Gauging Unbroken Symmetries in F-theory

TL;DR

This paper explores the unbroken symmetries in F-theory, highlighting the role of higher-dimensional brane current algebra and the necessity of worldvolume covariant derivatives to maintain symmetry.

Contribution

It introduces a method to incorporate unbroken symmetries in F-theory by using worldvolume covariant derivatives dependent on H coordinates.

Findings

F-theory's vacuum has certain unbroken symmetries 'H'.

Worldvolume indices are also spacetime indices, complicating symmetry currents.

Worldvolume covariant derivatives depend on H coordinates, resolving symmetry issues.

Abstract

F-theory attempts to include all U-dualities manifestly. Unlike its T-dual manifest partner, which is based on string current algebra, F-theory is based on higher dimensional brane current algebra. Like the T-dual manifest theory, which has $O(D-1,1)^2$ unbroken symmetry, the F-theory vacuum also enjoys certain symmetries ("$H$"). One of its important and exotic properties is that worldvolume indices are also spacetime indices. This makes the global brane current algebra incompatible with $H$ symmetry currents. The solution is to introduce worldvolume covariant derivatives, which depend on the $H$ coordinates even in a "flat" background. We will also give as an explicit example the 5-brane case.