Abstract
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.