BMN Vacua, Superstars and Non-Abelian T-duality
Yolanda Lozano, Carlos Nunez, Salomon Zacarias
TL;DR
This work constructs a new half-BPS Type IIA background by applying non-Abelian T-duality to the $S^3$ inside the $AdS_5$ of $AdS_5\times S^5$, obtaining a solution with $SU(2|4)$ symmetry that lies in the Lin-Lunin-Maldacena (LLM) classification. The authors interpret this geometry as the gravity dual of a BMN Plane Wave Matrix Model vacuum corresponding to a partition of $N$ with multiplicities equal to the dimensions of $SU(2)$ representations, linking it to giant gravitons in a maximally supersymmetric pp-wave. They show that the non-Abelian T-dual solution reproduces the Penrose limit of the $AdS_7\times S^4$ superstar, and discuss global completions in terms of M5-brane geometry and a smeared D0/D2/NS5 polarization picture. A complementary perspective recasts the NATD background as a patch of Lin-Maldacena geometries, amenable to a field-theory completion via a $(0+1)$-dimensional matrix model deformed from the BMN action, offering a concrete bridge between non-Abelian T-duality, BMN vacua, and higher-dimensional CFT constructions. The work thus strengthens the connection between NATD-generated backgrounds and global completions involving M-theory giant gravitons and six-dimensional (0,2) theories, with potential for testing holographic duals in strongly coupled regimes.
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.