BMN Vacua, Superstars and Non-Abelian T-duality

Abstract

Acting with non-Abelian T-duality on the $S^3$ inside the $Ad{S}_5$ subspace of $Ad{S}_5\times S^5$ 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 $Ad{S}_7\times S^4$. This suggests an interesting global completion of the non-Abelian T-dual solution in terms of an M5-brane geometry.

28 pages, discussion in section 5.1 improved, results unchanged, reference added. Matches published version

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Cited by in corpus (24)

• AdS${}_3$ solutions in Massive IIA with small $\mathcal{N}=(4,0)$ supersymmetry
• Holographic Aspects of Four Dimensional $\mathcal{N}=2$ SCFTs and their Marginal Deformations
• Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings
• AdS${}_3$ solutions in massive IIA, defect CFTs and T-duality
• 1/4 BPS AdS${}_3$/CFT${}_2$
• Integrability and non-Integrability in N=2 SCFTs and their Holographic Backgrounds
• The non-Integrability of Strings in Massive Type IIA and their Holographic duals
• The $Ad{S}_5$ non-Abelian T-dual of Klebanov-Witten as a $\mathcal{N}=1$ linear quiver from M5-branes
• $Ad{S}_6$ T-duals and Type IIB $Ad{S}_6\times S^2$ Geometries with 7-Branes
• ${\text{AdS}}_2\times {\text{S}}^2\times {\text{CY}}_2$ solutions in Type IIB with 8 supersymmetries
• Double and cyclic $\lambda$-deformations and their canonical equivalents
• Penrose limits of Abelian and non-Abelian T-duals of $Ad{S}_5\times S^5$ and their field theory duals
• On non-Abelian T-duality for non-semisimple groups
• Confinement/deconfinement transition in the D0-brane matrix model -- A signature of M-theory?
• Electrostatic description of 3d $\mathcal{N}=4$ linear quivers
• AdS${}_2$ geometries and non-Abelian T-duality in non-compact spaces
• Non-abelian T-folds
• Line defects as brane boxes in Gaiotto-Maldacena geometries
• AdS solutions and $\lambda$-deformations
• A Type IIB Matrix Model via non-Abelian T-dualities
• Plane-parallel waves as duals of the flat background III: T-duality with torsionless $B$-field
• Integrability and non-integrability for holographic dual of Matrix model and non-Abelian T-dual of AdS${}_5\times$S${}^5$
• Matrix models and non-Abelian T dual of $Ad{S}_5\times S^5$
• Nonrelativistic strings and the limits of $\mathcal{N}=2$ dualities