$T^{1,1}$ truncation on the spindle

TL;DR

This paper investigates the compactification of a specific supergravity truncation on a spindle, deriving BPS equations, solving them at the poles, and matching the results with dual field theory predictions, revealing new insights into the geometry and duality.

Contribution

It provides the first detailed analysis of the $ ext{T}^{1,1}$ truncation on the spindle, including BPS solutions and central charge calculations, with a comparison to dual field theory results.

Findings

Derived BPS equations for the truncation on the spindle

Solved BPS equations at the poles and computed central charges

Found exact agreement with dual field theory predictions

Abstract

We study the compactification of the $\mathcal{N}=2$ AdS$_5$ consistent truncation of the conifold, in presence of a Betti vector multiplet, on the spindle. We derive the BPS equations and solve them at the poles, computing the central charge for both the twist and the anti-twist class, turning on the magnetic charge associated to the baryonic symmetry. Then, in the anti-twist class, where there are choices of the quantized flux that give origin to a positive central charge, we numerically solve the BPS equations interpolating between the poles of the spindle. We conclude by comparing our results with the one obtained from the analysis of the dual field theory, finding an exact agreement.