On the gl(1|1) Wess-Zumino-Witten Model

We continue the study of the gl(1|1) Wess-Zumino-Witten model. The Knizhnik-Zamolodchikov equations for the one, two, three and four point functions are analyzed, for vertex operators corresponding to typical and projective representations. We illustrate their interplay with the logarithmic global conformal Ward identities. We compute the four point function for one projective and three typical representations. Three coupled first order Knizhnik-Zamolodchikov equations are integrated consecutively in terms of generalized hypergeometric functions, and we assemble the solutions into a local correlator. Moreover, we prove crossing symmetry of the four point function of four typical representations at generic momenta. Throughout, the map between the gl(1|1) Wess-Zumino-Witten model and symplectic fermions is exploited and extended.Comment: 37 page

An Elliptic Triptych

We clarify three aspects of non-compact elliptic genera. Firstly, we give a path integral derivation of the elliptic genus of the cigar conformal field theory from its non-linear sigma-model description. The result is a manifestly modular sum over a lattice. Secondly, we discuss supersymmetric quantum mechanics with a continuous spectrum. We regulate the theory and analyze the dependence on the temperature of the trace weighted by the fermion number. The dependence is dictated by the regulator. From a detailed analysis of the dependence on the infrared boundary conditions, we argue that in non-compact elliptic genera right-moving supersymmetry combined with modular covariance is anomalous. Thirdly, we further clarify the relation between the flat space elliptic genus and the infinite level limit of the cigar elliptic genus.Comment: 22 page

Higgsed antisymmetric tensors and topological defects

We find topological defect solutions to the equations of motion of a generalised Higgs model with antisymmetric tensor fields. These solutions are direct higher dimensional analogues of the Nielsen-Olesen vortex solution for a gauge field in four dimensions.Comment: 9 pages, final versio

Peinture et comédie : les scènes de théâtre de Cornelis Troost (1696-1750)

Le présent mémoire porte sur l’un des peintres néerlandais les plus connus de son époque, Cornelis Troost (1696-1750). Celui-ci tire son succès du traitement et de l’originalité de ses sujets dans la confection de ses scènes de théâtre, dont cinq sont abordées ici. Troost fut lui-même acteur de profession avant de se consacrer au métier de peintre. Tout comme les œuvres de Troost, l’art hollandais du XVIIIe siècle est un sujet rarement abordé en histoire de l’art. Plusieurs éléments historiques des Pays-Bas, notamment certains des bouleversements politiques, sont indispensables afin d'acquérir une meilleure compréhension des œuvres théâtrales de Troost. Dans ses scènes de théâtre, Troost embrasse le côté théâtral de celles-ci. Ses œuvres portent le même titre que les pièces desquelles elles sont tirées. De plus, Troost introduit ses personnages de près et cette particularité met l'accent sur les émotions des personnages et sur l’action. Un parallèle est tracé avec Jan Steen et Gérard De Lairesse, eux-mêmes des artistes hollandais s’inspirant du théâtre. La narration dans les œuvres de Troost est également un point important afin de bien comprendre ses scènes de théâtre.This master’s thesis focuses on one of the most famous Dutch painters of his time, Cornelis Troost (1696-1750). Troost’s success derives from the originality of his subjects in the theatrical scenes he depicts five of which are discussed here. Troost himself was a professional actor before devoting himself to the art of painting. Dutch art of the eighteenth century is a topic rarely discussed in art history. Several elements of Netherlandish history, including political changes, are essential in order to acquire a better understanding of Troost's theatrical work. Troost embraces the theatrical source. His works of art bear the same title as the plays from which they are drawn. Troost puts the emphasis on his characters, and this feature helps to put the focus on the emotions of the characters and the action. A parallel is made with Jan Steen and Gerard De Lairesse, other Dutch artists who were inspired by the theatrical world. The narrative aspect in the works of Troost is also an important aspect which needs to be approached in order to understand his theater scenes

Duality and Modularity in Elliptic Integrable Systems and Vacua of N=1* Gauge Theories

We study complexified elliptic Calogero-Moser integrable systems. We determine the value of the potential at isolated extrema, as a function of the modular parameter of the torus on which the integrable system lives. We calculate the extrema for low rank B,C,D root systems using a mix of analytical and numerical tools. For so(5) we find convincing evidence that the extrema constitute a vector valued modular form for a congruence subgroup of the modular group. For so(7) and so(8), the extrema split into two sets. One set contains extrema that make up vector valued modular forms for congruence subgroups, and a second set contains extrema that exhibit monodromies around points in the interior of the fundamental domain. The former set can be described analytically, while for the latter, we provide an analytic value for the point of monodromy for so(8), as well as extensive numerical predictions for the Fourier coefficients of the extrema. Our results on the extrema provide a rationale for integrality properties observed in integrable models, and embed these into the theory of vector valued modular forms. Moreover, using the data we gather on the modularity of complexified integrable system extrema, we analyse the massive vacua of mass deformed N=4 supersymmetric Yang-Mills theories with low rank gauge group of type B,C and D. We map out their transformation properties under the infrared electric-magnetic duality group as well as under triality for N=1* with gauge algebra so(8). We find several intriguing properties of the quantum gauge theories.Comment: 35 pages, many figure

Permutations of Massive Vacua

We discuss the permutation group G of massive vacua of four-dimensional gauge theories with N=1 supersymmetry that arises upon tracing loops in the space of couplings. We concentrate on superconformal N=4 and N=2 theories with N=1 supersymmetry preserving mass deformations. The permutation group G of massive vacua is the Galois group of characteristic polynomials for the vacuum expectation values of chiral observables. We provide various techniques to effectively compute characteristic polynomials in given theories, and we deduce the existence of varying symmetry breaking patterns of the duality group depending on the gauge algebra and matter content of the theory. Our examples give rise to interesting field extensions of spaces of modular forms.Comment: 44 pages, 1 figur