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The effective string spectrum in the orthogonal gauge

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.