"New" Veneziano amplitudes from "old" Fermat (hyper) surfaces

Abstract

The history of discovery of bosonic string theory is well documented. This theory evolved as an attempt to find a multidimensional analogue of Euler's beta function. Such an analogue had in fact been known in mathematics literature at least in 1922 and was studied subsequently by mathematicians such as Selberg, Weil and Deligne among others. The mathematical interpretation of this multidimensional beta function is markedly different from that described in physics literature. This paper aims to bridge the gap between the existing treatments. Preserving all results of conformal field theories intact, developed formalism employing topological, algebro-geometric, number-theoretic and combinatorial metods is aimed to provide better understanding of the Veneziano amplitudes and, thus, of string theories.

92 pages LaTex, some typos removed, discussion section is added along with several additional latest references

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Cited by in corpus (8)

• New Strings for Old Veneziano Amplitudes I.Analytical Treatment
• New strings for old Veneziano amplitudes II. Group-theoretic treatment
• From Ginzburg-Landau to Hilbert-Einstein via Yamabe
• New Strings for Old Veneziano Amplitudes III. Symplectic Treatment
• New Models for Veneziano Amplitudes: Combinatorial, Symplectic and Supersymmetric Aspects
• Traces of Mirror Symmetry in Nature
• Designing new apartment buildings for strings and conformal field theories. First steps
• On periods: from global to local