Twist Quantization of String and B Field Background

TL;DR

This paper explores how twist quantization applies to string theory in a nonzero B-field background, revealing new twisted Poincare symmetries and their relation to noncommutative geometry.

Contribution

It introduces a novel twist quantization scheme for string theory with B-field backgrounds and analyzes its implications for twisted Poincare symmetry.

Findings

New normal ordering required for B-field background

Decomposition of the twist reveals two types of twisted Poincare symmetries

Connection established between twist quantization and Moyal noncommutative space

Abstract

In a previous paper, we investigated the Hopf algebra structure in string theory and gave a unified formulation of the quantization of the string and the space-time symmetry. In this paper, this formulation is applied to the case with a nonzero B-field background, and the twist of the Poincare symmetry is studied. The Drinfeld twist accompanied by the B-field background gives an alternative quantization scheme, which requires a new normal ordering. In order to obtain a physical interpretation of this twisted Hopf algebra structure, we propose a method to decompose the twist into two successive twists and we give two different possibilities of decomposition. The first is a natural decomposition from the viewpoint of the twist quantization, leading to a new type of twisted Poincare symmetry. The second decomposition reveals the relation of our formulation to the twisted Poincare symmetry on the Moyal type noncommutative space.