Trace Anomaly Matching and Exact Results For Entanglement Entropy

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.

Latex, 25 Pages, When the theory reaches a non-trivial fixed point in the IR there is some problem due to IR divergence which need to be taken into account carefully. This will be the part of a forthcoming publication. The results of the previous version remain unchanged when the flow is towards a trivial IR fixed point