Shift-symmetries and gauge coupling functions in orientifolds and F-theory

TL;DR

This paper explores how gauge coupling functions in Type IIB orientifold and F-theory compactifications depend on fields, revealing new geometric structures and the importance of quantum corrections involving Riemann theta functions.

Contribution

It introduces a detailed analysis of gauge coupling functions' dependence on moduli, incorporating quantum corrections and extending the discussion to F-theory compactifications with a new dimensional reduction approach.

Findings

Quantum corrections involve Riemann theta functions.

Unification of bulk and brane degrees of freedom in F-theory.

New insights into holomorphicity and shift-symmetries of gauge couplings.

Abstract

We investigate the field dependence of the gauge coupling functions of four-dimensional Type IIB orientifold and F-theory compactifications with space-time filling seven-branes. In particular, we analyze the constraints imposed by holomorphicity and covariance under shift-symmetries of the bulk and brane axions. This requires introducing quantum corrections that necessarily contain Riemann theta functions on the complex torus spanned by the D7-brane Wilson line moduli. Our findings hint towards a new underlying geometric structure for gauge coupling functions in string compactifications. We generalize this discussion to a genuine F-theory compactification on an elliptically fibered Calabi-Yau fourfold. We perform the first general dimensional reduction of eleven-dimensional supergravity and dualization to the F-theory frame. The resulting effective action is compared with the circle reduction of a four-dimensional N=1 supergravity theory. The F-theory geometry elegantly unifies bulk and brane degrees of freedom and allows us to infer non-trivial results about holomorphicity and shift-symmetries. For instance, we gain new insight into kinetic mixing of bulk and brane gauge fields.