Results 1  10
of
39
Stability structures, motivic DonaldsonThomas invariants and cluster transformations
, 2008
"... ..."
Wall crossing in local Calabi Yau manifolds
, 2008
"... We study the BPS states of a D6brane wrapping the conifold and bound to collections of D2 and D0 branes. We find that in addition to the complexified Kähler parameter of the rigid P 1 it is necessary to introduce an extra real parameter to describe BPS partition functions and marginal stability wa ..."
Abstract

Cited by 47 (3 self)
 Add to MetaCart
We study the BPS states of a D6brane wrapping the conifold and bound to collections of D2 and D0 branes. We find that in addition to the complexified Kähler parameter of the rigid P 1 it is necessary to introduce an extra real parameter to describe BPS partition functions and marginal stability walls. The supergravity approach to BPS statecounting gives a simple derivation of results of Szendrői concerning DonaldsonThomas theory on the noncommutative conifold. This example also illustrates some interesting limitations on the supergravity approach to BPS statecounting and wallcrossing.
Crystal Melting and Toric CalabiYau Manifolds
"... We construct a statistical model of crystal melting to count BPS bound states of D0 and D2 branes on a single D6 brane wrapping an arbitrary toric CalabiYau threefold. The threedimensional crystalline structure is determined by the quiver diagram and the brane tiling which characterize the low ene ..."
Abstract

Cited by 30 (7 self)
 Add to MetaCart
(Show Context)
We construct a statistical model of crystal melting to count BPS bound states of D0 and D2 branes on a single D6 brane wrapping an arbitrary toric CalabiYau threefold. The threedimensional crystalline structure is determined by the quiver diagram and the brane tiling which characterize the low energy effective theory of D branes. The crystal is composed of atoms of different colors, each of which corresponds to a node of the quiver diagram, and the chemical bond is dictated by the arrows of the quiver diagram. BPS states are constructed by removing atoms from the crystal. This generalizes the earlier results on the BPS state counting to an arbitrary noncompact toric CalabiYau manifold. We point out that a proper understanding of the relation between the topological In type IIA superstring theory, supersymmetric bound states of D branes wrapping holomorphic cycles on a CalabiYau manifold give rise to BPS particles in four dimensions. In the past few years, remarkable connections have been found between the counting of such bound states and the topological string theory:
Hilbert schemes and stable pairs: GIT and derived category wall crossings
, 903
"... Abstract. We show that the Hilbert scheme of curves and Le Potier’s moduli space of stable pairs with one dimensional support have a common GIT construction. The two spaces correspond to chambers on either side of a wall in the space of GIT linearisations. We explain why this is not enough to prove ..."
Abstract

Cited by 22 (1 self)
 Add to MetaCart
Abstract. We show that the Hilbert scheme of curves and Le Potier’s moduli space of stable pairs with one dimensional support have a common GIT construction. The two spaces correspond to chambers on either side of a wall in the space of GIT linearisations. We explain why this is not enough to prove the “DT/PT wall crossing conjecture ” relating the invariants derived from these moduli spaces when the underlying variety is a 3fold. We then give a gentle introduction to a small part of Joyce’s theory for such wall crossings, and use it to give a short proof of an identity relating the Euler characteristics of these moduli spaces. When the 3fold is CalabiYau the identity is the Eulercharacteristic analogue of the DT/PT wall crossing conjecture, but for general 3folds it is something different, as we discuss.
Wall Crossing of BPS States on the Conifold from Seiberg Duality and Pyramid Partitions
, 810
"... Abstract: In this paper we study the relation between pyramid partitions with a general empty room configuration (ERC) and the BPS states of Dbranes on the resolved conifold. We find that the generating function for pyramid partitions with a length n ERC is exactly the same as the D6/D2/D0 BPS part ..."
Abstract

Cited by 16 (1 self)
 Add to MetaCart
(Show Context)
Abstract: In this paper we study the relation between pyramid partitions with a general empty room configuration (ERC) and the BPS states of Dbranes on the resolved conifold. We find that the generating function for pyramid partitions with a length n ERC is exactly the same as the D6/D2/D0 BPS partition function on the resolved conifold in particular Kähler chambers. We define a new type of pyramid partition with a finite ERC that counts the BPS degeneracies in certain other chambers. The D6/D2/D0 partition functions in different chambers were obtained by applying the wall crossing formula. On the other hand, the pyramid partitions describe T 3 fixed points of the moduli space of a quiver quantum mechanics. This quiver arises after we apply Seiberg dualities to the D6/D2/D0 system on the conifold and choose a particular set of FI parameters. The arrow structure of the dual quiver is confirmed by computation of the Ext group between the sheaves. We show that the superpotential and the stability condition of the dual quiver with this choice of the FI parameters give rise to the rules specifying pyramid partitions with length n ERC.
Wall crossing and Mtheory
, 2009
"... We study BPS bound states of D0 and D2 branes on a single D6 brane wrapping a CalabiYau 3fold X. When X has no compact 4cyles, the BPS bound states are organized into a free field Fock space, whose generators correspond to BPS states of spinning M2 branes in Mtheory compactified down to 5 dimens ..."
Abstract

Cited by 12 (5 self)
 Add to MetaCart
We study BPS bound states of D0 and D2 branes on a single D6 brane wrapping a CalabiYau 3fold X. When X has no compact 4cyles, the BPS bound states are organized into a free field Fock space, whose generators correspond to BPS states of spinning M2 branes in Mtheory compactified down to 5 dimensions by a CalabiYau 3fold X. The generating function of the Dbrane bound states is expressed as a reduction of the square of the topological string
Wallcrossing of D4D2D0 and flop of the conifold
 JHEP 09 (2010) 026, arXiv:1007.2731 [hepth
"... ar ..."
(Show Context)
Curve counting theories via stable objects II: DT/ncDT/flop formula
, 2009
"... The goal of the present paper is to show the transformation formula of DonaldsonThomas invariants on smooth projective CalabiYau 3folds under birational transformations via categorical method. We also generalize the noncommutative DonaldsonThomas invariants, introduced by B. Szendrői in a local ..."
Abstract

Cited by 12 (6 self)
 Add to MetaCart
(Show Context)
The goal of the present paper is to show the transformation formula of DonaldsonThomas invariants on smooth projective CalabiYau 3folds under birational transformations via categorical method. We also generalize the noncommutative DonaldsonThomas invariants, introduced by B. Szendrői in a local (−1, −1)curve example, to an arbitrary flopping contraction from a smooth projective CalabiYau 3fold. The transformation formula between such invariants and the usual DonaldsonThomas invariants are also established. These formulas will be deduced from the wallcrossing formula in the space of weak stability conditions on the derived category.