New strings for old Veneziano amplitudes II. Group-theoretic treatment
arXiv:hep-th/0411241 · doi:10.1016/j.geomphys.2005.10.004
Abstract
In this part of our four parts work (e.g see Part I, hep-th/0410242) we use the theory of polynomial invariants of finite pseudo-reflection groups in order to reconstruct both the Veneziano and Veneziano-like (tachyon-free) amplitudes and the generating function reproducing these amplitudes. We demonstrate that such generating function can be recovered with help of the finite dimensional exactly solvable N=2 supersymmetric quantum mechanical model known earlier from works by Witten, Stone and others. Using the Lefschetz isomorphisms theorem we replace traditional supersymmetric calculations by the group-theoretic thus solving the Veneziano model exactly using standard methods of representation theory. Mathematical correctness of our arguments relies on important theorems by Shepard and Todd, Serre and Solomon proven respectively in early fifties and sixties and documented in the monograph by Bourbaki. Based on these theorems we explain why the developed formalism leaves all known results of conformal field theories unchanged. We also explain why these theorems impose stringent requirements connecting analytical properties of scattering amplitudes with symmetries of space-time in which such amplitudes act.
arXiv comment57 pages J.Geom.Phys.(in press, available on line)
References in corpus (12)
- Lectures on 0/1-polytopes
- Scarred eigenstates for quantum cat maps of minimal periods
- Eigenstate structures around a hyperbolic point
- New Strings for Old Veneziano Amplitudes I.Analytical Treatment
- Kontsevich-Witten Model From 2+1 Gravity: New Exact Combinatorial Solution
- Lorentz-Invariant Hamiltonian and Riemann Hypothesis
- Boundary Conformal Field Theories, Limit Sets of Kleinian Groups and Holography
- Geometric Properties of QCD String From Willmore Functional
- Classical dynamics of rigid string from Willmore functional
- "New" Veneziano amplitudes from "old" Fermat (hyper) surfaces
- New Models for Veneziano Amplitudes: Combinatorial, Symplectic and Supersymmetric Aspects
- The supersymmetric sigma model and the geometry of the Weyl-Kac character formula
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