T-Reflection

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.

4 pages. v2: References and several clarifications added, some discussion reorganized. No changes to any conclusions

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Cited by in corpus (10)

• Bose-Fermi cancellations without supersymmetry
• Casimir energy of confining large $N$ gauge theories
• A 4D-2D equivalence for large-N Yang-Mills theory
• Lens elliptic gamma function solution of the Yang-Baxter equation at roots of unity
• From Hagedorn to Lee-Yang: Partition functions of $\mathcal{N}=4$ SYM theory at finite $N$
• Spectral sum rules for confining large-N theories
• L-functions for Meromorphic Modular Forms and Sum Rules in Conformal Field Theory
• Hagedorn transition and topological entanglement entropy
• Temperature-reflection II: Modular Invariance and T-reflection
• Supersymmetric zeta functions and determinants