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

TL;DR

This paper explores the mathematical foundations of Veneziano amplitudes, connecting historical mathematical functions with modern string theory, using advanced algebraic and geometric methods to deepen understanding.

Contribution

It introduces a formalism that bridges the gap between physics and mathematics, employing topological, algebro-geometric, and number-theoretic techniques to analyze Veneziano amplitudes.

Findings

Revealed connections between multidimensional beta functions and string amplitudes

Developed a new formalism integrating mathematical and physical perspectives

Enhanced understanding of the mathematical structure underlying string theory

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.