Related papers: Supersymmetry, a Biased Review
The paper contains a short review of the theory of symplectic and contact manifolds and of the generalization of this theory to the case of supermanifolds. It is shown that this generalization can be used to obtain some important results in…
This thesis is dedicated to the study of the geometry of six-dimensional superspace, endowed with the minimal amount of supersymmetry. In the first part of it, we unfold the main geometrical features of such superspace by solving completely…
Two-dimensional sigma-models describing superstrings propagating on manifolds of special holonomy are characterized by symmetries related to covariantly constant forms that these manifolds hold, which are generally non-linear and close in a…
We investigate the supersymmetric versions of Bondi-Metzner-Sachs or, equivalently, conformal Carroll symmetry in boundary dimensions $d>3$, with applications of flat space holography in mind. We identify the contraction of the relativistic…
We construct supersymmetric conformal sigma models in three dimensions. Nonlinear sigma models in three dimensions are nonrenormalizable in perturbation theory. We use the Wilsonian renormalization group equation method, which is one of the…
We consider a general N=(2,2) non-linear sigma model with a torsion. We show that the consistency of N=(2,2) supersymmetry implies that the target manifold is necessary equipped with two (in general, different) Poisson structures. Finally…
This thesis presents a framework in which to explore kinematical symmetries beyond the standard Lorentzian case. This framework consists of an algebraic classification, a geometric classification, and a derivation of the geometric…
These are the lecture notes from the 26th Winter School "Geometry and Physics", Czech Republic, Srni, January 14 - 21, 2006. These lectures are an introduction into the realm of generalized geometry based on the tangent plus the cotangent…
The field theory dual to the Freedman-Townsend model of a non-Abelian anti-symmetric tensor field is a nonlinear sigma model on the group manifold G. This can be extended to the duality between the Freedman-Townsend model coupled to…
The moduli space of the Calabi-Yau three-folds, which play a role as superstring ground states, exhibits the same {\em special geometry} that is known from nonlinear sigma models in $N=2$ supergravity theories. We discuss the symmetry…
We take supersymmetry in the Seiberg-Witten theory as a case study of the uses of (super)symmetry arguments in studying the ontology of four-dimensional interacting quantum field theories. Together with a double expansion, supersymmetry is…
We describe the relation between supersymmetric sigma-models on hyperkahler manifolds, projective superspace, and twistor space. We review the essential aspects and present a coherent picture with a number of new results.
The structure and properties of possible $q$-Minkowski spaces is discussed, and the corresponding non-commutative differential calculi are developed in detail and compared with already existing proposals. This is done by stressing its…
It has been shown recently that extended supersymmetry in twisted first-order sigma models is related to twisted generalized complex geometry in the target. In the general case there are additional algebraic and differential conditions…
This is an elementary introduction to basic tools of supersymmetry: the spacetime symmetries, gauge theory and its application in gravity, spinors and superalgebras. Special attention is devoted to conformal and anti-de Sitter algebras.
We review the superspace technique to determine supersymmetric spacetimes in the framework of off-shell formulations for supergravity in diverse dimensions using the case of 3D N=2 supergravity theories as an illustrative example. This…
Supersymmetric field theories on noncommutative spaces are constructed. We present two different representations of noncommutative space, but we can obtain supersymmetry algebla and supersymmetric Yang-Mills action independent of its…
Using gauge theory, we describe how to construct generalized Kahler geometries with (2,2) two-dimensional supersymmetry, which are analogues of familiar examples like projective spaces and Calabi-Yau manifolds. For special cases, T-dual…
Superspace is considered as space of parameters of the supercoherent states defining the basis for oscillator-like unitary irreducible representations of the generalized superconformal group SU(2m,2n/2N) in the field of quaternions H. The…
I will discuss the emergence of lorentzian symmetric spaces as supersymmetric supergravity backgrounds. I will focus on supergravity theories in dimension 11, 10, and 6, and will concentrate on the determination of the so-called maximally…