Boundary Operators in Effective String Theory

TL;DR

This paper investigates the structure of Neumann boundary operators in effective string theory, revealing their dressing by quarter-integer powers and implications for open relativistic strings modeling quark-antiquark pairs.

Contribution

It characterizes the organization of boundary operators in effective string theory, especially their scaling behavior and dressing rules, advancing understanding of open string boundary dynamics.

Findings

Neumann boundary operators are dressed by quarter-integer powers of an invariant.

Allowed target space coordinate scalings are bounded above by +1/2.

The dressing rule arises from regularization of short-distance singularities.

Abstract

Various universal features of relativistic rotating strings depend on the organization of allowed local operators on the worldsheet. In this paper, we study the set of Neumann boundary operators in effective string theory, which are relevant for the controlled study of open relativistic strings with freely moving endpoints. Relativistic open strings are thought to encode the dynamics of confined quark-antiquark pairs in gauge theories in the planar approximation. Neumann boundary operators can be organized by their behavior under scaling of the target space coordinates X, and the set of allowed X-scaling exponents is bounded above by +1/2 and unbounded below. Negative contributions to X-scalings come from powers of a single invariant, or "dressing" operator, which is bilinear in the embedding coordinates. In particular, we show that all Neumann boundary operators are dressed by quarter-integer powers of this invariant, and we demonstrate how this rule arises from various ways of regulating the short-distance singularities of the effective theory.