Related papers: Deformations of Superconformal Theories
We develop some basic facts on deformations of exterior differential ideals on a smooth complex algebraic variety. With these tools we study deformations of several types of differential ideals, leading to several irreducible components of…
We investigate N=2, D=5 supersymmetry and matter-coupled supergravity theories in a superconformal context. In a first stage we do not require the existence of a Lagrangian. Under this assumption, we already find at the level of rigid…
Any 4d theory possessing $\mathcal{N}=1$ supersymmetry admits a so called $\mathcal{S}$-multiplet, containing the conserved energy-momentum tensor and supercurrent. When a defect is introduced into such a theory, the $\mathcal{S}$-multiplet…
A fairly elementary introduction to supersymmetric field theories in general and the minimal supersymmetric Standard Model (MSSM) in particular is given. Topics covered include the cancellation of quadratic divergencies, the construction of…
We study two-dimensional non-linear sigma models with (2,2) supersymmetry and a holomorphic superpotential that are believed to flow to unitary compact (2,2) superconformal theories with equal left and right central charges c=9. The SCFTs…
We study partial supersymmetry breaking from ${\cal N}=2$ to ${\cal N}=1$ by adding non-linear terms to the ${\cal N}=2$ supersymmetry transformations. By exploiting the necessary existence of a deformed supersymmetry algebra for partial…
This is the abstract prepared for Workshop on Topology and Geometry (Zhang jiang, China, October 1994), and is a review of my recent works. What kinds of combinations of singularities can appear in small deformation fibers of a fixed…
In this note we consider low dimensional metric Leibniz algebras with an invariant inner product over the complex numbers up to five dimension. We study their deformations, and give explicit formulas for the cocycles and deformations. We…
The theory of Topological Modular Forms suggests the existence of deformation invariants for two-dimensional supersymmetric field theories that are more refined than the standard elliptic genus. In this note we give a physical definition of…
The study of exactly marginal deformations of superconformal field theories is a topic that has received considerable attention due to their rich properties. We investigate the $\mathcal{N}=2$ preserving exactly marginal operators of 3d…
This paper discusses the relationships between gauge theories defined by gauge groups with finite trivially-acting centers, and theories with restrictions on nonperturbative sectors, in two and four dimensions. In two dimensions, these…
We present a pedagogical review of our current understanding of the ultraviolet structure of N = (1,1) 6D supersymmetric Yang-Mills theory and of N = 8 4D supergravity. These theories are not renormalizable, they involve power ultraviolet…
We discuss the infinite dimensional algebras appearing in integrable perturbations of conformally invariant theories, with special emphasis in the structure of the consequent non-abelian infinite dimensional algebra generalizing $W_\infty$…
We study the realization of anomalous Ward identities in deconstructed (latticized) supersymmetric theories. In a deconstructed four-dimensional theory with N=2 supersymmetry, we show that the chiral symmetries only appear in the infrared…
This is the extended version of the paper "Special Lagrangian conifolds, I: Moduli spaces", which discusses the deformation theory of special Lagrangian (SL) conifolds in complex space C^m. Conifolds are a key ingredient in the…
Hypersurfaces embedded in conformal manifolds appear frequently as boundary data in boundary-value problems in cosmology and string theory. Viewed as the non-null conformal infinity of a spacetime, we consider hypersurfaces embedded in a…
The $T\bar{T}$ deformation of a supersymmetric two-dimensional theory preserves the original supersymmetry. Moreover, in several interesting cases the deformed theory possesses additional non-linearly realized supersymmetries. We show this…
We deform the standard four dimensional $\N=1$ superspace by making the odd coordinates $\theta$ not anticommuting, but satisfying a Clifford algebra. Consistency determines the other commutation relations of the coordinates. In particular,…
It has been shown recently that deformations of some integrable field theories in (1+1)-dimensions possess an infinite number of charges that are asymptotically conserved in the scattering of soliton like solutions. Such charges are not…
This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We…