| The two-dimensional bosonic O(N) sigma-model is an exactly solvable field theory. The thermodynamic Bethe Ansatz allows to find the expression for the mass gap in this theory. This expression was found a long time ago by Hasenfratz, Maggiore and Niedermayer (Phys. Lett B. 245 (1990) 522 and 529), however their derivation was semianalytical. We rederive their result analytically by refurmulating the integral TBA equation as a Riemann-Hilbert problem. Generically, proposed method can be used for the solution of Baxter equations in a special thermodynamic limit. In particular, it was used to find the strong coupling expansion of the cusp anomalous dimension and its generalization in the context of the AdS/CFT correspondence. |
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