A new approach to superstring

TL;DR

The paper introduces a BRST-centered framework in which the one-string state space $\mathcal{E}'$ carries all information needed to compute string scattering amplitudes across bosonic, superstring, and heterotic theories. By realizing a Lie algebra $\mathfrak{g}'$ action on $\mathcal{E}'$ and exponentiating to a semigroup $\mathcal{G}'$, BRST-closed forms pull back to $\mathcal{G}'$ and descend to quotients $\mathcal{G}/\mathfrak{k}$, yielding amplitudes as integrals over moduli spaces of (super)conformal manifolds. The construction leverages $L$-functionals, Segal-type CFT/SCFT/TSCFT formalisms, and the geometry of disks and annuli to connect operator formalism with moduli space integrals, producing string amplitudes via a principled, first-principles route. It accommodates closed bosonic strings and their superstring and heterotic generalizations, and suggests avenues for non-perturbative extensions through infinite-dimensional Grassmannian structures. Overall, the work provides a unifying algebraic-geometric framework linking BRST cohomology, moduli of (super)conformal surfaces, and explicit amplitude calculations.

Abstract

We show how starting with one-string space of states in BRST formalism one can construct a large class of physical quantities containing, in particular, scattering amplitudes for bosonic string and superstring. The same techniques work for heterotic string.