Ground Ring of Alpha-Symmetries and Sequence of RNS String Theories

TL;DR

This paper constructs a sequence of nilpotent BRST charges in RNS superstring theory based on new gauge symmetries derived from a noncommutative ground ring of alpha-symmetries, with implications for string backgrounds.

Contribution

It introduces new local gauge symmetries from alpha-symmetries forming a noncommutative ground ring, leading to novel BRST charges in RNS superstring theory.

Findings

Identification of a noncommutative ground ring of alpha-symmetries.

Construction of new nilpotent BRST charges.

Potential description of string field theories on curved backgrounds.

Abstract

We construct a sequence of nilpotent BRST charges in RNS superstring theory, based on new gauge symmetries on the worldsheet, found in this paper. These new local gauge symmetries originate from the global nonlinear space-time $\alpha$-symmetries, shown to form a noncommutative ground ring in this work. The important subalgebra of these symmetries is $U(3)\times{X_6}$, where $X_6$ is solvable Lie algebra consisting of 6 elements with commutators reminiscent of the Virasoro type. We argue that the new BRST charges found in this work describe the kinetic terms in string field theories around curved backgrounds of the $AdS\times{CP}_n$-type, determined by the geometries of hidden extra dimensions induced by the global $\alpha$-generators. The identification of these backgrounds is however left for the work in progress.