Non-Commutative Phase-Space Effects in Fermionic String Theory

TL;DR

This paper investigates how non-commutative phase space alters fermionic string theory, leading to anomalies and symmetry breaking, and demonstrates how redefinitions and constraints can restore standard properties.

Contribution

It introduces a framework for analyzing non-commutative effects in fermionic strings and shows how to cancel anomalies to recover the standard spectrum.

Findings

Non-commutativity causes anomalies in super-Virasoro algebra.

Redefining Fock space diagonalizes the mass operator.

Constraints on non-commutativity parameters restore the standard spectrum.

Abstract

We study free open fermionic strings on a non-commutative phase space. Modified super-Virasoro algebras in both Ramond and Neveu-Schwarz sectors acquire non-commutativity anomalies, and this noncommutativity also breaks Lorentz symmetry and give a non-diagonal mass operator. Redefining the Fock space diagonalizes the mass operator. Extra constraints on non-commutativity parameters cancel the anomalies, restore the standard spectrum and make the GSO projection possible.