NS5-branes on an ellipsis and novel marginal deformations with parafermions

TL;DR

This paper constructs gravitational backgrounds for NS5-branes distributed along an ellipsis, introducing novel marginal deformations with parafermions, and explores their relation to known models and dualities.

Contribution

It introduces a new non-factorizable marginal perturbation involving parafermions for ellipsoidal NS5-brane distributions, extending previous circle and bar cases.

Findings

Deformation from circle to ellipsoid described by parafermionic bilinears.

Connection between ellipsis distribution and Eguchi-Hanson metric via T-duality.

Potential to define parafermions at generic ellipsoidal points.

Abstract

We consider NS5-branes distributed along the circumference of an ellipsis and explicitly construct the corresponding gravitational background. This provides a continuous line of deformations between the limiting cases, considered before, in which the ellipsis degenerates into a circle or into a bar. We show that a slight deformation of the background corresponding to a circle distribution into an ellipsoidal one is described by a novel non-factorizable marginal perturbation of bilinears of dressed parafermions. The latter are naturally defined for the circle case since, as it was shown in the past, the background corresponds to an orbifold of the exact conformal field theory coset model SU(2)/U(1) times SL(2,R)/U(1). We explore the possibility to define parafermionic objects at generic points of the ellipsoidal families of backgrounds away from the circle point. We also discuss a new limiting case in which the ellipsis degenerates into two infinitely stretched parallel bars and show that the background is related to the Eguchi-Hanson metric, via T-duality.