Strings on Semisymmetric Superspaces
K. Zarembo
TL;DR
This paper classifies all semi-symmetric superspace cosets with a $\mathbb{Z}_4$ symmetry that have a vanishing one-loop beta-function and central charge $c\le 26$, contextualizing them as potential string backgrounds in AdS/CFT. It shows the one-loop beta-function is proportional to the Killing form and vanishes precisely when this form is zero, and derives expressions for left- and right-moving central charges, including the impact of kappa-symmetry and possible external CFTs. The authors enumerate conformal cosets built from $PSU(n|n)$ and $OSp(2n{+}2|2n)$, plus tensor-product variants, detailing which classes survive the Virasoro constraints and how many kappa-symmetries they possess. Among the conformal models, only two reach the critical value $c=26$ at one loop: the well-known $AdS_5\times S^5$ GS string on $PU(2,2|4)/SO(4,1)\times SO(5)$ and $AdS_4\times CP^3$ on $OSp(6|4)/U(3)\times SO(3,1)$; numerous non-critical backgrounds exist, some requiring an external CFT to balance the total central charge, with several cases where coupling breaks kappa-symmetry. The results provide a compact, integrable-cosmology-friendly catalog of candidate string backgrounds for AdS/CFT, suggesting a path toward a unified Bethe-Ansatz framework for semi-symmetric cosets.
Abstract
Several string backgrounds which arise in the AdS/CFT correspondence are described by integrable sigma-models. Their target space is always a Z(4) supercoset (a semi-symmetric superspace). Here we list all semi-symmetric cosets which have zero beta function and central charge c<=26 at one loop in perturbation theory.