A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper studies highest weight representations of Lie superalgebras and their geometric realizations.
We consider the generalized Kahler structures (g,J_+,J_-) that arise on a hyperkahler manifold (M,g,I,J,K) when we choose J_+ and J_- from the twistor space of M. We find a relation between semichiral and arctic superfields which can be used to determine the generalized Kahler potential for hyperkahler manifolds whose …
The study proves a localization theorem and calculates volumes for superspaces.
Classifies kinematical and aristotelian Lie superalgebras and their superspaces.
Over the -dimensional real superspace, , we classify -invariant binary differential operators acting on the superspaces of weighted densities, where is the Lie superalgebra of contact vector fields. This result allows us to compute the first differential cohomology of %the L…
We extend our previous analysis of Riemannian four-manifolds M admitting rigid supersymmetry to N=1 theories that do not possess a U(1)_R symmetry. With one exception, we find that M must be a Hermitian manifold. However, the presence of supersymmetry imposes additional restrictions. For instance, a supercharge that sq…
Extends Nambu-Poisson bracket to superspace R^{n|m}.
Researchers classify invariant operators on weighted densities.
New sigma models use supersymmetry for hyperkähler target spaces.
Researchers found a new 8D Taub-NUT-like metric using harmonic superspace.
Higher order anisotropic superspaces are constructed as generalized vector superbundles provided with compatible nonlinear connection, distinguished connection and metric structures.
Smooth superspace with special weights has a Fubini-Study form.
Torsions, curvatures, structure equations and Bianchi identities for locally anisotropic superspaces (containing as particular cases different supersymmetric extensions and prolongations of Riemann, Finsler, Lagrange and Kaluza--Klein spaces) are investigated.
Semichiral sigma models with target space are discussed. A novel description in superspace allows an analysis of possible extended supersymmetries. It is argued that a manifest semichiral realization of an extra supersymmetry is only possible for hyperkähler target geometry. A semichiral formulatio…
This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)kähler reduction; projective superspace; the generalized Legendre construction; generalized Kähler geometry and constructions of hyperkähler metrics on Hermitean symmetri…
We systematically analyze Riemannian manifolds M that admit rigid supersymmetry, focusing on four-dimensional N=1 theories with a U(1)_R symmetry. We find that M admits a single supercharge, if and only if it is a Hermitian manifold. The supercharge transforms as a scalar on M. We then consider the restrictions imposed…
The action of Batalin-Vilkovisky Delta-operator on semidensities in an odd symplectic superspace is defined. This is used for the construction of integral invariants on surfaces embedded in an odd symplectic superspace and for more clear interpretation of the Batalin-Vilkovisky formalism geometry.
Motivated by a paper of Zirnbauer, we develop a theory of Riemannian supermanifolds up to a definition of Riemannian symmetric superspaces. Various fundamental concepts needed for the study of these spaces both from the Riemannian and the Lie theoretical viewpoint are introduced, e.g. geodesics, isometry groups and inv…
10D IIA Superspace is put on shell by imposing duality-symmetric Bianchi identities on super-flux densities.
The divergence-like operator on an odd symplectic superspace which acts invariantly on a specially chosen odd vector field is considered. This operator is used to construct an odd invariant semidensity in a geometrically clear way. The formula for this semidensity is similar to the formula of the mean curvature of hype…
This research builds foundations for D3-branes in string theory.
T-duality rules for 2D (2,1) supersymmetric models clarified.
11D supergravity completes with quantized C-field flux.
We solve the long standing problem of finding an off-shell supersymmetric formulation for a general N = (2, 2) nonlinear two dimensional sigma model. Geometrically the problem is equivalent to proving the existence of special coordinates; these correspond to particular superfields that allow for a superspace descriptio…
The work proposes a geometric background of the theory of field interactions and strings in spaces with higher order anisotropy. Our approach proceeds by developing the concept of higher order anisotropic superspace which unifies the logical and mathematical aspects of modern Kaluza-Klein theories and generalized Lagra…
New supergroups created from odd involutions in supergeometry.
Study differential operators on superspaces with new filtrations.
