Perturbing the symmetric orbifold from the worldsheet

The symmetric orbifold of $\mathbb{T}^4$ is the analogue of free SYM in four dimensions, and its dual is described by a tensionless string propagating in ${\rm AdS}_3\times {\rm S}^3 \times \mathbb{T}^4$. In this paper we study the deformation of this exact AdS/CFT duality away from the free point. On the symmetric orbifold side this amounts to perturbing the theory by the exactly marginal operator from the $2$-cycle twisted sector. We identify the corresponding perturbation in the dual worldsheet description, and show that the anomalous conformal dimensions of a number of symmetric orbifold currents are correctly reproduced from this worldsheet perspective.Comment: 27 pages, 1 figur

The free field realisation of the BVW string

The symmetric orbifold of T-4 was recently shown to be exactly dual to string theory on AdS(3) x S-3 x T-4 with minimal (k = 1) NS-NS flux. The worldsheet theory is best formulated in terms of the hybrid formalism of Berkovits, Vafa & Witten (BVW), in terms of which the AdS(3) x S-3 factor is described by a psu(1, 1 vertical bar 2)(k) WZW model. At level k = 1, psu(1, 1 vertical bar 2)(1) has a free field realisation that is obtained from that of u(1, 1 vertical bar 2)(1) upon setting a u(1) field, often called Z, to zero. We show that the free field version of the N = 2 generators of BVW (whose cohomology defines the physical states) does not give rise to an N = 2 algebra, but is rather contaminated by terms proportional to the Z-field. We also show how to overcome this problem by introducing additional ghost fields that implement the quotienting by Z.ISSN:1126-6708ISSN:1029-847

Spectral flow and localisation in AdS3 string theory

Acknowledgements: We thank Andrea Dei, Yasuaki Hikida, Matthias Gaberdiel, Sylvain Lacriox, Nathan McStay, Kiarash Naderi, Beat Nairz, Ron Reid-Edwards, Volker Schomerus, and David Skinner for useful discussions. We also thank Andrea Dei, Lorenz Eberhardt, Matthias Gaberdiel, Ron Reid-Edwards and David Skinner for useful comments on an early version of the draft. We further thank Yasuaki Hikida and Volker Schomerus for sharing a preliminary version of their recent paper [32]. The work of VS is supported by a grant from the Swiss National Science Foundation. VS also acknowledges the support by the NCCR SwissMAP that is also supported by the Swiss National Science Foundation. The work of BK and SS is supported by STFC consolidated grants ST/T000694/1 and ST/X000664/1. The work of SS is also supported by the Trinity Internal Graduate studentship.Abstract We study string theory in three-dimensional Anti-de Sitter spacetime in the path integral formalism. We derive expressions for generic spectrally-flowed near-boundary vertex operators in the Wakimoto representation, and relate their correlation functions to covering maps from the worldsheet to the target space boundary. We show that the path integral structurally reproduces correlation functions of the dual symmetric orbifold theory. By rephrasing spectral flow as the introduction of a background gauge field, we provide a path integral derivation of the localisation property of the near boundary theory. We then focus on the case of IIB string theory on AdS3 × S3 × 4 with k = 1 units of NS-NS flux, where the relationship between correlation functions and covering maps can be made sharp. We also comment on the relation of the k = 1 theory and twistor theory.</jats:p