Theory HEP Seminar

Path integrals, finite temperature, and lattices

David McGady

Bohr Institute

Path integrals, finite temperature, and lattices *Abstract:* Surprisingly, partition functions for some model systems in statistical mechanics are invariant under formally reflecting the sign of temperature, T: +T -> -T. We call this T-reflection invariance. Clearly, partition functions for generic statistical systems cannot be invariant under T-reflection. However, in this talk we focus on finite-temperature path integrals and give a general picture for why finite-temperature path integrals in quantum field theory *should* behave well under T-reflection. We probe this general picture in the context of the harmonic oscillators (in one-dimension) and in conformal field theories on the two-torus (in two-dimensions) and in the mathematics of modular forms. We find that the relevant path integrals are often invariant only up to overall T-independent phases, which could be naturally interpreted as new anomalies under large coordinate transforms.

This talk is based off of work related to the following four recent papers:
arXiv:1711.07536 [hep-th]
arXiv:1806.09873 [hep-th]
arXiv:1806.09874 [hep-th]
arXiv:1806.09875 [hep-th]