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

**Authors:** Sergio E. Aguilar-Gutierrez, Klaas Parmentier, Thomas Van Riet  
**arXiv:** [2207.13692](https://arxiv.org/abs/2207.13692)  
**Date:** 2022-07-27  
**Summary page:** https://www.summarizepaper.com/en/paper/2207.13692v3/

## Key points

- Study focuses on connections between type IIB Euclidean supergravity solutions and $AdS_d\times S^d\times \mathbb{T}^{10-2d}$ vacua with (imaginary) self-dual $F_d$ flux
- Vacua originate from near-horizon of D$(d-2)$/D$(8-d)$ branes, exhibit supersymmetry for odd values of $d"
- Solution $\mathbb{R}\times S^1\times \mathbb{T}^8$ with imaginary self-dual $F_1$ flux belongs to the chain of vacua
- Speculation on implications for conformal symmetry in matrix model dual when $d=1; vanishing free energy could indicate conformal symmetry
- Matrix dual reveals connections to supergravity solution, highlights need to switch on specific $F_5$ fluxes due to T-dual Hanany-Witten effect
- Aim to explore alignment between proposed matrix model and vacuum solution, particularly focusing on scenarios without external sources
- Investigation will require consideration of normalizations and couplings to establish robust connection between frameworks

## Summary

In this work, we delve into the intricate connections between type IIB Euclidean supergravity solutions and the chain of $AdS_d\times S^d\times \mathbb{T}^{10-2d}$ vacua with (imaginary) self-dual $F_d$ flux. These vacua originate from the near-horizon of D$(d-2)$/D$(8-d)$ branes and exhibit supersymmetry for odd values of $d$. Specifically, we focus on a solution of the form $\mathbb{R}\times S^1\times \mathbb{T}^8$ with imaginary self-dual $F_1$ flux through $\mathbb{R}\times S^1$, which we argue belongs to this chain of vacua. Of particular interest is the case when $d=1$, where we speculate on the implications for conformal symmetry in the matrix model dual. We propose that a vanishing free energy could serve as a hallmark of conformal symmetry in this scenario. The matrix dual reveals intriguing connections to our supergravity solution and uncovers the necessity of switching on specific $F_5$ fluxes as a consequence of a T-dual version of the Hanany-Witten effect. This further enriches our understanding of the interplay between different flux configurations and their implications for theoretical physics. Looking ahead, we aim to explore in more depth how our proposed matrix model aligns with the vacuum solution, particularly focusing on scenarios where external sources are absent. This investigation will require careful consideration of normalizations and couplings to establish a robust connection between the two frameworks. By addressing these aspects in future research endeavors, we aim to shed further light on the intricate correspondence between AdS/CFT dualities and their implications for theoretical physics.