String theory in twistor space and minimal tension holography

TL;DR

This work develops a twistor-space sigma-model formulation of the minimal-tension string on $AdS_3\times S^3\times T^4$, showing that the worldsheet dynamics can be described by a minitwistor-space action whose incidence relations mix left- and right-moving sectors. The authors demonstrate that bulk information is encoded in boundary data through a novel bulk incidence relation and a map from twistor space to spacetime, with boundary-localised vertex operators and a boundary Penrose-like transform enabling bulk-boundary propagation. They uncover a partially broken global supersymmetry (PBGS) algebra that naturally motivates a worldsheet ${\cal N}=2$ formulation and derive a crucial ${\cal Q}$ constraint, clarifying the BRST structure and connecting to Berkovits' hybrid formalism at $k=1$. The paper provides a detailed Euclidean ($H^+_3$) analysis, realises Wakimoto currents, explains boundary reconstruction, and discusses how bulk physics can in principle be recovered from boundary data, while also addressing the unflowed sector and outlining paths to higher-dimensional generalizations such as $AdS_5/CFT_4$.

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.