• renormalization group flow
• AdS/CFT correspondence
• ABJM
• wilson loop

ABJM is a 3d CS-matter theory with gauge group U(N)xU(N) and holographic gravitational description in AdS4. A direct generalization of it is ABJ theory, with a gauge group U(N)xU(M). Wilson Loops are the principal observables of this thesis. An operator RGF, with the 1/6 BPS WL in the UV limit and the 1/2 BPS WL in the IR is present. So, a family of parametric WLs exists. With a proper choice of the WL parametrization, the parametric WL is 1/6 BPS along all the values of its parameters. It is taken to depend on a ζ parameter, that interpolates between an ordinary 1/6 BPS WL (ζ=1) and a 1/2 BPS WL (ζ=0). The expectation value of this 1/6 BPS parametric WL can be computed with the 1d auxiliar fermion method. A divergence arises in its expectation value, that can be cured with a renormalization of its parameters. However, no divergence was expected in the first place, since the parametric WL preserved 1/6 of the supercharges. In this Thesis, the study of a RGF in ABJ theory for a non-supersymmetric parametric operator running from 1/6 BPS to 1/2 BPS WL is performed. The generalized WL depends now on a fermionic (ζ) and a bosonic (θ) parameters, each of which has a β-function that determines the RGF equations. In the ζ=θ limit, the results just obtained go back to the 1/6 BPS case. (ζ=0,θ=0) and (ζ=1,θ=1) are the conformal fixed points, and their running may be considered as a RGF in an effective 1d defect theory defined on the WL and coupled to the bulk SYM theory.