On the Algebraic Structure of Gravitational Descendants in CP(n-1) Coset Models

TL;DR

This paper explores the algebraic structure of gravitational descendants in CP(n-1) coset models, revealing how free-field realizations and screening prescriptions relate to gravitational excitations and the $W_n$-ground ring spectra.

Contribution

It provides a new algebraic characterization of the $W_n$-gravitational ground ring spectra using affine-$SU(n)$ highest weights in twisted N=2 supersymmetric coset models.

Findings

Screening prescription enforces equivariance in cohomology.

Algebraic description of $W_n$-ground ring spectra.

Connection between free-field realizations and gravitational excitations.

Abstract

We investigate how specific free-field realizations of twisted N=2 supersymmetric coset models give rise to natural extensions of the ``matter'' Hilbert spaces in such a manner as to incorporate the various gravitational excitations. In particular, we show that adopting a particular screening prescription is equivalent to imposing the requisite equivariance condition on cohomology. We find a simple algebraic characterization of the $W_n$-gravitational ground ring spectra of these theories in terms of affine-$SU(n)$ highest weights..