New Geometrical Approach to Superstrings

TL;DR

This paper introduces a novel geometrical framework for superstring theory using supermanifold integration, enabling efficient multi-loop amplitude calculations and analysis of symmetries, especially for states lacking primary representatives.

Contribution

It develops a new supermanifold-based formalism for superstrings that simplifies amplitude calculations and enhances analysis of discrete states and background symmetries.

Findings

Allows calculation of multi-loop superstring amplitudes in arbitrary backgrounds.

Enables analysis of discrete states and background symmetries without primary representatives.

Provides a direct proof of the dilaton theorem.

Abstract

We present a new geometrical approach to superstrings based on the geometrical theory of integration on supermanifolds. This approach provides an effective way to calculate multi-loop superstring amplitudes for arbitrary backgrounds. It makes possible to calculate amplitudes for the physical states defined as BRST cohomology classes using arbitrary representatives. Since the new formalism does not rely on the presence of primary representatives for the physical states it is particulary valuable for analyzing the discrete states for which no primary representatives are available. We show that the discrete states provide information about symmetries of the background including odd symmetries which mix Bose and Fermi states. The dilaton is an example of a non-discrete state which cannot be covariantly represented by a primary vertex. The new formalism allows to prove the dilaton theorem by a direct calculation.