We consider certain 1/4 BPS Wilson loop operators in SU(N) ${\cal N}=4$ supersymmetric Yang-Mills theory, whose expectation value can be computed exactly via supersymmetric localization. Holographically, these operators are mapped to fundamental strings in AdS5 x S5. The string on-shell action reproduces the large N and large coupling limit of the gauge theory expectation value and, according to the AdS/CFT correspondence, there should also be a precise match between subleading corrections to these limits. We perform a test of such match at next-to-leading order in string theory, by deriving the spectrum of quantum fluctuations around the classical string solution and by computing the corresponding 1-loop effective action. We discuss in detail the supermultiplet structure of the fluctuations. To remove a possible source of ambiguity in the ghost zero mode measure, we compare the 1/4 BPS configuration with the 1/2 BPS one, dual to a circular Wilson loop. We find a discrepancy between the string theory result and the gauge theory prediction, confirming a previous result in the literature. We are able to track the modes from which this discrepancy originates, as well as the modes that by themselves would give the expected result.Comment: 5 pages; v2: 43 pages, long version fixing a mistake and altering the conclusion

In the holographic framework, a half BPS Wilson loop in N = 4 supersymmetric Yang-Mills 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. We derive the spectrum of excitations of such D3 brane in AdS 5 × S 5 explicitly, considering its action in both the bosonic and the fermionic sectors, and demonstrate that it is organized 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. In the case of the D5 brane the bosonic spectrum is only partially known but we argue that it also fills representations of OSp(4 * |4). This way we provide a step towards a unifying picture for the description of holographic excitations of the circular and straight supersymmetric Wilson loops in arbitrary representations. arXiv:1101.5145v3 [hep-th]

We systematically study the spectrum of excitations and the one-loop determinant of holographic Wilson loop operators in antisymmetric representations of N = 4 supersymmetric YangMills theory. Holographically, these operators are described by D5-branes carrying electric flux and wrapping an S 4 ⊂ S 5 in the AdS 5 × S 5 bulk background. We derive the dynamics of both bosonic and fermionic excitations for such D5-branes. A particularly important configuration in this class is the D5-brane with AdS 2 × S 4 worldvolume and k units of electric flux, which is dual to the circular Wilson loop in the totally antisymmetric representation of rank k. For this Wilson loop, we obtain the spectrum, show explicitly that it is supersymmetric and calculate the one-loop effective action using heat kernel techniques.

The gauge sector of three-dimensional higher spin gravities can be formulated as a Chern-Simons theory. In this context, a higher spin black hole corresponds to a flat connection with suitable holonomy (smoothness) conditions which are consistent with the properties of a generalized thermal ensemble. Building on these ideas, we discuss a definition of black hole extremality which is appropriate to the topological character of 3d higher spin theories. Our definition can be phrased in terms of the Jordan class of the holonomy around a non-contractible (angular) cycle, and we show that it is compatible with the zero-temperature limit of smooth black hole solutions. While this notion of extremality does not require supersymmetry, we exemplify its consequences in the context of sl(3|2) ⊕ sl(3|2) Chern-Simons theory and show that, as usual, not all extremal solutions preserve supersymmetries. Remarkably, we find in addition that the higher spin setup allows for non-extremal supersymmetric black hole solutions. Furthermore, we discuss our results from the perspective of the holographic duality between sl(3|2) ⊕ sl(3|2) ChernSimons theory and two-dimensional CFTs with W (3|2) symmetry, the simplest higher spin extension of the N = 2 super-Virasoro algebra. In particular, we compute W (3|2) BPS bounds at the full quantum level, and relate their semiclassical limit to extremal black hole or conical defect solutions in the 3d bulk. Along the way, we discuss the role of the spectral flow automorphism and provide a conjecture for the form of the semiclassical BPS bounds in general N = 2 two-dimensional CFTs with extended symmetry algebras.

We discuss the dimensional reduction of fermionic modes in a recently found class of consistent truncations of type IIB supergravity compactified on squashed five-dimensional Sasaki-Einstein manifolds. We derive the lower dimensional equations of motion and effective action, and comment on the supersymmetry of the resulting theory, which is consistent with N = 4 gauged supergravity in d = 5, coupled to two vector multiplets.We compute fermion masses by linearizing around two AdS 5 vacua of the theory: one that breaks N = 4 down to N = 2 spontaneously, and a second one which preserves no supersymmetries. The truncations under consideration are noteworthy in that they retain massive modes which are charged under a U (1) subgroup of the R-symmetry, a feature that makes them interesting for applications to condensed matter phenomena via gauge/gravity duality. In this light, as an application of our general results we exhibit the coupling of the fermions to the type IIB holographic superconductor, and find a consistent further truncation of the fermion sector that retains a single spin-1/2 mode.