Chiral Reductions in the Salam-Sezgin Model

TL;DR

This paper investigates two distinct methods of reducing the six-dimensional Salam-Sezgin supergravity model to four dimensions, analyzing their impact on chirality and gauge symmetry preservation.

Contribution

It demonstrates the existence of two consistent reduction schemes, one preserving gauge symmetry but resulting in non-chiral theories, and the other maintaining chirality with broken gauge symmetry.

Findings

One scheme retains SU(2) gauge symmetry but yields non-chiral theories.

The other scheme preserves chirality but breaks SU(2) gauge symmetry.

Extensions can produce genuinely chiral models with unbroken gauge symmetries.

Abstract

Reductions from six to four spacetime dimensions are considered for a class of supergravity models based on the six-dimensional Salam-Sezgin model, which is a chiral theory with a gauged U(1) R-symmetry and a positive scalar-field potential. Reduction on a sphere and monopole background of such models naturally yields four-dimensional theories without a cosmological constant. The question of chirality preservation in such a reduction has been a topic of debate. In this article, it is shown that the possibilities of dimensional reduction bifurcate into two separate consistent dimensional-reduction schemes. One of these retains the massless SU(2) vector gauge triplet arising from the sphere's isometries, but it produces a non-chiral four-dimensional theory. The other consistent scheme sets to zero the SU(2) gauge fields, but retains the gauged U(1) from six dimensions and preserves chirality although the U(1) is spontaneously broken. Extensions of the Salam-Sezgin model to include larger gauge symmetries produce genuinely chiral models with unbroken gauge symmetries.