Studies on Boundary Conditions and Noncommutativity in String Theory

TL;DR

This thesis investigates how noncommutative geometries naturally arise in string theory, especially in boundary conditions, and demonstrates their consistency with the fundamental algebraic structures of the theory.

Contribution

It provides detailed analysis showing noncommutativity emerges in both bosonic and fermionic sectors of string theory, ensuring compatibility with boundary conditions and preserving algebraic consistency.

Findings

Noncommutative structures are necessary for boundary condition compatibility.

String coordinates become noncommutative in various approaches.

Noncommutativity leads to new algebraic structures while preserving Virasoro algebra.

Abstract

The central theme of this thesis is noncommutativity in string theory. We explore in detail how noncommutative structures can emerge in case of the interacting bosonic string and even in the fermionic sector of superstring theory. We have shown in various approaches that string coordinates must be noncommutative in order to be compatible with boundary conditions. These noncommutative structures lead to new involutive algebra of constraints but generate same Virasoro algebra, indicating the internal consistency of our analysis