The higher-algebraic skeleton of the superstring -- a case study

TL;DR

This paper develops a higher-algebraic framework for the superstring using Lie superalgebras and super-1-gerbes, providing a topological and supersymmetric description of superstring dynamics.

Contribution

It introduces a novel hierarchy of Lie superalgebras and supergroups that geometrize the superstring's higher gauge fields in a supersymmetric and topological manner.

Findings

Hierarchical Lie superalgebraic description of superstring

Manifestly supersymmetric model of supermanifolds

Topological trivialisation of super-1-gerbe over superstring worldsheet

Abstract

A novel Lie-superalgebraic description of the superstring in the super-Minkowskian background is extracted from the Cartan-Eilenberg super-1-gerbe geometrising the higher gauge field (the Green-Schwarz super-3-cocycle) that couples to the supercharge carried by the superstring. The description assumes the form of a hierarchy of Lie superalgebras integrable to a hierarchy of Lie supergroups and provides a manifestly supersymmetric model of a family of supermanifolds defining a trivialisation of the super-1-gerbe over the embedded superstring worldsheet. The trivialisation, obtained in a purely topological formulation of the superstring dynamics dual to the standard Nambu-Goto-type one, conforms with the gerbe-theoretic representation of extended sources of higher gauge fields known from previous studies of the $\sigma$-model of the bosonic string.