相关论文: Picture changing operators in supergeometry and su…

We consider generalized inverses of linear operators on arbitrary vector spaces and study the question when their product in reverse order is again a generalized inverse. This problem is equivalent to the question when the product of two…

Generalised geometry studies structures on a d-dimensional manifold with a metric and 2-form gauge field on which there is a natural action of the group SO(d,d). This is generalised to d-dimensional manifolds with a metric and 3-form gauge…

We reexamine democratic open string field theories, namely, theories in which string fields are not constrained to a single picture number and picture changing is obtained as a gauge transformation. We describe several possibilities for…

We present a new open superstring field theory, whose string fields carry an arbitrary picture number and reside in the large Hilbert space. The redundancy related to picture number is resolved by treating picture changing as a gauge…

We discuss appropriate arrangement of picture changing operators required to construct gauge invariant interaction vertices involving Neveu-Schwarz states in heterotic and closed superstring field theory. The operators required for this…

Vertex operator algebras are mathematically rigorous objects corresponding to chiral algebras in conformal field theory. Operads are mathematical devices to describe operations, that is, $n$-ary operations for all $n$ greater than or equal…

The theory of operads (May, cyclic, modular, PROPs, etc) is extended to include higher dimensional phenomena, i.e. operations between operations, mimicking the algebraic structure on varieties of arbitrary dimensions, having marked…

We consider quantum field theories on supermanifolds using integral forms. The latter are used to define a geometric theory of integration and they are essential for a consistent action principle. The construction relies on Picture Changing…

The goal of inversion is to estimate the model which generates the data of observations with a specific modeling equation. One general approach to inversion is to use optimization methods which are algebraic in nature to define an objective…

String theory and supersymmetry are theoretical ideas that go beyond the standard model of particle physics and show promise for unifying all forces. After a brief introduction to supersymmetry, we discuss the prospects for its experimental…

The complete quantum theory of closed superstrings is constructed using string diagrams endowed with metric having constant curvature $-1$. The elementary string diagrams are equipped with the analytic local coordinates induced from the…

An overview of supersymmetry and its different applications is presented. We motivate supersymmetry in particle physics. We then explain how supersymmetry helps us analyze field theories exactly, and what dynamical lessons these solutions…

The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The…

Perturbative superstring theory is revisited, with the goal of giving a simpler and more direct demonstration that multi-loop amplitudes are gauge-invariant (apart from known anomalies), satisfy space-time supersymmetry when expected, and…

We interpret superfields in a functorial formalism that explains the properties that are assumed for them in the physical applications. The starting point of this research was the need to understand in a sound mathematical framework some…

The problem of construction of projection operators on eigen-subspaces of symmetry operators is considered. This problem arises in many approximate methods for solving time-independent and time-dependent quantum problems, and its solution…

Superstring compactifications have been vigorously studied for over four decades, and have flourished involving an active iterative feedback between physics and (complex) algebraic geometry. This led to an unprecedented wealth of…

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…

An appropriate field configuration in non-polynomial closed string field theory is shown to correspond to a general off-shell field configuration in low energy effective field theory. A set of string field theoretic symmetries that act on…

We point out that off-shell four-dimensional supersymmetry implies strange hermiticity properties for the N=1 RNS superstring. However, these hermiticity properties become natural when the N=1 superstring is embedded into an N=2…