Related papers: Split-complex representation of the universal hype…
In this note we speculate about the structure of maximal product subvarieties in moduli stacks of Calabi-Yau manifolds. We discuss examples for quintic hypersurfaces in the four dimensional projective space.
Complex Ricci-flat (i.e., Calabi-Yau) hypersurfaces in spaces admitting a maximal (toric) $U(1)^n$ gauge symmetry of general type (encoded by certain non-convex and multi-layered multitopes) may degenerate, but can be smoothed by rational…
Finite and Infinite-dimensional representations of symmetry algebras play a significant role in determining the spectral properties of physical Hamiltonians. In this paper, we introduce and apply a practical method to construct infinite…
We study a gauge coupling unification scenario based on a non-supersymmetric 5-dimensional model. Through an orbifold compactification, we obtain the Standard Model with split multiplets on a 4-dimensional wall, which is compatible with a…
The partial breaking of supersymmetry in flat space can be accomplished using any one of three dual representations for the massive N=1 spin-3/2 multiplet. Each of the representations can be ``unHiggsed'', which gives rise to a set of dual…
We apply a universal normal Calabi-Yau algebra to the construction and classification of compact complex $n$-dimensional spaces with SU(n) holonomy and their fibrations. This algebraic approach includes natural extensions of reflexive…
We derive the coupling of a hypermultiplet of N=2 global supersymmetry to the Dirac-Born-Infeld Maxwell theory with linear N=1 and a second nonlinear supersymmetry. At the level of global supersymmetry, this construction corresponds to the…
N-extended massless arbitrary integer and half-integer spin supermultiplets in four dimensional flat space are studied in the framework of light-cone gauge formalism. For such multiplets, by using light-cone momentum superspace, we build…
The representation theory of semisimple algebraic groups over the complex numbers (equivalently, semisimple complex Lie algebras or Lie groups, or real compact Lie groups) and the question of whether a given representation is symplectic or…
We develop a noncompact version of the Hopf maps based on the split algebras. The split algebras consist of three species: split-complex numbers, split quaternions, and split octonions. They correspond to three noncompact Hopf maps that…
In this paper we provide a manifestly N=2 supersymmetric formulation of the M-fivebrane in the presence of threebrane solitons. The superspace form of four-dimensional effective equations for the threebranes are readily obtained and yield…
In the context of studying the 4D effective potentials of type IIB non-geometric flux compactifications, this article has a twofold goal. First, we present a modular invariant symplectic rearrangement of the tree level non-geometric scalar…
Division algebras are used to explain the existence and symmetries of various sets of auxiliary fields for super Yang-Mills in dimensions $d=3,4,6,10$. (Contribution to G\"ursey Memorial Conference I: Strings and Symmetries)
Global symmetry anomalies of a quantum field theory (QFT) can be packaged as specific couplings of a higher-dimensional symmetry theory (SymTh). In this work we show that for 5D superconformal field theories (SCFTs) engineered from M-theory…
In this note, we establish the formulation of 6D, N=1 hypermultiplets in terms of 4D chiral-nonminimal (CNM) scalar multiplets. The coupling of these to 6D, N=1 Yang-Mills multiplets is described. A 6D, N=1 projective superspace formulation…
This is an expanded version of my plenary lecture at the 8th European Congress of Mathematics in Portoro\v{z} on 23 June 2021. The main part of the paper is a survey of recent applications of complex-analytic techniques to the theory of…
We analyze the hypermultiplet moduli space describing the universal sector of type IIA theory compactified on a Calabi-Yau threefold. The classical moduli space is described in terms of the coset $SU(2,1)/U(2)$. The flux quantization…
We give a new representation of Euclidean quantum fields as scaling limits of systems of interacting, continuous, classical particles in the grand canonical ensemble.
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…
We present a general method for calculating the moduli spaces of fivebranes wrapped on holomorphic curves in elliptically fibered Calabi-Yau threefolds, in particular, in the context of heterotic M theory. The cases of fivebranes wrapped…