Hopf Algebra Symmetry and String Theory

Details Hopf Algebra Symmetry and String Theory Hopf Algebra Symmetry and String Theory

2008-05-15

arxiv.org/abs/0805.2203v3

Prog. Theor. Phys. 120 (2008) 659-689

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1143/PTP.120.659

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 Poincar\'e 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.

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