  The low-energy effective action on long string-like objects in quantum field
theory, such as confining strings, includes the Nambu-Goto action and then
higher-derivative corrections. This action is diffeomorphism-invariant, and can
be analyzed in various gauges. Polchinski and Strominger suggested a specific
way to analyze this effective action in the orthogonal gauge, in which the
induced metric on the worldsheet is conformally equivalent to a flat metric.
Their suggestion leads to a specific term at the next order beyond the
Nambu-Goto action. We compute the leading correction to the Nambu-Goto spectrum
using the action that includes this term, and we show that it agrees with the
leading correction previously computed in the static gauge. This gives a
consistency check for the framework of Polchinski and Strominger, and helps to
understand its relation to the theory in the static gauge.
