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We study the sphere partition function of 3d $\mathcal{N}=2$ holographic SCFTs arising on the worldvolume of $N$ coincident M2-branes in the presence of squashing and real mass deformations. We argue that the all-order large $N$ perturbative expansion of the partition function resums into a compact expression in terms of an Airy function. We provide ample evidence for this conjecture using numerical methods, saddle point analysis in the 't Hooft limit, and the relation of the squashed sphere partition function to the Cardy-like limit of the superconformal index. We also discuss the relation of our results to topological string theory and the statistical mechanics of Fermi gases. Our conjecture has a bearing on the AdS/CFT correspondence and the structure of perturbative M-theory corrections to 11d supergravity which we discuss., Comment: v1: 64 pages

We study correlation functions of local operators and Wilson loop expectation values in the planar limit of a 4d $\mathcal{N}=2$ superconformal ${\rm SU}(N)$ YM theory with hypermultiplets in the symmetric and antisymmetric representations of the gauge group. This so-called $\mathbf{E}$ theory is closely related to $\mathcal{N}=4$ SYM and has a holographic description in terms of a $\mathbb{Z}_2$ orientifold of AdS$_5\times S^5$. Using recent matrix model results based on supersymmetric localization we develop efficient numerical methods to calculate two- and three-point functions of certain single trace operators as well as 1/2-BPS Wilson loop expectation values as a function of the 't Hooft coupling $\lambda$. We use our numerical results to arrive at simple analytic expressions for these correlators valid up to the sixth order in the $\lambda^{-1/2}$ strong coupling expansion. These results provide explicit field theory predictions for the $\alpha'$ corrections to the supergravity approximation of type IIB string theory on the AdS$_5\times S^5/\mathbb{Z}_2$ orientifold., Comment: v2: new results on subleading terms in the three point functions, comments added, referrences updated

Biadjoint scalar field theories are increasingly important in the study of scattering amplitudes in various string and field theories. Recently, some first exact nonperturbative solutions of biadjoint scalar theory were presented, with a pure power-like form corresponding to isolated monopole-like objects located at the origin of space. In this paper, we find a novel family of extended solutions, involving non-trivial form factors that partially screen the divergent field at the origin. All previous solutions emerge as special cases., Comment: 11 pages, 2 figures

We show that the BMPV metric has Petrov type 22. This means that the BMPV metric is less algebraically special than the five-dimensional Schwarzschild metric, which has Petrov type \underline{22}., Comment: 6 pages, 2 figures

We point out that the Myers-Perry metric in five dimensions is algebraically special. It has Petrov type \underline{22}, which is the Petrov type of the five-dimensional Schwarzschild metric., Comment: 4 pages, 1 figure

It is well-known that the Kerr-metric (rotating black hole in four dimensions) has Petrov type D. We prove a similar property in five dimensions. The Myers-Perry metric (rotating black hole in five dimensions) with one non-zero angular momentum has Petrov type \underline{22}. Conversely, we show that the Myers-Perry solution is unique within a certain restricted class of metrics of Petrov type \underline{22}., Comment: 8 pages

We classify all five-dimensional Einstein manifolds that are static, have an SO(3) isometry group and have Petrov type 22. We use this classification to show that the localized black hole in the Randall-Sundrum scenario necessarily has Petrov type 4., Comment: 13 pages, 1 figure

We give a Petrov classification for five-dimensional metrics. We classify Ricci-flat metrics that are static, have an SO(3) isometry group and have Petrov type 22. We use this classification to look for the metric of a black hole on a cylinder, i.e. a black hole with asymptotic geometry four-dimensional Minkowski space times a circle. Although a black string wrapped around the circle and the five-dimensional black hole are both algebraically special, it turns out that the black hole on a cylinder is not., Comment: 21 pages, 1 figure; v2: classification completed, discussion simplified, references added

In this Ph.D. thesis, we study tachyon condensation in string field theories. In chapter 2, we review Witten's bosonic string field theory and calculate the tachyon potential. In chapter 3, we calculate the tachyon potential in Berkovits' superstring field theory. In chapter 4, we look for exact solutions in a toy model. Unpublished result: we use conservation laws to calculate the level (4,8) approximation of the tachyon potential in Berkovits' superstring field theory. We verify Sen's conjecture up to 94.4%., Comment: Ph.D. thesis, K.U.Leuven, LaTeX, 130 pages, 20 figures

We study tachyon condensation in a baby version of Witten's open string field theory. For some special values of one of the parameters of the model, we are able to obtain closed form expressions for the stable vacuum state and for the value of the potential at the minimum. We study the convergence rate of the level truncation method and compare our exact results with the numerical results found in the full string field theory., Comment: 17 pages, 1 figure

We study the tachyon potential in the NS sector of Witten's cubic superstring field theory. In this theory, the pure tachyon contribution to the potential has no minimum. We find that this remains the case when higher modes up to level two are included., Comment: Latex, 10 pages, 1 figure, published version, comments added regarding the absence of the twist-invariance and the singular behaviour of the potential

We compute the tachyon potential to level 4 in NS superstring field theory. We obtain 89% of the conjectured vacuum energy., Comment: Latex, 8 pages, 1 figure, published version, references changed