AdS3 Holography from the Worldsheet

Abstract

The AdS/CFT correspondence has played a prominent role in developing our understanding of the holographic nature of quantum gravity, postulating that string theory on Anti-de Sitter (AdS) space is equivalent to a conformal field theory (CFT) on the boundary of AdS. Tractable examples in which both sides of the duality can be studied simultaneously are rare, but $AdS_3$ spacetimes have provided a fruitful setting for progress. In this thesis, the tensionless limit of pure NS-NS superstring theory on $AdS_3 \times S^3 \times T^4$ is studied using worldsheet methods. This is dual to a grand canonical ensemble of the symmetric product orbifold Sym$^N(T^4)$ and provides one of the few proven examples of the AdS/CFT correspondence. The primary aim of this thesis is to elucidate on the physics encoded in this tensionless string theory and we do this in several ways. For example, we discuss the utility of the Wakimoto representation of $\mathfrak{sl}(2,\R)_1$ in describing this string theory and argue for the exactness of the near-boundary approximation in which this description is valid. We study correlation functions of the string theory, including a discussion of its pole structure and a demonstration of a global translational symmetry in the radial direction. Another key result is that we show how tensionless string theory on $AdS_3 \times S^3 \times T^4$ can be naturally understood as a sigma model on the minitwistor space of $AdS_3$. The incidence relations are studied, showing how they encode both bulk and boundary physics simultaneously. The sigma model we present has several important differences with conventional twistor string constructions, most notably in its constraint algebra. We motivate the existence of an extended worldsheet symmetry algebra, beyond the usual Virasoro constraints, which leads to a precise agreement with the hybrid formalism of Berkovits, Vafa and Witten at level $k=1$. Along the way, we discuss several other interesting aspects of $AdS_3/CFT_2$, including a proposal for how open-closed-open triality can be realised in symmetric product orbifolds. We also provide a review of important background material on the formulation of superstring theory on both flat space and AdS using the RNS, GS and hybrid formalisms. This review contains a novel perspective on the GSO projection, explaining in a simplified model how the spin structure of spacetime is encoded in the RNS formalism.