New strings for old Veneziano amplitudes

Abstract

The bosonic string theory evolved as an attempt to find a physical/quantum mechanical model capable of reproducing Euler's beta function (Veneziano amplitude) and its multidimensional analogue. The multidimensional analogue of beta function was studied mathematically for some time from different angles by mathematicians such as Selberg,Weil and Deligne among many others. The results of their studies apparently were not taken into account in physics literature on string theory. In a recent publication [IJMPA 19 (2004) 1655] an attempt was made to restore the missing links. The results of this publication are incomplete, however, since no attempts were made at reproduction of known spectra of both open an closed bosonic strings or at restoration of the underlying model(s) reproducing such spectra. Nevertheless, discussed in this publication the existing mathematical interpretation of the multidimensional analogue of Euler's beta function as one of the periods associated with the corresponding differential form "living" on the Fermat-type (hyper) surfaces, happens to be crucial for restoration of the quantum/statistical mechanical model reproducing such generalized beta function. Unlike the traditional formulations, this model is supersymmetric. Details leading to restoration of this model will be presented in the forthcoming Parts 2-4 of our work. They are devoted respectively to the group-theoretic, symplectic and combinatorial treatments of this model. In this paper the discussion is restricted mainly to study of analytical properties of the multiparticle Veneziano and Veneziano-like (tachyon-free) amplitudes. In the last case, we demonstrate that the Veneziano-like amplitudes alone (with parameters adjusted accordingly) are capable of reproducing known spectra of both open and closed bosonic strings. The choice of parameters is subject to some constraints dictated by the mathematical interpretation of these amplitudes as periods of Fermat-type (hyper)surfaces considered as complex manifolds of Hodge type.

Veneziano amplitudes, spin chains and Abelian reduction of QCD

“…In this work results of our papers, Ref.s. [5][6][7], to be called respectively as Part I, Part II and Part III are developed further. This has become possible in view of the work by Reshetikhin and Varchenko, Ref.…”

“…Both papers invoke ADS/CFT correspondence. In this work, we reobtain these spin chain results using combinatorial arguments following Heisenberg's philosophy 7 .…”

A Study of the p-Adic Frobenius Lifts and p-Adic Periods, from a Deformation Theory Viewpoint

“…The Veneziano's "educated guess" for a Regge trajectory compatible scattering amplitude [27,28], which in some sense "started" the String Theory movement, is an iterated integral on moduli spaces of punctured Riemann spheres M 0,4 [29], Eq. (1.1), p.1, , with n = 1:…”

Veneziano Amplitudes, Spin Chains, and String Models

“…4 Parametersñ andm will be specified shortly below. 5 We have suppressed the tildas for n and m in this expression since these parameters are going to be redefined below anyway. 6 On page 15 of the book by Stanley [31], one can find that the number of solutions N (n, k)…”

“…In Sections 2-3 we provide needed physical motivations and background. For this purpose, in Section 2 we replaced mathematically sophisticated derivation of Veneziano partition function developed in [4][5][6] by a considerably simpler combinatorial derivation of this function analogous to that discussed in [7]. As a by-product of this effort, we were able to uncover connections with spin chains already at this stage of our investigation.…”