2004/11/30 by Arkady L. Kholodenko
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Amplitude #Black Holes and Theoretical Physics #Conformal map #Covariant transformation #Geometry #Holomorphic function #Homogeneous space #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum field theory #Quantum mechanics #Scattering amplitude #Tachyon #Theoretical physics #hep-th
paper · pdf · doi:10.1016/j.geomphys.2005.10.004
published as J.Geom.Phys. 56 (2006) 1387-1432 · 57 pages J.Geom.Phys.(in press, available on line)
openalex publication_date 2005/11/29 · arxiv created 2005/12/12 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.