598 research outputs found
HOMFLY polynomials, stable pairs and motivic Donaldson-Thomas invariants
Hilbert scheme topological invariants of plane curve singularities are
identified to framed threefold stable pair invariants. As a result, the
conjecture of Oblomkov and Shende on HOMFLY polynomials of links of plane curve
singularities is given a Calabi-Yau threefold interpretation. The motivic
Donaldson-Thomas theory developed by M. Kontsevich and the third author then
yields natural motivic invariants for algebraic knots. This construction is
motivated by previous work of V. Shende, C. Vafa and the first author on the
large duality derivation of the above conjecture.Comment: 59 pages; v2 references added, minor corrections; v3: exposition
improved, proofs expanded, results unchanged, to appear in Comm. Num. Th.
Phy
Freed-Witten anomaly in general flux compactification
Turning on a NS-NS three-form flux in a compact space drives some D-branes to
be either Freed-Witten anomalous or unstable to decay into fluxes by the
appearance of instantonic branes. By applying T-duality on a toroidal
compactification, the NS-flux is transformed into metric fluxes. We propose a
T-dual version of the Atiyah-Hirzebruch Spectral Sequence upon which we
describe the Freed-Witten anomaly and the brane-flux transition driven by NS
and metric fluxes in a twisted torus. The required conditions to cancel the
anomaly and the appearance of new instantonic branes are also described. In
addition, we give an example in which all D6-branes wrapping Freed-Witten
anomaly-free three-cycles in the twisted torus T^6/Z(2)XZ(2) are nevertheless
unstable to be transformed into fluxes. Evenmore we find a topological
transformation between RR, NS-NS and metric fluxes driven by a chain of
instantonic branes.Comment: v3: Shortened version. Examples added. Main results unchange
Domain Walls on Singularities
We describe domain walls that live on and singularities. The
walls are BPS if the singularity is resolved and non--BPS if it is deformed and
fibered. We show that these domain walls may interpolate between vacua that
support monopoles and/or vortices.Comment: 16 pages in phyzzx.te
Duality symmetry and the form fields of M-theory
In previous work we derived the topological terms in the M-theory action in
terms of certain characters that we defined. In this paper, we propose the
extention of these characters to include the dual fields. The unified treatment
of the M-theory four-form field strength and its dual leads to several
observations. In particular we elaborate on the possibility of a twisted
cohomology theory with a twist given by degrees greater than three.Comment: 12 pages, modified material on the differentia
Large N Duality, Lagrangian Cycles, and Algebraic Knots
We consider knot invariants in the context of large N transitions of topological strings. In particular we consider aspects of Lagrangian cycles associated to knots in the conifold geometry. We show how these can be explicitly constructed in the case of algebraic knots. We use this explicit construction to explain a recent conjecture relating study of stable pairs on algebraic curves with HOMFLY polynomials. Furthermore, for torus knots, using the explicit construction of the Lagrangian cycle, we also give a direct A-model computation and recover the HOMFLY polynomial for this case.Engineering and Physical Sciences Research CouncilSimons Foundatio
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