The Orbifold-String Theories of Permutation-Type: I. One Twisted BRST per Cycle per Sector

TL;DR

This paper develops an algebraic framework for orbifold-string theories of permutation type, constructing twisted BRST systems for each cycle and sector, and establishing physical state conditions related to cycle length.

Contribution

It introduces a novel algebraic formulation of twisted BRST systems for permutation-type orbifold-string theories, verifying key algebraic properties and physical state conditions.

Findings

Constructed one twisted BRST system per cycle and sector.

Verified the algebra of BRST charges is anticommutative.

Derived physical state conditions based on cycle length and central charge.

Abstract

We resume our discussion of the new orbifold-string theories of permutation-type, focusing in the present series on the algebraic formulation of the general bosonic prototype and especially the target space-times of the theories. In this first paper of the series, we construct one twisted BRST system for each cycle $j$ in each twisted sector $\sigma$ of the general case, verifying in particular the previously-conjectured algebra $[Q_{i}(\sigma),Q_{j}(\sigma)]_{+} =0$ of the BRST charges. The BRST systems then imply a set of extended physical-state conditions for the matter of each cycle at cycle central charge $\hat{c}_{j}(\sigma)=26f_{j}(\sigma)$ where $f_{j}(\sigma)$ is the length of cycle $j$.