Conformal line defects at finite temperature

TL;DR

This paper investigates conformal field theories with a thermal line defect, deriving new sum rules and bootstrap constraints for thermal one-point functions, and applies the framework to various models including the O(N) model.

Contribution

It introduces a formalism to analyze thermal conformal defects, deriving sum rules and bootstrap equations for thermal one-point functions from the KMS condition.

Findings

Derived sum rules for thermal defect one-point functions.

Established a bootstrap problem constrained by KMS conditions.

Validated the approach with free scalar theory and predictions for the O(N) model.

Abstract

We study conformal field theories at finite temperature in the presence of a temporal conformal line defect, wrapping the thermal circle, akin to a Polyakov loop in gauge theories. Although several symmetries of the conformal group are broken, the model can still be highly constrained from its features at zero-temperature. In this work we show that the defect and bulk one and two-point correlators can be written as functions of zero-temperature data and thermal one-point functions (defect and bulk). The defect one-point functions are new data and they are induced by thermal effects of the bulk. For this new set of data we derive novel sum rules and establish a bootstrap problem for the thermal defect one-point functions from the KMS condition. We also comment on the behaviour of operators with large scaling dimensions. Additionally, we relate the free energy and entropy density to the OPE data through the one-point function of the stress-energy tensor. Our formalism is validated through analytical computations in generalized free scalar field theory, and we present new predictions for the O(N) model with a magnetic impurity in the $\varepsilon$-expansion and the large N limit.