$\tau_{RR}$ minimization in presence of hypermultiplets

TL;DR

This paper calculates the $ au_{RR}$ function in gauged supergravity with hypermultiplets, demonstrating the necessity of constraints for massive vectors and confirming the supergravity results align with dual field theory predictions.

Contribution

It explicitly shows how to incorporate constraints for massive vector fields in $ au_{RR}$ minimization within supergravity, extending previous work to include new truncations and gaugings.

Findings

Massive vector fields require constraints via Lagrange multipliers.

Supergravity $ au_{RR}$ minimization matches dual field theory results.

Explicit examples include $U(1)^2$ and ISO(7) truncations.

Abstract

We compute $\tau_{RR}$ minimization in gauged supergravity for M-theory and String Theory truncations with both massless and massive vector multiplets. We explicitly compute, as anticipated in \cite{Amariti:2015ybz}, that massive vector fields at the vacuum require the introduction of a constraint through a Lagrange multiplier. We illustrate this explicitly in two examples, namely the $U(1)^2$-invariant truncation dual to the mABJM model and the ISO(7) truncation in massive IIA, the latter being a theory with both electric and magnetic gauging. We revisit the vacuum constraints at $AdS_4$ and show how the supergravity analysis matches the results of the field theory dual computation.