Diagrammatic encoding of sine-Gordon model TBA equations

In this work it is presented a study on the sine-Gordon model thermodynamic Bethe Ansatz (TBA) equations, with particular emphasis on its underlying mathematical structures and diagrammatic encoding. An outline of the sine-Gordon model foundations and main features, it is proposed an in-depth review of the TBA system derivation up to its 'raw' formulation. Some Fourier-space identities are introduced in order to simplify the equations and bring them in their 'universal' form. This is done for all the rational values of the sine-Gordon parameter. The 'universal' TBA equations enjoy a diagrammatic representation that casts light on the inherent mathematical structures of the theory. The Y-system formulation is also considered at reflectionless points: possible generalizations are discussed.