Free energy and defect C-theorem in free scalar theory

Tatsuma Nishioka,Yoshiki Sato

doi:10.1007/jhep05(2021)074

Abstract

We describe conformal defects of p dimensions in a free scalar theory on a d-dimensional flat space as boundary conditions on the conformally flat space ℍp+1× \U0001d54ad−p−1. We classify two types of boundary conditions, Dirichlet type and Neumann type, on the boundary of the subspace ℍp+1 which correspond to the types of conformal defects in the free scalar theory. We find Dirichlet boundary conditions always exist while Neumann boundary conditions are allowed only for defects of lower codimensions. Our results match with a recent classification of the non-monodromy defects, showing Neumann boundary conditions are associated with non-trivial defects. We check this observation by calculating the difference of the free energies on ℍp+1× \U0001d54ad−p−1 between Dirichlet and Neumann boundary conditions. We also examine the defect RG flows from Neumann to Dirichlet boundary conditions and provide more support for a conjectured C-theorem in defect CFTs.

Highlights

A conventional view of quantum field theories (QFTs) relies on particle picture of quantum fields as a fundamental description of the theories, but the importance of non-local objects has been increasingly recognized in recent studies to discriminate theories from those having the same local descriptions but different global structures [1, 2]
We describe conformal defects of p dimensions in a free scalar theory on a ddimensional flat space as boundary conditions on the conformally flat space Hp+1 × Sd−p−1
We find Dirichlet boundary conditions always exist while Neumann boundary conditions are allowed only for defects of lower codimensions

Summary

Introduction

A conventional view of quantum field theories (QFTs) relies on particle picture of quantum fields as a fundamental description of the theories, but the importance of non-local objects has been increasingly recognized in recent studies to discriminate theories from those having the same local descriptions but different global structures [1, 2]. Extended observables such as Wilson-’t Hooft loops rarely have concrete realizations in terms of fundamental fields in Lagrangian and are typically defined as boundary conditions, called defects in general.

Objectives

Discussion

Conclusion