Fluxes and Warping for Gauge Couplings in F-theory

TL;DR

This paper calculates flux-induced corrections to gauge couplings in F-theory using M-theory duality, revealing new warp factor effects and flux contributions that extend beyond weak coupling approximations.

Contribution

It provides explicit flux-dependent corrections to gauge couplings in F-theory via M-theory, including warp factor effects and quadratic flux terms, advancing beyond weak coupling results.

Findings

Real part of gauge coupling modified by warp factor

Imaginary part corrected by three-form potential

Additional flux terms suppressed at weak coupling

Abstract

We compute flux-dependent corrections in the four-dimensional F-theory effective action using the M-theory dual description. In M-theory the 7-brane fluxes are encoded by four-form flux and modify the background geometry and Kaluza-Klein reduction ansatz. In particular, the flux sources a warp factor which also depends on the torus directions of the compactification fourfold. This dependence is crucial in the derivation of the four-dimensional action, although the torus fiber is auxiliary in F-theory. In M-theory the 7-branes are described by an infinite array of Taub-NUT spaces. We use the explicit metric on this geometry to derive the locally corrected warp factor and M-theory three-from as closed expressions. We focus on contributions to the 7-brane gauge coupling function from this M-theory back-reaction and show that terms quadratic in the internal seven-brane flux are induced. The real part of the gauge coupling function is modified by the M-theory warp factor while the imaginary part is corrected due to a modified M-theory three-form potential. The obtained contributions match the known weak string coupling result, but also yield additional terms suppressed at weak coupling. This shows that the completion of the M-theory reduction opens the way to compute various corrections in a genuine F-theory setting away from the weak string coupling limit.