Aspects of Symmetries in Field and String Theories

TL;DR

This thesis explores gauge symmetries in field and string theories, examining their manifestations, interconnections with diffeomorphisms, and impacts on noncommutative space-time, including boundary conditions and gauge equivalences.

Contribution

It provides a comprehensive analysis of gauge symmetries in various models, introduces the use of Seiberg--Witten maps for noncommutative theories, and establishes bounds on noncommutative parameters.

Findings

Gauge symmetries relate to diffeomorphisms in covariant models.

Noncommutative string coordinates exhibit inherent noncommutativity.

Upper bounds on space-time noncommutative parameters were derived.

Abstract

The focus of the present thesis is on the analysis of gauge symmetry and its various impacts on gauge theories. In the first part of this thesis, we have studied different aspects of symmetries in connection with various field and string theoretic models. The manifestations of gauge symmetries and their interconnection with the diffeomorphism invariances have been discussed in the context of different generally covariant models like string, membrane, $p-$brane and metric gravity. Analysis of interacting string with proper inclusion of the stringy boundary conditions led to the noncommutative nature of the string coordinates. In the second part of the thesis the emphasis was primarily on the impact of gauge symmetries on the field theories defined over noncommutative space-time. The correspondence between the NC gauge symmetry and ordinary gauge symmetry manifest by Seiberg--Witten maps between the NC gauge fields and ordinary gauge fields have been used to construct equivalent commutative theories describing the original NC gauge theories. Using this commutative equivalent approach we have analysed several NC gauge field theories of current interest. A upper-bound on the time-space noncommutative parameter has also been worked out.