Noncommutative Superstring Worldsheet

TL;DR

This paper explores the implications of modeling the superstring worldsheet as a noncommutative space, leading to new supersymmetric actions, boundary states, and generalized noncommutativity conditions.

Contribution

It introduces a novel noncommutative framework for superstring worldsheets, extending the action and boundary conditions, and proposing definitions for the noncommutativity parameter.

Findings

Derived a new supersymmetric string action incorporating noncommutativity.

Obtained boundary states describing branes in the noncommutative setting.

Generalized noncommutativity of spacetime from open string boundary conditions.

Abstract

In this paper we consider the worldsheet of superstring as a noncommutative space. Some additional terms can be added to the superstring action, such that for ordinary worldsheet they are zero. Expansion of this extended action up to the first order of the noncommutativity parameter, leads to the new supersymmetric action for string. For the closed superstring, we obtain the boundary state that describes a brane. From the open string point of view, the new boundary conditions on the worldsheet bosons, generalize the noncommutativity of spacetime. Finally, we suggest some definitions for the noncommutativity parameter of superstring worldsheet.