the edge mode contribution evaluated in this paper coincides with the a-anomaly coefficients [21,26]. It was first observed for free Maxwell field in d = 4 dimension [27] and we find the same pattern for the critical p-forms in even dimension.…”