Global symmetry-breaking and generalized theta-terms in Type IIB EFTs

TL;DR

This paper investigates how generalized theta-terms in Type IIB $ $ effective field theories break global symmetries, revealing a lattice structure of charged states generated by monodromy transformations, supporting the conjecture against global symmetries in quantum gravity.

Contribution

It demonstrates that generalized theta-terms induce a lattice of charged states via a generalized Witten effect, providing new insights into symmetry breaking in Type IIB EFTs.

Findings

Generalized theta-terms break large subsets of global symmetries.

The spectrum of charged states forms an infinite lattice.

Monodromy transformations generate the charged state lattice.

Abstract

A longstanding conjecture states that global symmetries should be absent in quantum gravity. By investigating large classes of Type IIB four-dimensional $\mathcal{N}=2$ effective field theories, we enlist the potential generalized global symmetries that could be present and explore how they are avoided. Crucial ingredients that arise in such effective field theories are generalized $\theta$-terms. These introduce non-linear couplings between axion fields and topological terms quadratic in the gauge field strengths which break a large subset of the global symmetries. Additional residual global symmetries may further be broken by assuming the existence of some charged states. However, we illustrate that the presence of generalized $\theta$-terms leads to a generalized Witten effect, which implies that the spectrum of charged states is constituted by an infinitely populated lattice. We further show that such a lattice is generated by the action of the monodromy transformation that characterizes the moduli space boundary near which the effective theory is defined.