Related papers: Some remarks on Gopakumar-Vafa invariants
We consider special geometry of the vector multiplet moduli space in compactifications of the heterotic string on $K3 \times T^2$ or the type IIA string on $K3$-fibered Calabi-Yau threefolds. In particular, we construct a modified dilaton…
We study de Rham cohomology for various differential calculi on finite groups G up to order 8. These include the permutation group S_3, the dihedral group D_4 and the quaternion group Q. Poincare' duality holds in every case, and under some…
For the kappa-symmetric super IIA D-brane action by the canonical approach we construct an equivalent effective action which is characterized by an auxiliary scalar field. By analyzing the canonical equations of motion for the…
We present a method to construct matrix models on arbitrary simply connected oriented real two dimensional Riemannian manifolds. The actions and the path integral measure are invariant under holomorphic transformations of matrix…
This paper contains some applications of Bridgeland-Douglas stability conditions on triangulated categories, and Joyce's work on counting invariants of semistable objects, to the study of birational geometry. We introduce the notion of…
We derive the couplings of noncommutative D-branes to spatially varying Ramond-Ramond fields, extending our earlier results in hep-th/0009101. These couplings are expressed in terms of *n products of operators involving open Wilson lines.…
Given a (not necessarily regular) holonomic D-module defined on the product of two complex manifolds, we prove that the associated correspondence commutes (in some sense) with the De Rham functor. We apply this result to the study of the…
We compute the $\bar{\nu}$-invariant of homogeneous nearly-parallel $G_2$-structures on Aloff--Wallach spaces $N_{k,l} = SU(3)/S^1_{k,l}$. Using Goette's formulas for the $\eta$-invariants of homogeneous spaces, we derive an explicit…
In systems of intersecting branes, we consider sets of directions in which one type of brane is pointlike, with transverse fluctuations described by matrix coordinates X, and the other set of branes is space-filling, with a local symmetry…
We calculate the quantum cohomology of the moduli space of stable $\PGL_2$-bundles over a smooth curve of genus $g\ge 2$.
We introduce the $\mathrm{SL}(2,\mathbb{C})$ group action on a partition function of a Cohomological field theory via the certain Givental's action. Restricted to the small phase space we describe the action via the explicit formulae on a…
By replacing ten-dimensional pure spinors with eleven-dimensional pure spinors, the formalism recently developed for covariantly quantizing the d=10 superparticle and superstring is extended to the d=11 superparticle and supermembrane. In…
A couple of issues concerning the effective dynamics of D-branes in string theory are discussed. Primarily, I am concerned with linearization of the actions by introduction of non-propagating fields and a full super- and kappa-symmetric…
In this short note we formulate an action for N D0-branes that is manifestly invariant under gauged Galilean transformations. We also find its canonical form and determine first class constraints that are generators of gauge…
We describe a categorical framework for the classification of D-branes on noncommutative spaces using techniques from bivariant K-theory of C*-algebras. We present a new description of bivariant K-theory in terms of noncommutative…
We explore the possibility of constructing p-brane world-volume actions with the requirements of kappa-symmetry and gauge invariance as the only input. In the process, we develop a general framework which leads to actions interpolating…
In this note we present an approach using both constructive and Hopf algebraic methods to contribute to the not yet fully satisfactory definition of an integral on kappa-deformed spacetime. The integral presented here is based on the inner…
We provide and study an equivariant theory of group (co)homology of a group G with coefficients in a gamma-equivariant G-module A, when a separate group "gamma" acts on G and A, generalizing the classical Eilenberg-MacLane (co)homology of…
This is my master thesis, under the supervision of Professor Amiram Braun. We classify in these paper the Gorenstein invariant rings in the modular case, where the group that acts on the 3-variable polynomial ring is finite , and the Char…
We develop a theory of Gopakumar-Vafa (GV) invariants for a Calabi-Yau threefold (CY3) $X$ which is equipped with an involution $\imath$ preserving the holomorphic volume form. We define integers $n_{g,h}(\beta) $ which give a virtual count…