Master's thesis defence by Franciszek Nawrocki

Title:  Aspects of Defect ABJM Theory

Abstract: We introduce ABJM theory, quantised around the 1/2 BPS domain wall defect background. In this vacuum, two of the four scalars acquire vacuum expectation values, introducing mass terms for the scalars and a highly non-trivial mixing matrix. We decompose the mixing using tools from su(2) representation theory and exploit the diagonalised fields to construct propagators of the scalars. As the defect effectively constrains the fields to move in an effective AdS space, we construct the corresponding AdS propagator of the diagonalised fields. Working in the large N limit, we use the latter to compute the one-loop correction to a certain one-point function of a chiral primary operator to any length. The result follows the nice form of a power sum in the variable q, which is related to the symmetry breaking across the defect. Curiously, the form of the q polynomial at one loop and tree level are identical. Additionally, we introduce the fuzzy spherical harmonics, which furnish the (q − 1) x q dimensional representation of su(2) and compute the normalisation of the states in this representation.