The 6D SuperSwirl

TL;DR

This paper introduces a new supersymmetric 6D solution involving hypermultiplets and gauge fields, differing from traditional cosmic strings, with implications for understanding the cosmological constant problem.

Contribution

It presents a novel supersymmetric solution in 6D supergravity with active hyperscalars, gravity, and gauge fluxes, expanding the known solution space beyond conventional cosmic strings.

Findings

Solution features two timelike singularities in the internal manifold.

The 4D spacetime remains flat under this configuration.

The solution deforms the 'rugby ball' model, relevant to the cosmological constant problem.

Abstract

We present a novel supersymmetric solution to a nonlinear sigma model coupled to supergravity. The solution represents a static, supersymmetric, codimension-two object, which is different to the familiar cosmic strings. In particular, we consider 6D chiral gauged supergravity, whose spectrum contains a number of hypermultiplets. The scalar components of the hypermultiplet are charged under a gauge field, and supersymmetry implies that they experience a simple paraboloid-like (or 2D infinite well) potential, which is minimised when they vanish. Unlike conventional vortices, the energy density of our configuration is not localized to a string-like core. The solutions have two timelike singularities in the internal manifold, which provide the necessary boundary conditions to ensure that the scalars do not lie at the minimum of their potential. The 4D spacetime is flat, and the solution is a continuous deformation of the so-called ``rugby ball'' solution, which has been studied in the context of the cosmological constant problem. It represents an unexpected class of supersymmetric solutions to the 6D theory, which have gravity, gauge fluxes and hyperscalars all active in the background.