Hopf Algebra Symmetry and String Theory

Abstract

We investigate the Hopf algebra structure in string worldsheet theory and give a unified formulation of the quantization of string and the space-time symmetry. We reformulate the path integral quantization of string as a Drinfeld twist at the worldsheet level. The coboundary relation shows that the Drinfeld twist defines a module algebra which is equivalent to operators with normal ordering. Upon applying the twist, the space-time diffeomorphism is deformed into a twisted Hopf algebra, while the Poincaré symmetry is unchanged. This suggests a characterization of the symmetry: unbroken symmetries are twist invariant Hopf subalgebras, while broken symmetries are realized as twisted ones. We provide arguments that relate this twisted Hopf algebra to symmetries in path integral quantization.

35 pages, no figure, v2: references and comments added, typos corrected, v3: requires PTP style, title changed, final version published in PTP

References in corpus (8)

• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• A Gravity Theory on Noncommutative Spaces
• Comments on noncommutative gravity
• Twisting all the way: from Classical Mechanics to Quantum Fields
• Twists and spectral triples for isospectral deformations
• Lorentz invariant and supersymmetric interpretation of noncommutative quantum field theory
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Cited by in corpus (5)

• 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 B Field Background
• Twist Quantization of String and Hopf Algebraic Symmetry