821 research outputs found
Stability and Fourier-Mukai Transforms on Higher Dimensional Elliptic Fibrations
We consider elliptic fibrations with arbitrary base dimensions, and
generalise previous work by the second author. In particular, we check
universal closedness for the moduli of semistable objects with respect to a
polynomial stability that reduces to PT-stability on threefolds. We also show
openness of this polynomial stability. On the other hand, we write down
criteria under which certain 2-term polynomial semistable complexes are mapped
to torsion-free semistable sheaves under a Fourier-Mukai transform. As an
application, we construct an open immersion from a moduli of complexes to a
moduli of Gieseker stable sheaves on higher dimensional elliptic fibrations.Comment: 26 pages. Minor corrections. To appear in Comm. Anal. Geo
The higher rank local categorical DT/PT correspondence
In this paper we derive the higher rank local DT/PT models via the perverse
coherent systems on the resolved conifold and the extended ADHM quiver, as
critical loci. We generalize the categorical DT/PT correspondence by
P\u{a}durariu and Toda to higher ranks and obtain the categorical wallcrossing
formula as semiorthogonal decompositions.Comment: 15 pages. v2: presentation shortened. Comments are welcom
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Geometric Transitions, Topological Strings, and Generalized Complex Geometry
Mirror symmetry is one of the most beautiful symmetries in string theory. It helps us very effectively gain insights into non-perturbative worldsheet instanton effects. It was also shown that the study of mirror symmetry for Calabi-Yau flux compactification leads us to the territory of ''Non-Kaehlerity''. In this thesis we demonstrate how to construct a new class of symplectic non-Kaehler and complex non-Kaehler string theory vacua via generalized geometric transitions. The class admits a mirror pairing by construction. From a variety of sources, including super-gravity analysis and KK reduction on SU(3) structure manifolds, we conclude that string theory connects Calabi-Yau spaces to both complex non-Kaehler and symplectic non-Kaehler manifolds and the resulting manifolds lie in generalized complex geometry. We go on to study the topological twisted models on a class of generalized complex geometry, bi-Hermitian geometry, which is the most general target space for (2, 2) world-sheet theory with non-trivial H flux turned on. We show that the usual Kaehler A and B models are generalized in a natural way. Since the gauged supergravity is the low energy effective theory for the compactifications on generalized geometries, we study the fate of flux-induced isometry gauging in N = 2 IIA and heterotic strings under non-perturbative instanton effects. Interestingly, we find we have protection mechanisms preventing the corrections to the hyper moduli spaces. Besides generalized geometries, we also discuss the possibility of new NS-NS fluxes in a new doubled formalism
Geometric engineering of (framed) BPS states
BPS quivers for N=2 SU(N) gauge theories are derived via geometric
engineering from derived categories of toric Calabi-Yau threefolds. While the
outcome is in agreement of previous low energy constructions, the geometric
approach leads to several new results. An absence of walls conjecture is
formulated for all values of N, relating the field theory BPS spectrum to large
radius D-brane bound states. Supporting evidence is presented as explicit
computations of BPS degeneracies in some examples. These computations also
prove the existence of BPS states of arbitrarily high spin and infinitely many
marginal stability walls at weak coupling. Moreover, framed quiver models for
framed BPS states are naturally derived from this formalism, as well as a
mathematical formulation of framed and unframed BPS degeneracies in terms of
motivic and cohomological Donaldson-Thomas invariants. We verify the
conjectured absence of BPS states with "exotic" SU(2)_R quantum numbers using
motivic DT invariants. This application is based in particular on a complete
recursive algorithm which determine the unframed BPS spectrum at any point on
the Coulomb branch in terms of noncommutative Donaldson-Thomas invariants for
framed quiver representations.Comment: 114 pages; v2:minor correction
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