Holographic Wilson Loops and Fermions in Consistent Truncations of String Theory and M-Theory.

Abstract

In the holographic framework, a half-BPS Wilson loop in N=4 supersymmetric Yang-Mills theory in the fundamental, symmetric or antisymmetric representation of SU(N), is best described by a fundamental string, a D3-brane or a D5-brane with fluxes in their worldvolumes, respectively. In this thesis, we derive the spectra of excitations of such D3 and D5-branes in AdS_5xS^5 explicitly, considering both the bosonic and the fermionic sectors, and demonstrate that they organize according to short multiplets of the supergroup OSp(4*|4). We also show that the modes of the fundamental string form an ultra-short multiplet of this supergroup. This way we provide a step towards a unifying picture for the description of holographic excitations of supersymmetric Wilson loops in arbitrary representations. In the case of the D5-brane, we compute the effective action due to the brane fluctuations using heat kernel techniques, thus providing the first correction to the expectation value of the circular Wilson loop in the antisymmetric representation of SU(N).

We also discuss the dimensional reduction of fermionic modes in a recently found class of consistent truncations of type IIB and eleven-dimensional supergravity compactified on squashed Sasaki-Einstein manifolds. Such reductions are of interest, for example, in that they have 3+1 and (2+1)-dimensional holographic duals, and the fermionic content and their interactions with charged scalars are an important aspect of their applications. We derive the lower-dimensional equations of motion for the fermions and exhibit their couplings to the various bosonic modes present in the truncations under consideration, which most notably include charged scalar and form fields. We demonstrate that our results are consistent with the expected supersymmetric structure of the lower dimensional theory, and apply them to a specific examples which are relevant to the study of holographic superconductors.