On entropy bounds for irrelevant operators

A bstract 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 $$ T\overline{T} $$ T 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.