Branes in $L^{(p,q,r)}$

TL;DR

This paper constructs supergravity solutions involving D3 and D5 branes in warped geometries based on Sasaki-Einstein spaces, revealing cascading features and suggesting dual theories with irrational central charges.

Contribution

It provides explicit back-reacted solutions for branes in $L^{(p,q,r)}$ spaces, extending the understanding of fluxes and dual gauge theories in these geometries.

Findings

Presence of non-contractible 2-cycle indicated by fluxes

Warp factor exhibits cascading behavior

Dual theories likely have irrational central charges

Abstract

We have found the solution to the back reaction of putting a stack of coincident D3 and D5 branes in $R^{3,1}\times M_6$, where $M_6$ is constructed from an infinite class of Sasaki-Einstein spaces, $L^{(p,q,r)}$. The non-zero fluxes associated to 2-form potential suggests the presence of a non-contractible 2-cycle in this geometry. The radial part of the warp factor has the usual form and possess the cascading feature. We argue that generically the duals of these SE spaces will have irrational central charges.