Integrability of Type II Superstrings on Ramond-Ramond Backgrounds in Various Dimensions

TL;DR

The paper presents a unified treatment of type II superstrings on RR AdS backgrounds realized as $G/H$ supercosets with a $\mathbb{Z}_4$ automorphism, using both Green--Schwarz and pure spinor formalisms. It constructs a one-parameter family of flat currents $a(\mu)$, proving classical integrability, and shows that BRST symmetry in the pure spinor formalism ensures quantum integrability; it also analyzes one-loop conformal invariance and boundary D-branes across non-critical and critical backgrounds, including AdS$_{2d}$ and AdS$_p\times S^p\times CY_{5-p}$. The work provides explicit Lax connections, BRST-invariant non-local charges, and a detailed account of the backgrounds, boundary conditions, and central-charge considerations, highlighting a Yangian-like symmetry structure beyond the canonical AdS$_5\times S^5$ case. These results illuminate how RR backgrounds may admit exact integrable structures and offer avenues to study spectra via algebraic curves or Bethe ansatz in lower-dimensional settings, with potential holographic implications for non-critical duals such as SQCD-like fixed points. The findings underscore the role of BRST symmetry in maintaining integrability at the quantum level and set the stage for exploring holographic duals of non-critical RR backgrounds.

Abstract

We consider type II superstrings on AdS backgrounds with Ramond-Ramond flux in various dimensions. We realize the backgrounds as supercosets and analyze explicitly two classes of models: non-critical superstrings on AdS_{2d} and critical superstrings on AdS_p\times S^p\times CY. We work both in the Green--Schwarz and in the pure spinor formalisms. We construct a one-parameter family of flat currents (a Lax connection) leading to an infinite number of conserved non-local charges, which imply the classical integrability of both sigma-models. In the pure spinor formulation, we use the BRST symmetry to prove the quantum integrability of the sigma-model. We discuss how classical κ-symmetry implies one-loop conformal invariance. We consider the addition of space-filling D-branes to the pure spinor formalism.