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$AdS_6$ T-duals and Type IIB $AdS_6\times S^2$ Geometries with 7-Branes

Yolanda Lozano, Niall T. Macpherson, Jesús Montero

TL;DR

This work shows that the first Type IIB $AdS_6$ backgrounds obtained by Abelian and non-Abelian T-duality of the Brandhuber-Oz solution fit within an extended global DGKU/DGU framework of $AdS_6\times S^2\times\Sigma$ warped by a two-dimensional Riemann surface. The Abelian case maps to an annulus topology with smeared NS5 and D7/O7 branes, while the non-Abelian case corresponds to an infinite strip (upper half-plane) with smeared branes, enabling a consistent holographic interpretation via the DGKU/DGU data. Central charges and entanglement entropies are computed from the DGKU data, showing $N^{5/2}$ scaling for the Abelian case and an intervalwise $n^3$ growth for the non-Abelian case, consistent with a USp$(2N)$-like CFT structure and an infinite linear quiver that requires a completion. The paper also details the monodromy realization of 7-branes, the matching of fluxes, and the worldsheet mapping under non-Abelian T-duality, providing a framework to interpret these T-duals as holographic duals of 5d fixed-point theories with extended brane configurations.

Abstract

We show that the first $AdS_6$ backgrounds in Type IIB supergravity known in the literature, namely those constructed via T-duality from the Brandhuber-Oz solution to massive IIA, fit within an extension of the global $AdS_6 \times S^2$ solutions with 7-branes warped over a Riemann surface $Σ$, recently classified by D'Hoker, Gutperle and Uhlemann, that describes delocalised 5-branes and 7-branes. The solution constructed through Abelian T-duality provides an explicit example of a Riemann surface with the topology of an annulus, that includes D7/O7-branes. In turn, the solution generated through non-Abelian T-duality arises from the upper half-plane.

$AdS_6$ T-duals and Type IIB $AdS_6\times S^2$ Geometries with 7-Branes

TL;DR

This work shows that the first Type IIB backgrounds obtained by Abelian and non-Abelian T-duality of the Brandhuber-Oz solution fit within an extended global DGKU/DGU framework of warped by a two-dimensional Riemann surface. The Abelian case maps to an annulus topology with smeared NS5 and D7/O7 branes, while the non-Abelian case corresponds to an infinite strip (upper half-plane) with smeared branes, enabling a consistent holographic interpretation via the DGKU/DGU data. Central charges and entanglement entropies are computed from the DGKU data, showing scaling for the Abelian case and an intervalwise growth for the non-Abelian case, consistent with a USp-like CFT structure and an infinite linear quiver that requires a completion. The paper also details the monodromy realization of 7-branes, the matching of fluxes, and the worldsheet mapping under non-Abelian T-duality, providing a framework to interpret these T-duals as holographic duals of 5d fixed-point theories with extended brane configurations.

Abstract

We show that the first backgrounds in Type IIB supergravity known in the literature, namely those constructed via T-duality from the Brandhuber-Oz solution to massive IIA, fit within an extension of the global solutions with 7-branes warped over a Riemann surface , recently classified by D'Hoker, Gutperle and Uhlemann, that describes delocalised 5-branes and 7-branes. The solution constructed through Abelian T-duality provides an explicit example of a Riemann surface with the topology of an annulus, that includes D7/O7-branes. In turn, the solution generated through non-Abelian T-duality arises from the upper half-plane.

Paper Structure

This paper contains 26 sections, 183 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. The DGKU/DGU $AdS_6\times S^2 \times \Sigma$ solutions to Type IIB
  3. Realising $(p,q)$ 7-branes
  4. Global solutions for the upper half-plane
  5. Addition of seven branes
  6. The annulus
  7. Realising 7-branes in the annulus
  8. The $AdS_6$ T-duals of Brandhuber-Oz
  9. The Brandhuber-Oz $AdS_6$ solution
  10. The $AdS_6$ Abelian T-dual (ATD) solution
  11. The $AdS_6$ non-Abelian T-dual (NATD) solution
  12. The Abelian T-dual as a DGU solution for the annulus
  13. The non-Abelian T-dual as a DGU solution for the upper half-plane
  14. Holographic central charge and entanglement entropy
  15. Holographic central charge
  16. ...and 11 more sections

Figures (3)

  • Figure 1: The annulus for the Abelian T-dual background. NS5-branes are smeared along the lower boundary at $\theta=0$, and D7/O7 branes are smeared at the upper boundary at $\theta=\pi/2$. The annulus topology follows from the periodicity under $\psi\rightarrow \psi+\pi$, or $w\rightarrow w+1$, shifts.
  • Figure 2: The infinite strip for the non-Abelian T-dual background. NS5-branes are smeared along the lower boundary at $\theta=0$ and D7/O7 branes are smeared along the upper boundary at $\theta=\pi/2$. The strip topology follows from the unboundness of the $r$ direction, $r\in \mathbb{R}^+$.
  • Figure 3: 5-brane web consistent with the quantised charges of the non-Abelian T-dual solution. The dashed line represents the branch-cut created by the D7/O7 branes at each $r\in [p\pi,(p+1)\pi]$ interval. At each interval a new, smeared, D7/O7 brane system adds to the discontinuity in the 5-brane charge created by the branch cut.