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Three-dimensional N=4 Linear Quivers and non-Abelian T-duals

Yolanda Lozano, Niall T. Macpherson, Jesus Montero, Carlos Nunez

TL;DR

This work constructs a new Type IIB $AdS_4$ background with ${\cal N}=4$ supersymmetry by performing an $SU(2)$ non-Abelian T-duality on the Type IIA reduction of $AdS_4\times S^7$, and interprets it as a patch of a larger brane system dual to the IR fixed point of a $T_{\rho}^{\hat{\rho}}(SU(N))$ 3d CFT. It embeds the NATD solution into the Abelian–Beisert–Etxebarria–Gaiotto (ABEG) class of $AdS_4$ geometries, showing how harmonic functions on a Riemann surface encode the D5/NS5/D3 brane data and linking numbers that define the corresponding quiver theory. A careful completion of the geometry with flavour branes yields a consistent $T_{\rho}^{\hat{\rho}}(SU(N))$ dual, and the computed free energy scales as $N^2\log N$, consistent with an upper bound for this class of CFTs. The results illustrate how non-Abelian T-duality can be connected to Dp–D(p+2)–NS5 brane intersections and how holographic data constrain global properties and CFT interpretations of NATD backgrounds.

Abstract

In this paper we construct a new Type IIB background with an $AdS_4$ factor that preserves ${\cal N}=4$ Supersymmetry. This solution is obtained using a non-Abelian T-duality transformation on the Type IIA reduction of the $AdS_4\times S^7$ background. We interpret our configuration as a patch of a more general background with localised sources, dual to the renormalisation fixed point of a $T_ρ^{\hatρ} (SU(N))$ quiver field theory. This relates explicitly the $AdS_4$ geometry to a D3-D5-NS5 brane intersection, illuminating what seems to be a more general phenomenon, relating $AdS_{p+1}$ backgrounds generated by non-Abelian T-duality to Dp-D(p+2)-NS5 branes intersections.

Three-dimensional N=4 Linear Quivers and non-Abelian T-duals

TL;DR

This work constructs a new Type IIB background with supersymmetry by performing an non-Abelian T-duality on the Type IIA reduction of , and interprets it as a patch of a larger brane system dual to the IR fixed point of a 3d CFT. It embeds the NATD solution into the Abelian–Beisert–Etxebarria–Gaiotto (ABEG) class of geometries, showing how harmonic functions on a Riemann surface encode the D5/NS5/D3 brane data and linking numbers that define the corresponding quiver theory. A careful completion of the geometry with flavour branes yields a consistent dual, and the computed free energy scales as , consistent with an upper bound for this class of CFTs. The results illustrate how non-Abelian T-duality can be connected to Dp–D(p+2)–NS5 brane intersections and how holographic data constrain global properties and CFT interpretations of NATD backgrounds.

Abstract

In this paper we construct a new Type IIB background with an factor that preserves Supersymmetry. This solution is obtained using a non-Abelian T-duality transformation on the Type IIA reduction of the background. We interpret our configuration as a patch of a more general background with localised sources, dual to the renormalisation fixed point of a quiver field theory. This relates explicitly the geometry to a D3-D5-NS5 brane intersection, illuminating what seems to be a more general phenomenon, relating backgrounds generated by non-Abelian T-duality to Dp-D(p+2)-NS5 branes intersections.

Paper Structure

This paper contains 16 sections, 114 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. The Type IIB $\mathcal{N}=4$ $AdS_4$ solution
  3. Reduction of $\mathbb{Z}_k$ orbifold to IIA
  4. The non-Abelian T-dual solution
  5. Aspects of 3d ${\cal N}=4$ CFTs and their holographic duals
  6. 3d ${\cal N}=4$ CFTs
  7. The ABEG dual geometries
  8. The Type IIB $\mathcal{N}=4$ $AdS_4$ solution and CFT
  9. The Type IIB $\mathcal{N}=4$ $AdS_4$ solution as a ABEG geometry
  10. Free energy
  11. Summary and conclusions
  12. The Abelian T-dual limit
  13. The solution
  14. Connection with ABEG geometries
  15. Free energy
  16. ...and 1 more sections

Figures (8)

  • Figure 1: $b_0$ as a function of $r$
  • Figure 2: (NS5, D3, D5) brane set-up. The number of D3-branes is given in $N_{D5}$ units and that of D5-branes in $k_0$ units.
  • Figure 3: 5-branes distribution along the strip, parameterised by $z=x + iy$.
  • Figure 4: Completed (NS5, D3, D5) brane set-up.
  • Figure 5: Quiver associated to the (NS5, D3, D5) brane set-up in Figure \ref{['stacks2']}.
  • ...and 3 more figures