Global Anomalies and Effective Field Theory

TL;DR

The paper investigates how global anomalies associated with large gauge transformations and large diffeomorphisms constrain the coefficients of couplings in thermal effective field theories. It develops a global anomaly matching framework showing that local EFT actions must reproduce the anomalous phases, often through unusual Chern-Simons-type terms involving the graviphoton $a$. Through explicit dimensional-reduction examples in 2D, 3D, and 4D, it demonstrates that the chiral vortical effect (CVE) coefficient is fixed by global anomaly data and can be computed from correlation functions instead of $\eta$-invariants. The results generalize to higher dimensions, providing compact expressions like $S_{\text{eff}} = \int a \wedge \widehat{A}(X_{d-2}) \wedge \mathrm{ch}(V)$ and concrete 6D instances.

Abstract

We show that matching anomalies under large gauge transformations and large diffeomorphisms can explain the appearance and non-renormalization of couplings in effective field theory. We focus on thermal effective field theory where we argue that the appearance of certain unusual Chern-Simons couplings is a consequence of global anomalies. As an example, we show that a mixed global anomaly in four dimensions fixes the chiral vortical effect coefficient. This is an experimentally measurable prediction from a global anomaly. For certain situations, we propose a simpler method for calculating global anomalies which uses correlation functions rather than eta invariants.

Figures (1)

• Figure 1: The 1-point stress correlator which gives the global diffeomorphism anomaly.