Noncommutative geometry in string and twisted Hopf algebra of diffeomorphism

Abstract

We discuss the Hopf algebra structure in string theory and present the twist quantization as a unified formulation of the world sheet quantization of the string and the symmetry of the target spacetime. Applying it to the case with a nonzero B-field background, we explain a method to decompose the twist into two successive twists. There are 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 Poincaré symmetry. The second decomposition reveals the relation of our formulation to the twisted Poincaré symmetry on the Moyal type noncommutative space.

Twist Quantization of String and Hopf Algebraic Symmetry

“…One of purposes of this paper is to give a overview on the twist quantization developed in [1,2] so far. Part of the paper's results was previously presented at the workshop on Quantum Gravity and Quantum Geometry (Corfu, 2009) and published in its proceedings [7]. We repeat this material here for completeness' sake and for readers' convenience.…”