Dirichlet String Theory and Singular Random Surfaces

TL;DR

This paper establishes an equivalence between Dirichlet boundary string theory and string theory with singular surfaces, revealing connections to lattice QCD and conformal geometry.

Contribution

It introduces a novel perspective linking singular surfaces in string theory to Dirichlet boundaries and their moduli, with implications for strong coupling expansions.

Findings

Singular surfaces with Dirichlet boundaries are equivalent to certain string theories.

Moduli parameters of singular and smooth surfaces with boundaries coincide.

Saddle points of infinite order arise in the strong coupling expansion of lattice QCD.

Abstract

We show that string theory with Dirichlet boundaries is equivalent to string theory containing surfaces with certain singular points. Surface curvature is singular at these points. A singular point is resolved in conformal coordinates to a circle with Dirichlet boundary conditions. We also show that moduli parameters of singular surfaces coincide with those of smooth surfaces with boundaries. Singular surfaces with saddle points indeed arise in the strong coupling expansion in lattice QCD. The kind of saddle point, which may be the origin of a singular point we need, is of infinite order.