Related papers: $A_\infty$-Algebra from Supermanifolds
We discuss general properties of classical string field theories with symmetric vertices in the context of deformation theory. For a given conformal background there are many string field theories corresponding to different decomposition of…
We discuss the differential algebras used in Connes' approach to Yang-Mills theories with spontaneous symmetry breaking. These differential algebras generated by algebras of the form functions $\otimes$ matrix are shown to be skew…
A Lie superalgebra is attached to any finite-dimensional J-ternary algebra over an algebraically closed field of characteristic 3, using a process of semisimplification via tensor categories. Some of the exceptional simple Lie algebras,…
We continue our study of zero-dimensional field theories in which the fields take values in a strong homotopy Lie algebra. In a first part, we review in detail how higher Chern-Simons theories arise in the AKSZ-formalism. These theories…
After briefly reviewing the methods that allow us to derive consistently new Lie (super)algebras from given ones, we consider enlarged superspaces and superalgebras, their relevance and some possible applications.
We study moduli spaces of mirror non-compact Calabi-Yau threefolds enhanced with choices of differential forms. The differential forms are elements of the middle dimensional cohomology whose variation is described by a variation of mixed…
We construct the general formulation of N=1 supersymmetric self-dual abelian gauge theory involving auxiliary chiral spinor superfields. Self-duality in this context is just U(N) invariance of the nonlinear interaction of the auxiliary…
Building over recent results, we expand the basic theory of algebraic extensions to the realm of superfields -a field with multivalued sum and product-, showing that every superfield has a (unique up to isomorphism) strong algebraic…
We construct a hierarchy of supersymmetric string theories by showing that the general N-extended superstrings may be viewed as a special class of the (N+1)-extended superstrings. As a side result, we find a twisted (N+2) superconformal…
The purpose of this work is to study Lie superalgebroid structures on the space of superdifferential $1$-forms over the supermanifolds whose superfunctions are the differential forms on its underlying manifold. These superalgbroids are…
We introduce a notion of Q-algebra that can be considered as a generalization of the notion of Q-manifold (a supermanifold equipped with an odd vector field obeying {Q,Q} =0). We develop the theory of connections on modules over Q-algebras…
A series of nonrepresentable relation algebras is constructed from groups. We use them to prove that there are continuum many subvarieties between the variety of representable relation algebras and the variety of coset relation algebras. We…
We construct a complex of differential forms on a local $C^\infty$-ringed space. The two main classes of spaces we have in mind are differential spaces in the sense of Sikorski and $C^\infty$-schemes. Just as in the case of manifolds the…
A new class of infinite dimensional simple Lie algebras over a field with characteristic 0 are constructed. These are examples of non-graded Lie algebras. The isomorphism classes of these Lie algebras are determined. The structure space of…
We present here a cohomological analysis of the new spacetime superalgebras that arise in the context of superbrane theory. They lead to enlarged superspaces that allow us to write D-brane actions in terms of fields associated with the…
We represent B fields and higher p-form potentials on a manifold M as connections on affine bundles over M. We realize D branes on M as special submanifolds of these affine bundles. We check the physical relevance of this representation by…
The polysymplectic $(n+1)$-form is introduced as an analogue of the symplectic form for the De Donder-Weyl polymomentum Hamiltonian formulation of field theory. The corresponding Poisson brackets on differential forms are constructed. The…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
The theory of non-linear realizations is used to derive the dynamics of the branes of M theory. A crucial step in this procedure is to use the enlarged automorphism group of the supersymmetry algebra recently introduced. The field strengths…
We use freely acting asymmetric orbifolds of type IIB string theory to construct a class of theories in four dimensions with eight supercharges. Their low energy effective field theories resemble $STU$ models, but have different duality…