相关论文: The mystery of the brane relation
We discuss brane webs preserving eight supercharges and derive geometries produced by them. Consistency conditions of supergravity are shown to impose certain requirements on the locations of the sources, and these restrictions are found to…
We introduce topological invariants of knots and braid conjugacy classes, in the form of differential graded algebras, and present an explicit combinatorial formulation for these invariants. The algebras conjecturally give the relative…
In the appropriate limit, a type IIB string theory setup involving D3 branes, wrapped D5 branes, and fluxes on a conifold generally leads to a supergravity background involving a warped version of the conifold with fluxes. We study the…
Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of…
We perform a Hodge theoretic study of parameter dependent families of D-branes on compact Calabi-Yau manifolds in type II and F-theory compactifcations. Starting from a geometric Gauss-Manin connection for B type branes we study the…
The addition of fundamental degrees of freedom to a theory which is dual (at low energies) to N=2 SYM in 1+3 dimensions is studied. The gauge theory lives on a stack of Nc D5 branes wrapping an S^2 with the appropriate twist, while the…
We construct a combinatorial invariant of 3-orbifolds with singular set a link that generalizes the Turaev torsion invariant of 3-manifolds. We give several gluing formulas from which we derive two consequences. The first is an…
We construct ten-dimensional supergravity solutions corresponding to the near horizon limit of IIB fivebranes wrapping special Lagrangian three-cycles of constant curvature. The case of branes wrapping a three-sphere provides a gravity dual…
We consider the $U(1) ^{n}$ extension of the effective $\mathcal{N}=2$ supersymmetric $U(1) \times U(1) $ model of $arXiv:1204.2141$; and study the explicit relationship between partial breaking of $\mathcal{N}=2$ supersymmetry constraint…
When can one 3-manifold be transformed to another by a finite sequence of Dehn surgeries which are restricted to preserve the first homology of the manifolds ? What is the resulting equivalence relation on 3-manifolds ? What if the surgery…
Topological gauge theories in four dimensions which admit surface operators provide a natural framework for realizing homological knot invariants. Every such theory leads to an action of the braid group on branes on the corresponding moduli…
In the work we discuss two invariants of conjugacy classes of braids. The first invariant is the conformal module which occurred in connection with the interest in the 13th Hilbert Problem. The second is a popular dynamical invariant, the…
We present an alternative definition for the Goussarov--Habiro filtration of the Z-module freely generated by oriented integral homology 3-spheres, by means of Lagrangian-preserving homology handlebody replacements (LP-surgeries).…
The conifold is a basic example of a noncompact Calabi-Yau threefold that admits a simple flop, and in M-theory, gives rise to a 5d hypermultiplet at low energies, realized by an M2-brane wrapped on the vanishing sphere. We develop a novel…
We derive and study supergravity BPS flow equations for M5 or D3 branes wrapping a Riemann surface. They take the form of novel geometric flows intrinsically defined on the surface. Their dual field-theoretic interpretation suggests the…
We introduce the notion of infinitesimal variations of mixed Hodge structures and invariants associated to them. We describe these invariants in the case of a pair $(X,Y)$ with $X$ a Fano 3-fold and $Y$ a smooth anticanonical K3 surface and…
We find further evidence for the conjecture relating large N Chern-Simons theory on S^3 with topological string on the resolved conifold geometry by showing that the Wilson loop observable of a simple knot on S^3 (for any representation)…
We extend Matveev's complexity of 3-manifolds to PL compact manifolds of arbitrary dimension, and we study its properties. The complexity of a manifold is the minimum number of vertices in a simple spine. We study how this quantity changes…
The type IIB supergravity solution describing a collection of regular and fractional D3 branes on the conifold (hep-th/0002159) was recently generalized to the case of the deformed conifold (hep-th/0007191). Here we present another…
We investigate further on the correspondence between branes on a Calabi-Yau in the large volume limit and in the orbifold limit. We conjecture a new procedure which improves computationally the McKay correspondence and prove it in a non…