Trace Anomaly Matching and Exact Results For Entanglement Entropy

TL;DR

This paper uses trace anomaly matching and dilaton effective actions to derive exact, non-perturbative entanglement entropy results for even-dimensional non-conformal field theories flowing to trivial IR fixed points, matching known weak and strong coupling results.

Contribution

It provides the first exact non-perturbative calculations of entanglement entropy coefficients in these theories, extending previous results to arbitrary even dimensions.

Findings

Exact coefficients for logarithmic divergence in entanglement entropy obtained.

Results agree with both weak coupling and holographic strong coupling calculations.

Universal terms characterized for theories interpolating between scale-invariant UV and trivial IR fixed points.

Abstract

Following the ideas developed by Komargodski and Schwimmer in arXiv:1107.3987 and arXiv:1112.4538, we argue that the IR dilaton effective action on the cone computes the entanglement entropy of an even dimensional non-conformal field theory interpolating between a UV and an IR fixed point. We restrict our attention to theories which flow to trivial IR fixed point. We get exact non-perturbative results for the coefficients of the logarithmically divergent term of the entanglement entropy in these field theories in arbitrary even dimensions. The results match precisely with the weak coupling results available in the literature and also with the strong coupling results obtained via holography. We also write the universal terms for field theories which interpolate between a scale invariant but not conformally invariant UV fixed point and a trivial IR fixed point.