On Entropy Bounds for Irrelevant Operators

TL;DR

This paper explores the relationship between entropy bounds and irrelevant operators in low-energy theories, proposing that certain deformations increase entropy and testing this across various models.

Contribution

It introduces an entropy-positivity conjecture for irrelevant operators and evaluates its validity against multiple physical theories and bounds.

Findings

Broad agreement with the entropy-positivity conjecture across models

Entropy increase correlates with a decrease in the thermal grand potential

Identifies cases where the conjecture cannot be applied

Abstract

Consistency constraints for low-energy theories, especially those lacking Lorentz invariance, have recently garnered attention. Building on results from black hole thermodynamics, we investigate the conjecture that leading irrelevant deformations of a conformal field theory in the infrared must increase the system's entropy. We show that this entropy-positivity conjecture is equivalent to a decrease in the thermal grand potential at a fixed temperature. We then evaluate this proposal against various known positivity bounds and other physical constraints on effective theories: for $U(1)$ Goldstone bosons with a quartic self-interaction at (non-)zero chemical potential, for the Euler-Heisenberg model, for the $O(N)$ nonlinear sigma model in $(2+1)D$, and for $T\bar{T}$ deformations of the 2D Ising CFT. We find broad agreement with the entropy-positivity conjecture, and we discuss test cases where the conjecture cannot be applied.