Understand
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.