Content area
In this thesis, we study the spectrum of excitations of D3-branes with worldvolume flux in AdS5xS5. We present a closed-form expression for the second-order action of the D3-brane in the bosonic sector, constructed using methods of differential geometry of embedded manifolds. The quadratic action is formulated by introducing a basis adapted to curved backgrounds, which allows us to decompose fluctuations into parallel and normal components with respect to the worldvolume. Motivated by the AdS/CFT correspondence, we compute the spectrum of excitations of three distinct D3-brane configurations. The first two correspond to 1/2- and 1/4-BPS spherical D3-branes without worldvolume flux i.e. giant graviton. The 1/2-BPS case is known to be dual to the 1/2-BPS superconformal index in N=4 Super Yang–Mills. For the 1/4-BPS case, we analyze the spectrum with the motivation of extending this duality prescription to the 1/4-BPS index, although a precise matching remains an open problem. For these configurations, the normal fluctuations in S5 reduce to a Landau model, and we identify the conserved charges associated with the system. The third case is the $D3$-brane configuration with worldvolume flux dual to the 1/4-BPS latitude Wilson loop in N=4 SYM in the k-symmetric representation of the gauge group SU(N). For this configuration, we find a complicated quadratic action that contains a non-trivial normal connection and a coupling between the scalar and vectorial fluctuation fields.