Monodromy Defects in Free Field Theories

2021-04-06

Authors: Lorenzo Bianchi, Adam Chalabi, Vladimír Procházka, Brandon Robinson, and
Jacopo Sisti

Preprint number: UUITP 16/21

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. Moreover, we leverage the non-supersymmetric free field results to compute a
novel defect Weyl anomaly coefficient in a d = 4 theory of free N = 2 hypermultiplets.
In carefully studying the defect operator product expansion, we identify notable relevant
operators in the defect theories and use them to study the behaviour of the defect under
renormalisation group flow.