相关论文: Making the hyper--K\"ahler structure of N=2 quantu…
Based on a simple adiabatic argument and by considering the heterotic string counterpart of certain symmetries of Type II superstrings such as $(-1)^{F_L}$ and orientation reversal, we construct orbifold candidates for dual pairs of…
The notion of a K\"ahler structure for a differential calculus was recently introduced by the second author as a framework in which to study the noncommutative geometry of the quantum flag manifolds. It was subsequently shown that any…
Hitchin has shown that the moduli space ${\mathcal M}$ of the dimensionally reduced self-dual Yang-Mills equations has a hyperK\"{a}hler structure. In this paper we first explicitly show the hyperK\"{a}hler structure, the details of which…
The implications of N=1 superconformal symmetry for four dimensional quantum field theories are studied. Superconformal covariant expressions for two and three point functions of quasi-primary superfields of arbitrary spin are found and…
We study the metrics on the families of moduli spaces arising from probing with a brane the ten and eleven dimensional supergravity solutions corresponding to renormalisation group flows of supersymmetric large n gauge theory. In comparing…
We derive necessary conditions for a complex projective structure on a complex surface to arise via the Levi-Civita connection of a (pseudo-)K\"ahler metric. Furthermore we show that the (pseudo-)K\"ahler metrics defined on some domain in…
We give the superalgebra of $N=2$ chiral (and antichiral) quantum superfields realized as a subalgebra of the quantum supergroup $\mathrm{SL}_q(4|2)$. The multiplication law in the quantum supergroup induces a coaction on the set of chiral…
We show that the graded commutative ring structure of the Hochschild cohomology HH*(A) is trivial in case A is a triangular quadratic string algebra. Moreover, in case A isgentle, the Lie algebra structure on HH*(A) is also trivial.
We describe all supersymmetric solutions of the heterotic string which preserve 8 supersymmetries and show that are distinguished by the holonomy, ${\rm hol}(\hat\nabla)$, of the connection, $\hat\nabla$, with skew-symmetric torsion. The…
We study a deformed $su(m|n)$ algebra on a quantum superspace. Some interesting aspects of the deformed algebra are shown. As an application of the deformed algebra we construct a deformed superconformal algebra. {}From the deformed…
We describe representations of certain superconformal algebras in the semi-infinite Weil complex related to the loop algebra of a complex finite-dimensional Lie algebra and in the semi-infinite cohomology. We show that in the case where the…
We study the class $\mathcal{K}_{2}+\mathcal{K}_{4}$ of homogeneous pseudo-K\"ahler structures in the strongly degenerate case. The local form and the holonomy of a pseudo-K\"ahler manifold admitting such a structure is obtained, leading to…
This paper is devoted to constructing a quantum version of the famous KP hierarchy, by deforming its second Hamiltonian structure, namely the nonlinear $\hat{W}_{\infty}$ algebra. This is achieved by quantizing the conformal noncompact…
The recent developments in string theory suggest that the space-time coordinates should be generalized to non-commuting matrices. Postulating this suggestion as the fundamental geometrical principle, we formulate a candidate for covariant…
We study the correspondence between AdS$_3$ massive IIA supergravity vacua and two-dimensional $\mathcal{N}=(0,4)$ quiver quantum field theories. After categorizing all kinds of gravity solutions, we demystify the ones that seem to reflect…
We give the formulation in extended superspace of an $N=2$ supersymmetric KP hierarchy using chirality preserving pseudo-differential operators. We obtain two quadratic hamiltonian structures, which lead to different reductions of the KP…
We give a Lagrangian and display all local symmetries for N=4 topological string by Berkovits, Vafa and Siegel, the latter previously known in the superconformal gauge. Leading to a small N=4 superconformal algebra and exhibiting the…
Quaternion Kahler manifolds are known to be the target spaces for matter hypermultiplets coupled to N=2 supergravity. It is also known that there is a one-to-one correspondence between 4n-dimensional quaternion Kahler manifolds and those…
Whenever the N=(2,2) supersymmetry algebra of non-linear sigma-models in two dimensions does not close off-shell, a holomorphic two-form can be defined. The only known superfields providing candidate auxiliary fields to achieve an off-shell…
Generalized coherent states provide a means of connecting square integrable representations of a semi-simple Lie group with the symplectic geometry of some of its homogeneous spaces. In the first part of the present work this point of view…