Corrections to Nambu-Goto energy levels from the effective string action

TL;DR

This paper calculates the leading corrections to Nambu-Goto string energy levels using a Hamiltonian approach, clarifying their order in 1/R and comparing with lattice data.

Contribution

It explicitly computes the leading corrections to Nambu-Goto energy levels for open and closed strings, confirming their consistency with effective string theory predictions.

Findings

Open string correction of order 1/R^4

Closed string excited state correction of order 1/R^5

Ground state closed string correction of order 1/R^7

Abstract

The effective action on long strings, such as confining strings in pure Yang-Mills theories, is well-approximated by the Nambu-Goto action, but this action cannot be exact. The leading possible corrections to this action (in a long string expansion in the static gauge), allowed by Lorentz invariance, were recently identified, both for closed strings and for open strings. In this paper we compute explicitly in a Hamiltonian formalism the leading corrections to the lowest-lying Nambu-Goto energy levels in both cases, and verify that they are consistent with the previously computed effective string partition functions. For open strings of length R the leading correction is of order 1/R^4, for excited closed strings of length R in D>3 space-time dimensions it is of order 1/R^5, while for the ground state of the closed string in any dimension it is of order 1/R^7. We attempt to match our closed string corrections to lattice results, but the latter are still mostly outside the range of convergence of the 1/R expansion that we use.