Integrable Boundary Flows and the g-function

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 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 g-function are discussed, as is initial work on the g-function for the theory, which describes flows that emerge when the bulk coupling is taken to have the opposite sign to that in . Expressions are also found for excited state versions of the g-function, and these allow the unique identification of certain boundary flows.