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Compactifications of the Klebanov-Witten CFT and new $AdS_3$ backgrounds

Yago Bea, Jose D. Edelstein, Georgios Itsios, Karta S. Kooner, Carlos Nunez, Daniel Schofield, J. Anibal Sierra-Garcia

TL;DR

This work constructs new smooth $AdS_3$ backgrounds in Type IIB, IIA, and M-theory by applying non-Abelian T-duality to the Klebanov-Witten CFT compactified to two dimensions, and analyzes the dual 2d CFT observables. The authors compute central charges, entanglement entropy, and Wilson loops across flows from $AdS_5$ to $AdS_3$, revealing a brane-quiver interpretation with cubic scaling $c \sim n^3$ in certain NATD constructions. They show that NATD chains map the original D3-brane data to D6/D2/D4 sectors and induce an effective quiver growth via the $\rho$ coordinate, interpreted as un-Higgsing along a linear quiver. Uplifts to M-theory and back-T-dualizations yield additional smooth backgrounds, expanding the landscape of holographic duals to 2d CFTs arising from higher-dimensional theories. The results provide a concrete framework to study strong coupling dynamics of 2d CFTs sourced from 4d quiver theories and Sicilian-type constructions, with clear observables supporting the proposed dual field theories.

Abstract

In this paper we find various new backgrounds in Type IIB, IIA and M-theory with an $AdS_3$-factor. The solutions are smooth and preserve small amounts of SUSY. These new backgrounds are found by application of non-Abelian T-duality (sometimes combined with T-duality) on the supergravity solution dual to the Klebanov-Witten CFT compactified to two dimensions. The field theory aspects encoded by these backgrounds are studied. We give a detailed account of conserved charges, central charges, entanglement entropy and Wilson loops. Further, we present a possible field theory interpretation for our backgrounds.

Compactifications of the Klebanov-Witten CFT and new $AdS_3$ backgrounds

TL;DR

This work constructs new smooth backgrounds in Type IIB, IIA, and M-theory by applying non-Abelian T-duality to the Klebanov-Witten CFT compactified to two dimensions, and analyzes the dual 2d CFT observables. The authors compute central charges, entanglement entropy, and Wilson loops across flows from to , revealing a brane-quiver interpretation with cubic scaling in certain NATD constructions. They show that NATD chains map the original D3-brane data to D6/D2/D4 sectors and induce an effective quiver growth via the coordinate, interpreted as un-Higgsing along a linear quiver. Uplifts to M-theory and back-T-dualizations yield additional smooth backgrounds, expanding the landscape of holographic duals to 2d CFTs arising from higher-dimensional theories. The results provide a concrete framework to study strong coupling dynamics of 2d CFTs sourced from 4d quiver theories and Sicilian-type constructions, with clear observables supporting the proposed dual field theories.

Abstract

In this paper we find various new backgrounds in Type IIB, IIA and M-theory with an -factor. The solutions are smooth and preserve small amounts of SUSY. These new backgrounds are found by application of non-Abelian T-duality (sometimes combined with T-duality) on the supergravity solution dual to the Klebanov-Witten CFT compactified to two dimensions. The field theory aspects encoded by these backgrounds are studied. We give a detailed account of conserved charges, central charges, entanglement entropy and Wilson loops. Further, we present a possible field theory interpretation for our backgrounds.

Paper Structure

This paper contains 28 sections, 208 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction and General Idea
  2. Geometry
  3. Simple flows from $AdS_5 \times T^{1,1}$ to $AdS_3\times M_7$ in Type IIB
  4. Solution of the form $AdS_3\times H_2$, $AdS_3\times S^2$ and $AdS_3\times T^2$ with 'twisting'
  5. The Donos-Gauntlett-(Kim) background
  6. New backgrounds in Type IIA: use of non-Abelian T-duality
  7. The non-Abelian T-dual of the twisted solutions
  8. The non-Abelian T-dual of the Donos-Gauntlett solution
  9. T-dualizing back from Type IIA to IIB
  10. Lift to M - theory
  11. Uplift of the NATD of the twisted solutions
  12. Uplift of the NATD of the Donos-Gauntlett solution
  13. Field Theory Observables
  14. General comments on the Quantum Field Theory
  15. Quantized charges
  16. ...and 13 more sections

Figures (4)

  • Figure 1: On the left: known solutions on which NATD is performed. On the right: QFT's that correspond to the NATD SUGRA solutions.
  • Figure 2: $S'$ as a function of $d$ for twisted $H_2$ (left) and Donos-Gauntlett solution (right). The continuous curves correspond to the numerical value, while the dashed red ones to the UV and IR limits.
  • Figure 3: The quark-antiquark potential $\frac{E}{\alpha' L^{2}}$ as a function of the distance $d$ in the cases of the twisted $H_2$ (left) and Donos-Gauntlett (right) solutions. The continuous curves correspond to the numerical results and the dashed ones to the UV and IR limits.
  • Figure 4: From top to bottom: the numerical and analytical approximation values of the functions $A',U,B',V$. The solid lines correspond to the numerical solutions and the dashed lines to the analytical approximations. Notice that the plots for the functions $U$ and $V$ are rescaled by a factor of $15$.