It is shown that two definitions for an exterior differential in superspace, giving the same exterior calculus, yet lead to different results when applied to the Poisson bracket. A prescription for the transition with the help of these exterior differentials from the given Poisson bracket of definite Grassmann parity t…
We introduce a wide category of superspaces, called locally finitely generated, which properly includes supermanifolds but enjoys much stronger permanence properties, as are prompted by applications. Namely, it is closed under taking finite fibre products (i.e. is finitely complete) and thickenings by spectra of Weil s…
In 1996/7, J. Bernstein observed that smooth or analytic supermanifolds that mathematicians study are real or (almost) complex ones, while Minkowski superspaces are completely different objects. They are what we call almost real-complex supermanifolds, i.e., real supermanifolds with a non-integrable distribution, the c…
Superconformal geometries discussed in various spacetime dimensions using local supertwistor bundles.
Reconstructs supersymmetry and supergravity in complexified Z/2-graded Algebraic Geometry.
This is an expository paper about the geometry of the torsion constraints in the superspace formulation of supergravity theories. It was prepared for the 2001 Park City Research Program in Supergeometry.
Reproduces basic supersymmetric QFTs using complexified graded algebraic geometry.
We study power expansions of the characteristic function of a linear operator in a -dimensional superspace . We show that traces of exterior powers of satisfy universal recurrence relations of period . `Underlying' recurrence relations hold in the Grothendieck ring of representations of $\GL(V)$. The…
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.
We reexamine the relation between contact structures on supermanifolds and supersymmetric mechanics in the superspace formulation. This allows one to use the language of contact geometry when dealing with the d = 1, N = 2 super-Poincare algebra.
The monograph summarizes the author's results on the geometry of anholonomic and locally anisotropic interactions, published in J. Math. Phys., Nucl. Phys. B, Ann. Phys. (NY), JHEP, Rep. Math. Phys., Int. J. Theor. Phys. and in some former Soviet Union and Romanian scientific journals. The main subjects are in the theo…
We establish a relation between higher contact-like structures on supermanifolds and the N = 1 super-Poincare group via its superspace realisation. To do this we introduce a vector-valued contact structure, which we refer to as a polycontact structure.
A general approach to formulation of supergravity in higher order anisotropic superspaces (containing as particular cases different supersymmetric extensions and prolongations of Riemann, Finsler, Lagrange and Kaluza--Klein spaces) is given. We analyze three models of locally anisotropic supergravity.
Supergeneralization of $\DC P(N)$ provided by even and odd Kählerian structures from Hamiltonian reduction are construct.Operator which used in Batalin-- Vilkovisky quantization formalism and mechanics which are bi-Hamiltonian under corresponding even and odd Poisson brackets are considered.
We consider an example of tubes of hypersurfaces in Euclidean space and generalise the tube formula to supercase. By this we assign to a point of the hypersurface in superspace a rational characteristic function. Does this rational function appear when we calculate the zeta-function of an arithmetic variety?
We construct N=2 supersymmetric nonlinear sigma models whose target spaces are tangent as well as cotangent bundles over the quadric surface Q^{n-2} = SO(n)/[SO(n-2)\times U(1)]. We use the projective superspace framework, which is an off-shell formalism of N=2 supersymmetry.
New risk measures for incomplete markets without lattice structures.
The theory of locally anisotropic superspaces (supersymmetric generalizations of various types of Kaluza--Klein, Lagrange and Finsler spaces) is laid down. In this framework we perform the analysis of construction of the supervector bundles provided with nonlinear and distinguished connections and metric structures. Tw…
We study "higher-dimensional" generalizations of differential forms. Just as differential forms can be defined as the universal commutative differential algebra containing C^\infty(M), we can define differential gorms as the universal commutative bidifferential algebra. From a more conceptual point of view, differentia…
A new formulation of theories of supergravity as theories satisfying a generalized Principle of General Covariance is given. It is a generalization of the superspace formulation of simple 4D-supergravity of Wess and Zumino and it is designed to obtain geometric descriptions for the supergravities that correspond to the…
Unified super-symmetry and higher fluxes using super-Lie-infinity algebras.