# Holography, Matrix Factorizations and K-stability

## TL;DR

This paper integrates differential geometry and algebraic techniques to construct new AdS5/CFT4 duals from conical Calabi-Yau singularities, especially non-toric ones, advancing the understanding of holography.

## Contribution

It combines K-stability and matrix factorizations to generate novel dual pairs for non-toric Calabi-Yau singularities.

## Key findings

- Established a method linking K-stability with matrix factorizations.
- Constructed explicit examples of duals for non-toric singularities.
- Enhanced the toolkit for identifying holographic duals in string theory.

## Abstract

Placing D3-branes at conical Calabi-Yau threefold singularities produces many AdS$_5$/CFT$_4$ duals. Recent progress in differential geometry has produced a technique (called K-stability) to recognize which singularities admit conical Calabi-Yau metrics. On the other hand, the algebraic technique of non-commutative crepant resolutions, involving matrix factorizations, has been developed to associate a quiver to a singularity. In this paper, we put together these ideas to produce new AdS$_5$/CFT$_4$ duals, with special emphasis on non-toric singularities.