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The effective action on long strings, such as confining strings in pureYang-Mills theories, is well-approximated by the Nambu-Goto action, but thisaction cannot be exact. The leading possible corrections to this action (in along string expansion in the static gauge), allowed by Lorentz invariance, wererecently identified, both for closed strings and for open strings. In thispaper we compute explicitly in a Hamiltonian formalism the leading correctionsto the lowest-lying Nambu-Goto energy levels in both cases, and verify thatthey are consistent with the previously computed effective string partitionfunctions. For open strings of length R the leading correction is of order1/R^4, for excited closed strings of length R in D>3 space-time dimensions itis of order 1/R^5, while for the ground state of the closed string in anydimension it is of order 1/R^7. We attempt to match our closed stringcorrections to lattice results, but the latter are still mostly outside therange of convergence of the 1/R expansion that we use.

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