Related papers: Algebroid Structures on Para-Hermitian Manifolds
Given a manifold M with an action of a quadratic Lie algebra d, such that all stabilizer algebras are co-isotropic in d, we show that the product M\times d becomes a Courant algebroid over M. If the bilinear form on d is split, the choice…
In this paper, we construct non-trivial solutions to the $2D$-dimensional field equations of Double Field Theory (DFT) by using a consistent Scherk-Schwarz ansatz. The ansatz identifies $2(D-d)$ internal directions with a twist $U^M{}_N$…
The T-duality transformations between open and closed superstrings in different D-manifolds are generalized to curved backgrounds with commuting isometries. We address some global aspects like the occurrence of orientifold boundaries in…
Given a six-dimensional symplectic manifold $(M, B)$, a nondegenerate, co-closed four-form $C$ introduces a dual symplectic structure $\widetilde{B} = *C $ independent of $B$ via the Hodge duality $*$. We show that the doubling of…
We prove that the linear matroid that defines generic rigidity of $d$-dimensional body-rod-bar frameworks (i.e., structures consisting of disjoint bodies and rods mutually linked by bars) can be obtained from the union of ${d+1 \choose 2}$…
We consider Hull's doubled formalism for open strings on D-branes in flat space and construct the corresponding effective double field theory. We show that the worldsheet boundary conditions of the doubled formalism describe in a unified…
We describe applications of the gluing formalism discussed in the companion paper. When a $d$-dimensional local theory $\text{QFT}_d$ is supersymmetric, and if we can find a supersymmetric polarization for $\text{QFT}_d$ quantized on a…
Courant sigma-models encode the geometric and non-geometric fluxes of compactified closed string theory as generalized Wess-Zumino terms and exhibit their relation to Courant algebroids. In recent work, we proposed a doubled membrane…
We show that the perfect derived categories of Iyama's $d$-dimensional Auslander algebras of type $\mathbb{A}$ are equivalent to the partially wrapped Fukaya categories of the $d$-fold symmetric product of the $2$-dimensional unit disk with…
Infinite dimensional Hamiltonian systems appear naturally in the rich algebraic structure of Symplectic Field Theory. Carefully defining a generalization of gravitational descendants and adding them to the picture, one can produce an…
In his study of Dirac structures, a notion which includes both Poisson structures and closed 2-forms, T. Courant introduced a bracket on the direct sum of vector fields and 1-forms. This bracket does not satisfy the Jacobi identity except…
A self-contained description of algebraic structures, obtained by combinations of various limit procedures applied to vertex and face sl(2) elliptic quantum affine algebras, is given. New double Yangians structures of dynamical type are in…
This paper exposes the fundamental role that the Drinfel'd double $\dkg$ of the group ring of a finite group $G$ and its twists $\dbkg$, $\beta \in Z^3(G,\uk)$ as defined by Dijkgraaf--Pasquier--Roche play in stringy orbifold theories and…
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…
Using parafermionic field theoretical methods, the fundamentals of 2d fractional supersymmetry ${\bf Q}^{K} =P$ are set up. Known difficulties induced by methods based on the $U_{q}(sl(2))$ quantum group representations and non commutative…
This paper classifies Hermitian structures on 6-dimensional nilmanifolds M=G/L for which the fundamental 2-form is d d-bar closed, a condition that is shown to depend only on the underlying complex structure J of M. The space of such J is…
It is well known that for many semilinear parabolic equations there is a global attractor which has a cell complex structure with finite dimensional cells. Additionally, many semilinear parabolic equations have equilibria with finite…
The disk partition function of the open topological string computes the spacetime superpotential for D-branes wrapping cycles of a compact Calabi-Yau threefold. We use string duality to show that when appropriately formulated, the problem…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
We generalize the geometric structures generated by Witten's ground ring. It is shown that these generalized structures involve in a natural way some geometric constructions from Self-dual gravity [1,12]. The formal twistor construction on…