String fine tuning

TL;DR

This paper introduces a geometrical model of discretized strings extending Feynman’s random walk amplitudes to random surfaces, analyzing its physical properties, boundary effects, and potential for nontrivial scaling limits.

Contribution

It develops a new geometrical discretized string model with boundary contributions, finite triangulation effects, and explores its potential for nontrivial scaling and hadronic applications.

Findings

Partition function contribution is finite for each triangulation.

Explicit upper bounds for the partition function are derived.

The model allows for a vanishing string tension at a critical point.

Abstract

We develop further a new geometrical model of a discretized string, proposed in [1] and establish its basic physical properties. The model can be considered as the natural extention of the usual Feynman amplitude of the random walks to random surfaces. Both amplitudes coinside in the case, when the surface degenarates into a single particle world line. We extend the model to open surfaces as well. The boundary contribution is proportional to the full length of the boundary and the coefficient of proportionality can be treated as a hopping parameter of the quarks. In the limit, when this parameter tends to infinity, the theory is essentialy simlplified. We prove that the contribution of a given triangulation to the partition function is finite and have found the explicit form for the upper bound. The question of the convergence of the full partition function remains open. In this model the string tension may vanish at the critical point, if the last one exists, and possess a nontrivial scaling limit. The model contains hidden fermionic variables and can be considered as an independent model of hadrons.