Twist Quantization of String and B Field Background

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.

25 pages, no figure, typos corrected, references and comments added, published version

References in corpus (24)

• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Noncommutative Open String and D-brane
• D-branes and Deformation Quantization
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• A Gravity Theory on Noncommutative Spaces
• Noncommutative Geometry and Gravity
• Nonassociative Star Product Deformations for D-brane Worldvolumes in Curved Backgrounds
• Symmetry, Gravity and Noncommutativity
• Untwisting Noncommutative R^d and the Equivalence of Quantum Field Theories
• Comments on noncommutative gravity
• Twisting of quantum differentials and the Planck scale Hopf algebra
• Construction of $\theta$-Poincaré Algebras and their Invariants on ${\mathcal{M}}_{\theta }$
• Star Products from Open Strings in Curved Backgrounds
• Twists and spectral triples for isospectral deformations
• Open String Field Theory on Noncommutative Space
• Normal ordering and noncommutativity in open bosonic strings
• Normal ordering and boundary conditions in open bosonic strings
• Open-Closed String Field Theory in the Background B-Field
• Normal ordering and non(anti)commutativity in open super strings
• Hopf Algebra Symmetry and String Theory
• Normal ordering and boundary conditions for fermionic string coordinates
• Non-topological non-commutativity in string theory

Cited by in corpus (4)

• Braided $L_{\infty }$-Algebras, Braided Field Theory and Noncommutative Gravity
• Braided Symmetries in Noncommutative Field Theory
• Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra
• Twist Quantization of String and Hopf Algebraic Symmetry