String theory in twistor space and minimal tension holography

TL;DR

This paper explores the construction of sigma models on twistor space for minimal tension strings in AdS3, revealing new incidence relations, vertex operators, and supersymmetry properties that deepen understanding of bulk-boundary correspondence.

Contribution

It introduces a novel twistor space sigma model for minimal tension strings, deriving incidence relations and analyzing supersymmetry, advancing the understanding of AdS3/CFT2 holography.

Findings

Derived new incidence relations linking twistor space and bulk

Identified vertex operators in twistor variables

Found partial supersymmetry breaking and an  formulation

Abstract

Explicit examples of the AdS/CFT correspondence where both bulk and boundary theories are tractable are hard to come by, but the minimal tension string on $AdS_3 \times S^3 \times T^4$ is one notable example. In this paper, we discuss how one can construct sigma models on twistor space, with a particular focus on applying these techniques to the aforementioned string theory. We derive novel incidence relations, which allow us to understand to what extent the minimal tension string encodes information about the bulk. We identify vertex operators in terms of bulk twistor variables and a map from twistor space to spacetime is presented. We also demonstrate the presence of a partially broken global supersymmetry algebra in the minimal tension string and we argue that this implies that there exists an $\mathcal{N} = 2$ formulation of the theory. The implications of this are studied and we demonstrate the presence of an additional constraint on physical states.