×

Traces of mirror symmetry in nature. (English) Zbl 1154.81022

The author first presents some physical arguments why generalizations of the Veneziano amplitude are desirable and then aims at finding the dynamical models that reproduce such amplitudes. His starting point is the combinatorial nature of Veneziano-like amplitudes which is revealed by connecting them with the generating function for the Ehrhart polynomial associated with an integral polytope. He then uses known connections between polytopes and dynamical systems. Two types of models, symplectic and supersymmetric, are obtained. The latter is finite-dimensional with a degenerate groundstate and is obtained using results of M. Atiyah and R. Bott [Topology 23, 1–28 (1984; Zbl 0521.58025)] and of E. Witten [J. Differ. Geom. 17, 661–692 (1982; Zbl 0499.53056)] on supersymmetric quantum mechanics. The derivation of this result is difficult to follow because of the author’s extensive use of referrals to the mathematical literature.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
52C07 Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry)
81Q60 Supersymmetry and quantum mechanics
83C45 Quantization of the gravitational field
PDFBibTeX XMLCite
Full Text: arXiv