$1/4$ BPS solutions and the ${\mathrm{AdS}}_3/{\mathrm{CFT}}_2$ correspondence

We discuss new solutions in massive type IIA supergravity with ${\mathrm{AdS}}_3\times {\mathrm{S}}^2$ factors, preserving $\mathcal{N}=(0,4)$ supersymmetry. We propose a duality with a precise family of quivers that flow to $\mathcal{N}=(0,4)$ fixed points at low energies. These quivers consist on two families of linear quivers coupled by matter fields. Physical observables such as the central charges provide stringent checks of the proposed duality. A formal mapping is presented connecting our backgrounds with those dual to six dimensional $\mathcal{N}=(1,0)$ conformal field theories (CFTs), suggesting the existence of a flow across dimensions between the CFTs.

Figure 1

The generic Hanany-Witten setup associated with our backgrounds. The vertical lines are NS-five branes. The horizontal lines represent D2 and wrapped D6 branes. The crosses indicate D4 and wrapped D8 branes.

Figure 2

The building block of our theories.

Figure 3

A generic quiver field theory whose IR is dual to the holographic background defined by Eqs. (1)–(3).

Figure 4

Hanany-Witten setup associated with our generic quiver in Fig. 3.

Figure 5

Quiver consisting of two rows of linearly increasing color groups, terminated with the addition of flavour groups.