Hidden symmetries from extra dimensions

TL;DR

This paper explores how certain symmetries, broken during dimensional reduction in theories like supergravity and string theory, can be realized as global symmetries in lower dimensions, constraining couplings and interactions.

Contribution

It demonstrates that broken higher-dimensional symmetries can be realized as global symmetries in lower dimensions, constraining couplings in supergravity and string theory.

Findings

Symmetries broken during reduction can be realized as global symmetries.

The principle constrains couplings in supergravity and string theory.

Application to quartic Ramond-Ramond couplings in Type IIA.

Abstract

In Kaluza-Klein compactifications, some symmetries of the higher dimensional theory are preserved in lower dimensions, others are broken, and occasionally, there are symmetry enhancements. The symmetries that are enhanced by toroidal compactifications were recently shown to define a symmetry principle with constrained parameters that fixes the action before dimensional reduction. Here we show the opposite: symmetries of the higher dimensional theory that are broken in the reduction process, can actually be realized after dimensional reduction as a global symmetry principle with constrained parameters that fixes couplings in the lower dimensional theory. We implement this principle in pure gravity, half-maximal supergravity and the circle reduction of 11 dimensional supergravity to Type IIA superstring theory. As a further application, we show that it can be used to constrain the quartic Ramond-Ramond couplings in Type IIA superstring theory from the four-point $\zeta(3)\, \alpha'{}^3\, t_8 t_8 R^{(-) 4}$ interactions.