Noncommutative Field Theories and (Super)String Field Theories

TL;DR

This paper reviews noncommutative geometry, quantum field theories, and string field theories, focusing on their mathematical structures, renormalization issues, and applications to D-brane physics and tachyon condensation.

Contribution

It provides a comprehensive overview of noncommutative field theories and string field theories, including formulations, technical tools, and recent developments in D-brane decay analysis.

Findings

Discussion of renormalizability and UV/IR mixing in noncommutative QFTs

Review of string field theory formulations and tachyon condensation methods

Analysis of D-brane decay into closed string vacuum

Abstract

In this lecture notes we explain and discuss some ideas concerning noncommutative geometry in general, as well as noncommutative field theories and string field theories. We consider noncommutative quantum field theories emphasizing an issue of their renormalizability and the UV/IR mixing. Sen's conjectures on open string tachyon condensation and their application to the D-brane physics have led to wide investigations of the covariant string field theory proposed by Witten about 15 years ago. We review main ingredients of cubic (super)string field theories using various formulations: functional, operator, conformal and the half string formalisms. The main technical tools that are used to study conjectured D-brane decay into closed string vacuum through the tachyon condensation are presented. We describe also methods which are used to study the cubic open string field theory around the tachyon vacuum: construction of the sliver state, ``comma'' and matrix representations of vertices.