The notion of integrability can be extended to systems with boundaries. In large volume and finite temperature, the free energy of such systems – unlike those periodic – contains a non-extensive piece, called g-function, with many physical interpretations. We present a method [1906.07733] hybrid of [1003.5542, 1007.1148, 1809.05705] to calculate the g-function from the TBA partition function. NOTE: Thus is an online seminar using Zoom. Please follow the registration link on https://integrability-london.weebly.com/

In this talk, based on [1906.07733] and [1907.11242] with Y. Jiang and S. Komatsu, we derive the first non-perturbative result for the structure constant of two determinant operators and a non-BPS single-trace operator of finite length in planar N=4 SYM. First, we introduce an effective theory for such correlators at zero coupling. The form of the result supports the interpretation of the three-point function as an overlap between an integrable boundary state, which we determine using symmetry and integrability, and the state describing the single-trace operator. Second, we use thermodynamic Bethe ansatz to derive a non-perturbative expression for such overlap. Finally, we discuss applications that could be addressed with these methods.