Theta-problem and the String Swampland

TL;DR

This paper explores the constraints on the theta-angle in certain supergravity theories, proposing that quantum gravity may fix the theta-angle to specific values, with implications for QCD and QED.

Contribution

It conjectures that in $ =2$ supergravity coupled only to hypermultiplets, the theta-angle is fixed to 0 or pi, linking string theory conjectures to the swampland.

Findings

The coupling constant $ au$ is constrained to real values.

The theta-angle is conjectured to be 0 or pi in consistent theories.

Implications suggest theta-angle may be fixed in quantum gravity theories.

Abstract

In the context of $\mathcal{N}=2$ supergravity without vector multiplets coupled to hypermultiplets, the coupling constant of graviphoton $\tau$ is apriori a free parameter. Stringy realization of this and using a mathematical conjecture leads to the statement that $j(\tau)\in \mathbb{R}$ so that the $\theta$-angle is $0$ or $\pi$. We conjecture that for any consistent realization of $\mathcal{N}=2$ supergravity theories coupled only to hypermultiplets this is the case and the rest belong to the swampland. This leads to the speculation that the $\theta$-angle for QCD or QED may also be fixed to $0$ for quantum gravitational consistency.