Modular invariance and thermal effective field theory in CFT

TL;DR

This paper uses thermal effective field theory to relate the subleading thermal free energy coefficient to Casimir energy in CFTs, proposing a positivity bound and exploring various applications including background geometries and chemical potentials.

Contribution

It establishes a connection between thermal free energy coefficients and Casimir energy in CFTs and introduces a conjectured positivity bound supported by evidence.

Findings

The coefficient c_1 equals the subleading Casimir energy term.

Proposed a sign constraint c_1 ≥ 0 for CFTs.

Derived high-temperature partition functions with angular velocities.

Abstract

We use thermal effective field theory to derive that the coefficient of the first subleading piece of the thermal free energy, $c_1$, is equal to the coefficient of the subleading piece of the Casimir energy on $S^1 \times S^{d-2}$ for $d \geq 4$. We conjecture that this coefficient obeys a sign constraint $c_1 \geq 0$ in CFT and collect some evidence for this bound. We discuss various applications of the thermal effective field theory, including placing the CFT on different spatial backgrounds and turning on chemical potentials for $U(1)$ charge and angular momentum. Along the way, we derive the high-temperature partition function on a sphere with arbitrary angular velocities using only time dilation and length contraction.