Noncommutativity in interpolating string: A study of gauge symmetries in noncommutative framework

TL;DR

This paper introduces a new interpolating Lagrangian for strings that reveals how noncommutativity arises from boundary conditions, affecting gauge symmetries and their algebra in noncommutative string frameworks.

Contribution

It provides a novel Lagrangian formulation interpolating between Nambu-Goto and Polyakov strings, highlighting the origin of noncommutativity from boundary conditions and analyzing its impact on gauge symmetries.

Findings

Noncommutativity arises from modified Poisson brackets due to boundary conditions.

A new constraint algebra consistent with noncommutative structures is derived.

Gauge symmetry and reparametrisation invariance are shown to be smoothly connected.

Abstract

A new Lagrangian description that interpolates between the Nambu--Goto and Polyakov version of interacting strings is given. Certain essential modifications in the Poission bracket structure of this interpolating theory generates noncommutativity among the string coordinates for both free and interacting strings. The noncommutativity is shown to be a direct consequence of the nontrivial boundary conditions. A thorough analysis of the gauge symmetry is presented taking into account the new modified constraint algebra, which follows from the noncommutative structures and finally a smooth correspondence between gauge symmetry and reparametrisation is established.