Spectral flow and the exact AdS3/CFT2 chiral ring

We present a detailed study of spectrally flowed four-point functions in the SL(2,ℝ) WZW model, focusing on their conformal block decomposition. Dei and Eberhardt conjectured a general formula relating these observables to their unflowed counterparts. Although the latter are not known in closed form, their conformal block expansion has been formally established. By combining this information with the integral transform that encodes the effect of spectral flow, we show how to describe a considerable number of s-channel exchanges, including cases with both flowed and unflowed intermediate states. For all such processes, we compute the normalization of the corresponding conformal blocks in terms of products of the recently derived flowed three-point functions with arbitrary spectral flow charges. Our results constitute a highly non-trivial consistency check, thus strongly supporting the aforementioned conjecture, and establishing its computational power.

Spectral flow and the conformal block expansion for strings in AdS3

Iguri,

Kovensky,

Toro

2024

Superstrings near the conformal boundary of AdS3

Sriprachyakul

2024

We study worldsheet sphere amplitudes, in the RNS formalism, in superstring theory on AdS3 × X with pure NS-NS flux using the near-boundary approximation. By computing a number of amplitudes at low-lying spectral flow, we deduce a candidate for a dual CFT for generic X. Specialising to X = S3 × 𝕋4 and with minimal NS-NS flux, i.e., to the tensionless limit, we explore the effect of the interaction term which we ignore in the near-boundary consideration. We show, under some assumptions, that amplitudes in the tensionless superstring theory on AdS3 × S3 × 𝕋4 do not receive perturbative contributions from such an interaction term.

Solving AdS3 string theory at minimal tension: tree-level correlators

Dei,

Knighton,

Naderi

2024

We revisit the minimal tension (k = 1) string theory on AdS3 × S3 × 𝕋4. We propose a new free-field description of the worldsheet theory and show how localization of string amplitudes emerges from the path integral. We exemplify our proposal by reproducing the worldsheet partition function of the $$ \mathfrak{psu} $$ psu (1, 1|2)1 WZW model and providing explicit expressions for spectrally-flowed vertex operators and DDF operators. We compute string correlators in the path integral formalism and obtain a precise tree-level match with correlation functions of the boundary symmetric orbifold.