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arXiv · 1810.06995

Towards a $C$-theorem in defect CFT

Nozomu Kobayashi·Tatsuma Nishioka·Yoshiki Sato·Kento Watanabe
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Abstract

We explore a $C$-theorem in defect conformal field theories (DCFTs) that unify all the known conjectures and theorems until now. We examine as a candidate $C$-function the additional contributions from conformal defects to the sphere free energy and the entanglement entropy across a sphere in a number of examples including holographic models. We find the two quantities are equivalent, when suitably regularized, for codimension-one defects (or boundaries), but differ by a universal constant term otherwise. Moreover, we find in a few field theoretic examples that the sphere free energy decreases but the entanglement entropy increases along a certain renormalization group (RG) flow triggered by a defect localized perturbation which is assumed to have a trivial IR fixed point without defects. We hence propose a $C$-theorem in DCFTs stating that the increment of the regularized sphere free energy due to the defect does not increase under any defect RG flow. We also provide a proof of our proposal in several holographic models of defect RG flows.

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Nozomu Kobayashi, Tatsuma Nishioka, Yoshiki Sato, Kento Watanabe. 2018-10-16. Towards a $C$-theorem in defect CFT. https://doi.org/10.1007/jhep01(2019)039

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