Related papers: The Witten Index Revisited
We consider the topological theory of Witten type for gauge differential p-forms. It is shown that some topological invariants such as linking numbers appear under quantization of this theory. The non-abelian generalization of the model is…
In this paper, we study the analytic properties of solutions to the Vafa-Witten equation over a compact Kaehler manifold. Simple obstructions to the existence of nontrivial solutions are identified. The gauge theoretical compactness for the…
Magnetized orbifolds play an important role in compactifications of string theories and higher-dimensional field theories to four dimensions. Magnetic flux leads to chiral fermions, it can be a source of supersymmetry breaking and it is an…
We consider two dimensional $\mathcal{N}=(4,4)$ superconformal field theories in the moduli space of symmetric orbifolds of K3. We complete a classification of the discrete groups of symmetries of these models, conditional to a series of…
We consider a compact abelian Higgs model in 3+1 dimensions with a topological axion term and construct its dual theories for both bulk and boundary at strong coupling. The model may be viewed as describing a superconductor with magnetic…
We study the connectedness of the moduli space of gauge equivalence classes of flat G-connections on a compact orientable surface or a compact nonorientable surface for a class of compact connected Lie groups. This class includes all the…
We are solving for the case of flat superspace some homological problems that were formulated by Berkovits and Howe. (Our considerations can be applied also to the case of supertorus.) These problems arise in the attempt to construct…
In this paper we will use our results about the local deformation theory of Calabi-Yau manifolds to define a Higgs field on the tangent bundle of the moduli space of CY threefolds. Combining this Higgs field with the Levi-Chevitta…
We analyze the superstring propagating on a Calabi-Yau threefold. This theory naturally leads to the consideration of Witten's topological non-linear sigma-model and the structure of rational curves on the Calabi-Yau manifold. We study in…
The moduli space of flat SL(2,R)-connections modulo gauge transformations on the torus may be described by ordered pairs of commuting SL(2,R) matrices modulo simultaneous conjugation by SL(2,R) matrices. Their spectral properties allow a…
This is a survey article for the mathematical theory of Witten's Gauged Linear Sigma Model, as developed recently by the authors. Instead of developing the theory in the most general setting, in this paper we focus on the description of the…
We propose a topological version of four-dimensional (Euclidean) Einstein gravity, in which anti-self-dual 2-forms and an SU(2) connection are used as fundamental fields. The theory describes the moduli space of conformally self-dual…
We define the notion of Witt structure on the tangent bundle of a pseudo-Riemannian manifold and we introduce a connection adapted to a such structure. The notions of geodesics and symmetric spaces are revisited in this setting and…
The particle spectrum of the supersymmetric extension of the standard model with a gauge singlet is studied. Soft supersymmetry breaking terms are explicitly chosen to be non-universal according to orbifold string theory. they depend on…
We lay the foundation for a version of $r$-spin theory in genus zero for Riemann surfaces with boundary. In particular, we define the notion of $r$-spin disks, their moduli space, and the Witten bundle, we show that the moduli space is a…
The Witten index for certain supersymmetric lattice models treated by de Boer, van Eerten, Fendley, and Schoutens, can be formulated as a topological invariant of simplicial complexes arising as independence complexes of graphs. We prove a…
Type II string theory compactified on a Calabi-Yau manifold, with a singularity modeled by a hypersurface in an orbifold, is considered. In the limit of vanishing string coupling, one expects a non gravitational theory concentrated at the…
We study the planar equivalence of orbifold field theories on a small three-torus with twisted boundary conditions, generalizing the analysis of hep-th/0507267. The nonsupersymmetric orbifold models exhibit different large N dynamics from…
We study the structure of anomalies in general heterotic string theories by considering general 2-dimensional $\mathcal{N}=(0,1)$ supersymmetric quantum field theories (SQFTs), without assuming conformal invariance nor the correct central…
The structure of the moduli space of N=1 supersymmetric gauge theories is analyzed from an algebraic geometric viewpoint. The connection between the fundamental fields of the ultraviolet theory, and the gauge invariant composite fields of…