Monodromy Defects in Free Field Theories

TL;DR

This paper investigates co-dimension two monodromy defects in free conformal field theories, computing correlation functions and anomaly coefficients to understand their structure and effects on entanglement and renormalization group flows.

Contribution

It provides explicit calculations of defect correlation functions, anomaly coefficients, and entanglement entropy contributions in free scalar and fermion theories, including novel defect Weyl anomaly coefficients.

Findings

Defect central charges are related to Weyl anomalies in 4D.

Universal parts of entanglement and Rènyi entropies are computed.

Gukov-Witten defects in Maxwell theory have vanishing central charges.

Abstract

We study co-dimension two monodromy defects in theories of conformally coupled scalars and free Dirac fermions in arbitrary $d$ dimensions. We characterise this family of conformal defects by computing the one-point functions of the stress-tensor and conserved current for Abelian flavour symmetries as well as two-point functions of the displacement operator. In the case of $d=4$, the normalisation of these correlation functions are related to defect Weyl anomaly coefficients, and thus provide crucial information about the defect conformal field theory. We provide explicit checks on the values of the defect central charges by calculating the universal part of the defect contribution to entanglement entropy, and further, we use our results to extract the universal part of the vacuum R\'enyi entropy. Moreover, we leverage the non-supersymmetric free field results to compute a novel defect Weyl anomaly coefficient in a $d=4$ theory of free $\mathcal{N}=2$ hypermultiplets. Including singular modes in the defect operator product expansion of fundamental fields, we identify notable relevant deformations in the singular defect theories and show that they trigger a renormalisation group flow towards an IR fixed point with the most regular defect OPE. We also study Gukov-Witten defects in free $d=4$ Maxwell theory and show that their central charges vanish.