T-Reflection

TL;DR

The paper identifies a temperature-reflection symmetry in the partition functions of various physical systems, including conformal and non-conformal field theories, and explores its properties and conditions for breaking.

Contribution

It demonstrates the presence of T-reflection symmetry across multiple models and discusses its invariance and potential breaking mechanisms without relying on the symmetry's fundamental origin.

Findings

T-reflection symmetry exists in many models' partition functions.

All minimal model partition functions in 2D CFTs are invariant under T-reflections.

Shifts in vacuum energy can break T-reflection symmetry.

Abstract

We point out the presence of a $T \to -T$ temperature-reflection ($T$-reflection) symmetry for the partition functions of many physical systems. Without knowledge of the origin of the symmetry, we have only been able to test the existence of $T$-reflection symmetry in systems with exactly-calculable partition functions. We show that $T$-reflection symmetry is present in a variety of conformal and non-conformal field theories and statistical mechanics models with known partition functions. For example, all minimal model partition functions in two-dimensional conformal field theories are invariant under $T$-reflections. An interesting property of the $T$-reflection symmetry is that it can be broken by shifts of the vacuum energy.