Twisted holography without conformal symmetry

TL;DR

This paper explores the holographic duality between 2d chiral algebras and topological string theory, analyzing vacuum states, correlation functions, and their geometric duals in a non-conformal setting.

Contribution

It introduces a framework for understanding translation-invariant vacua in 2d chiral algebras and connects them to Calabi-Yau geometries via holography, extending the duality beyond conformal symmetry.

Findings

Correlation functions are affected by vacuum expectation values.

Large N analysis matches boundary correlators with bulk D-brane configurations.

Proposes a new holographic dual involving non-conformal Calabi-Yau geometries.

Abstract

We discuss the notion of translation-invariant vacua for 2d chiral algebras and relate it to the notion of the associated variety. The two-dimensional chiral algebra associated to four-dimensional ${\cal N}=4$ $U(N)$ SYM has a conjectural holographic dual involving the B-model topological string theory. We study the effect of non-zero vacuum expectation values on the chiral algebra correlation functions and derive a holographic dual Calabi-Yau geometry. We test our proposal by a large $N$ analysis of correlation functions of determinant operators, whose saddles can be matched with semi-classical configurations of "Giant Graviton" D-branes in the bulk