Integrable Boundary Flows and the g-function

TL;DRAbstract

This thesis explores renormalisation group flows in integrable quantum field theories with boundaries, as described by the g-function. The main focus is on the g-function in the staircase model, the renormalisation group flow of which passes close to the unitary minimal models. This g-function is used to identify flows between boundary conditions both within and between the minimal models. In certain limits the $\\mathcal{M}A_m^{(+)}$ theories which interpolate between pairs of minimal models emerge from the staircase model, and exact expressions for the g-function in these models are extracted from the staircase g-function. Perturbative tests on the $\\mathcal{M}A_4^{(+)}$ g-function are discussed, as is initial work on the g-function for the $\\mathcal{M}A_4^{(-)}$ theory, which describes flows that emerge when the bulk coupling is taken to have the opposite sign to that in $\\mathcal{M}A_4^{(+)}$. Expressions are also found for excited state versions of the $\\mathcal{M}A_m^{(+)}$ g

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