Article

# Derived categories of small toric Calabi-Yau 3-folds and counting invariants

09/2008;

Source: arXiv

- [Show abstract] [Hide abstract]

**ABSTRACT:**Using the compatibility of the anomalous Chern-Simons couplings on D p -branes with the linear T-duality and with the antisymmetric B-field gauge transformations, some couplings have been recently found for C (p−3) at order O(α′2). We examine these couplings with the S-matrix element of one RR and two antisymmetric B-field vertex operators. We find that the S-matrix element reproduces these couplings as well as some other couplings. Each of them is invariant under the linear T-duality and the B-field gauge transformations.Journal of High Energy Physics 02/2011; 2011(5):1-29. · 6.22 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**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.Advances in Theoretical and Mathematical Physics 01/2013; · 1.78 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper, we study the Bogomolny-Prasad-Sommerfeld (BPS) state counting in the geometry of local obstructed curve with normal bundle O⊕O(−2). We find that the BPS states have a framed quiver description. Using this quiver description along with the Seiberg duality and the localization techniques, we can compute the BPS state indices in different chambers dictated by stability parameter assignments. This provides a well-defined method to compute the generalized Donaldson–Thomas invariants. This method can be generalized to other affine ADE quiver theories.Journal of Mathematical Physics 05/2010; 51(5):052305-052305-22. · 1.18 Impact Factor

Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.