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arXiv · 2508.14978

On Entropy Bounds for Irrelevant Operators

Lucas Fernández-Sarmiento·Riccardo Penco·Rachel A Rosen
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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 symmetry-preserving irrelevant deformations of a conformal field theory (CFT) 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 is not expected to apply, such as deformations that break internal symmetries of the CFT.

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Lucas Fernández-Sarmiento, Riccardo Penco, Rachel A Rosen. 2025-08-20. On Entropy Bounds for Irrelevant Operators. https://arxiv.org/abs/2508.14978

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