Towards an "AdS$_1/$CFT$_0$" correspondence from the D$(-1)/$D$7$ system?

TL;DR

This paper explores a supergravity solution related to a proposed AdS$_1$/CFT$_0$ correspondence, connecting D(-1)/D7 branes to a matrix model dual with vanishing free energy, indicating potential conformal symmetry.

Contribution

It proposes a supergravity background corresponding to an AdS$_1$/CFT$_0$ duality from D(-1)/D7 branes and demonstrates the vanishing on-shell action consistent with the matrix model dual.

Findings

Supergravity solution has vanishing on-shell action.

The background involves specific fluxes, including F5, due to T-duality effects.

Supports the conjecture of a conformal matrix model dual with zero free energy.

Abstract

We argue that a type IIB Euclidean supergravity solution of the form $\mathbb{R}\times S^1\times \mathbb{T}^8$ with imaginary self-dual $F_1$ flux through $\mathbb{R}\times S^1$ belongs to the chain of $AdS_d\times S^d\times \mathbb{T}^{10-2d}$ vacua with (imaginary) self-dual $F_d$ flux, where $d\leq 5$. Such vacua come from the near-horizon of D$(d-2)$/D$(8-d)$ branes and are supersymmetric for odd values of $d$. For $d=1$ we speculate that the hallmark of conformal symmetry for the matrix model dual is a vanishing free energy. The matrix dual was recently constructed by arXiv:2101.01732 by adding matrix interactions coming from strings stretching between the D$(-1)$ and D$7$ branes to the IKKT matrix model. We find that the corresponding supergravity solution indeed has vanishing on-shell action. Specific $F_5$ fluxes need to be switched on as a consequence of (a T-dual version of) the Hanany-Witten effect.