Angular fractals in thermal QFT

TL;DR

This paper explores the fractal-like structure of thermal partition functions in quantum field theories, revealing new insights into their angular dependence and the role of defects, with applications to free and holographic models.

Contribution

It introduces a long-distance expansion controlled by thermal effective field theory for QFTs with spatial isometries, uncovering fractal structures and defect contributions in the partition function.

Findings

Partition function on a sphere shows fractal-like angular dependence.

High-temperature free energy differs for even and odd spin operators by a factor of 1/2^d.

Classification of Kaluza-Klein vortex defects affecting the partition function.

Abstract

We show that thermal effective field theory controls the long-distance expansion of the partition function of a $d$-dimensional QFT, with an insertion of any finite-order spatial isometry. Consequently, the thermal partition function on a sphere displays a fractal-like structure as a function of angular twist, reminiscent of the behavior of a modular form near the real line. As an example application, we find that for CFTs, the effective free energy of even-spin minus odd-spin operators at high temperature is smaller than the usual free energy by a factor of $1/2^d$. Near certain rational angles, the partition function receives subleading contributions from "Kaluza-Klein vortex defects" in the thermal EFT, which we classify. We illustrate our results with examples in free and holographic theories, and also discuss nonperturbative corrections from worldline instantons.