The plane-wave spectrum from the worldsheet

TL;DR

This work derives the plane-wave spectrum for string theory on AdS$_3$ backgrounds with mixed NS-NS and R-R flux directly from the worldsheet, using the Berkovits–Vafa–Witten hybrid formalism. By solving the two-parameter PSU$(1,1|2)$ sigma-model in a BMN-like large-charge limit, the authors identify a contracted, tractable spectrum-generating algebra and compute exact conformal weights for BMN-type excitations, reproducing the expected plane-wave masses. They develop an explicit affine primaries framework, incorporate spectral flow, and obtain a complete plane-wave spectrum for both $AdS_3\times S^3\times \mathcal{M}_4$ ($\mathcal{M}_4=\mathbb{T}^4$ or K3) and $AdS_3\times S^3\times S^3\times S^1$, including the $\mathfrak{d}(2,1;\alpha)$ case, with matching BMN formulas. This work provides a direct link between worldsheet current algebras and spacetime spectra in backgrounds with mixed flux, offering a principled route to the plane-wave limit and informing integrability and higher-spin considerations in holography.

Abstract

We study string theory on $\mathrm{AdS}_3$ backgrounds with mixed flux using the hybrid formalism of Berkovits, Vafa and Witten. We solve the worldsheet description of the theory completely in the plane-wave limit. This constitutes a direct derivation of the plane-wave spectrum from the worldsheet with mixed flux.