# BMN Vacua, Superstars and Non-Abelian T-duality

## TL;DR

This paper constructs a new half-BPS supergravity solution via non-Abelian T-duality, interprets it as a dual to a specific vacuum of the BMN matrix model, and relates it to M-theory giant gravitons and the superstar solution.

## Contribution

It introduces a novel supergravity background obtained through non-Abelian T-duality and provides a detailed interpretation in terms of BMN matrix model vacua and M-theory objects.

## Key findings

- The new solution has $SU(2|4)$ symmetry and belongs to the Lin-Lunin-Maldacena class.
- It matches the Penrose limit of the superstar solution in $AdS_7\times S^4$.
- The geometry suggests a global completion involving M5-branes.

## Abstract

Acting with non-Abelian T-duality on the $S^3$ inside the $AdS_5$ subspace of $AdS_5\times S^5$ with $N$ units of flux, we generate a new half-BPS solution with $SU(2|4)$ symmetry that belongs to the Lin-Lunin-Maldacena class of geometries. The analysis of the asymptotics, quantised charges and probe branes in this geometry suggests an interpretation as the gravity dual to the Berenstein-Maldacena-Nastase Plane Wave Matrix Model, in a particular vacuum associated to a partition of $N$, in which the multiplicity of each $SU(2)$ irreducible representation is equal to its dimension. This vacuum is interpreted in M-theory in terms of giant gravitons backreacting in the maximally supersymmetric pp-wave geometry. Consistently with this, we show that the non-Abelian T-dual solution exactly agrees with the Penrose limit of the superstar solution in $AdS_7\times S^4$. This suggests an interesting global completion of the non-Abelian T-dual solution in terms of an M5-brane geometry.