Perturbative BPS algebras in superstring theory |
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| Institution: | 1. Centro Marplatense de Investigaciones Matemáticas, FCEyN, Universidad Nacional de Mar del Plata, CONICET, Funes 3350, 7600 Mar del Plata, Argentina;2. Laboratoire de Mathématiques, Université Blaise Pascal & CNRS, Complexe Scientifique Les Cézeaux, BP 80026, 63171 Aubière cedex, France;1. School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QW, UK;2. Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195-4350, USA;3. Department of Mathematics, University of Southern California, 3620 S. Vermont Ave., Los Angeles, CA 90089-2532, USA;1. I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute, Leninsky ave. 53, 119991 Moscow, Russia;2. Moscow Institute of Physics and Technology, Dolgoprudnyi, 141700 Moscow region, Russia;3. Department of Quantum Physics, Institute for Information Transmission Problems, Bolshoy Karetny per. 19, 127994 Moscow, Russia;1. Faculty of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan;2. Institute for Information Transmission Problems Russian Academy of Sciences, Russian Federation;3. Division of Mathematics, Sophia University, Kioicho 7-1, Chiyoda-ku, Tokyo 102-8554, Japan |
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| Abstract: | This paper investigates the algebraic structure that exists on perturbative BPS states in the superstring, compactified on the product of a circle and a Calabi-Yau fourfold. This structure was defined in a recent article by Harvey and Moore. It is shown that for a toroidal compactification this algebra is related to a generalized Kac-Moody algebra. The BPS algebra itself is not a Lie algebra. However, it turns out to be possible to construct a Lie algebra with the same graded dimensions, in terms of a half-twisted model. The dimensions of these algebras are related to the elliptic genus of the transverse part of the string algebra. Finally, the construction is applied to an orbifold compactification of the superstring. |
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