Abstract
Symmetries of string theory are responsible for fundamental properties of nature. Non-abelian gauge symmetry and its affine Kac-Moody extension provide the origin of the four-dimensional interactions and their gauge bosons from ten or eleven-dimensional coordinate invariance. Supersymmetry provides the origin of fermions. Supersymmetry breaking will provide the origin of mass. In addition, several discrete symmetry groups, including the modular groups SL(n,Z), and other duality groups are associated with the formulation and consistency of the quantum theory of perturbative string physics and non-perturbative branes. In these lectures, an SL(6, Z) invariant partition function for the fivebrane is derived, and constrasted with SL(2,Z) invariant string (onebrane) partition functions. This is a first step in describing the analog of unitarity of perturbative string theory for brane physics. It also shows that higher automorphic forms as well as SL(2, Z) modular functions can be explicitly constructed in brane theories, and may play a central role in their quantization.
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References
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Dolan, L. (1999). Quantized Branes and Symmetries of String Theory. In: DeWitt-Morette, C., Zuber, JB. (eds) Quantum Field Theory: Perspective and Prospective. NATO Science Series, vol 530. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4542-8_7
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DOI: https://doi.org/10.1007/978-94-011-4542-8_7
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