$c=r_g$ Theories of $W_G$-Gravity: The Set of Observables as a Model of Simply Laced $G$

Abstract

We propose to study a generalization of the Klebanov-Polyakov-Witten (KPW) construction for the algebra of observables in the $c=1$ string model to theories with $c>1$. We emphasize the algebraic meaning of the KPW construction for $c=1$ related to occurrence of a {\it model} of {\it SU}(2) as original structure on the algebra of observables. The attempts to preserve this structure in generalizations naturally leads to consideration of $W$-gravities. As a first step in the study of these generalized KPW constructions we design explicitly the subsector of the space of observables in appropriate $W_G$-string theory, which forms the {\it model} of $G$ for any simply laced {\it G}. The {\it model} structure is confirmed by the fact that corresponding one-loop Kac-Rocha-Caridi $W_G$-characters for $c=r_G$ sum into a chiral (open string) $k=1$ $G$-WZW partition function.

arXiv comment36 p

References in corpus (1)

• Ground Rings and Their Modules in 2D Gravity with $c\le 1$ Matter

Cited by in corpus (6)

• Integrability and Matrix Models
• On AGT relation in the case of U(3)
• Conformal Matrix Models as an Alternative to Conventional Multi-Matrix Models
• The Kazhdan-Lusztig conjecture for W-algebras
• Twist-field representations of W-algebras, exact conformal blocks and character identities
• The W_3 algebra: modules, semi-infinite cohomology and BV-algebras