On the effective theory of long open strings

TL;DR

This paper analyzes the low-energy effective action of long open strings, revealing that the leading deviations from Nambu-Goto energy levels occur at order 1/R^4, with implications for confining gauge theories and holographic duals.

Contribution

It determines the order of the leading deviation from Nambu-Goto energy levels for open strings and computes the correction coefficient in holographic confining theories.

Findings

Leading deviation occurs at order 1/R^4 for open strings.

Boundary conditions (Dirichlet/Neumann) do not change the deviation order.

Non-zero correction coefficient computed for holographic confining theories.

Abstract

We study the general low-energy effective action on long open strings, such as confining strings in pure gauge theories. Using Lorentz invariance, we find that for a string of length R, the leading deviation from the Nambu-Goto energy levels generically occurs at order 1/R^4 (including a correction to the ground state energy), as opposed to 1/R^5 for excited closed strings in four dimensions, and 1/R^7 for closed strings in three dimensions. This is true both for Dirichlet and for Neumann boundary conditions for the transverse directions, though the worldsheet boundary actions are different. The Dirichlet case is relevant (for instance) for the force between external quarks in a confining gauge theory, and the Neumann case for a string stretched between domain walls. In the specific case of confining gauge theories with a weakly curved holographic dual, we compute the coefficient of the leading correction when the open string ends on two D-branes, and find a non-vanishing result.