MPS degeneration formula for quiver moduli and refined GW/Kronecker correspondence

Reineke, Markus; Stoppa, Jacopo; Weist, Thorsten

doi:10.2140/gt.2012.16.2097

Cited by 24 publications

(43 citation statements)

References 21 publications

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“…Wall-crossing. It was shown in §4.1 and §5.4 of [9] that the Coulomb branch formula satisfies the wall-crossing formula given in [14] (and further elaborated in [19][20][21]), provided the single-centered invariants Ω S (γ) stay constant across the wall.…”

Section: Aspects Of the Coulomb Branch Formulamentioning

confidence: 85%

The Coulomb Branch Formula for Quiver Moduli Spaces

Manschot¹,

Pioline²,

Sen³

2017

Confluentes Mathematici

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In recent series of works, by translating properties of multi-centered supersymmetric black holes into the language of quiver representations, we proposed a formula that expresses the Hodge numbers of the moduli space of semi-stable representations of quivers with generic superpotential in terms of a set of invariants associated to `single-centered' or `pure-Higgs' states. The distinguishing feature of these invariants is that they are independent of the choice of stability condition. Furthermore they are uniquely determined by the $\chi_y$-genus of the moduli space. Here, we provide a self-contained summary of the Coulomb branch formula, spelling out mathematical details but leaving out proofs and physical motivations.Comment: 24 pages. v2: final version; minor changes, including a new diagra

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Section: Aspects Of the Coulomb Branch Formulamentioning

confidence: 85%

The Coulomb Branch Formula for Quiver Moduli Spaces

Manschot¹,

Pioline²,

Sen³

2017

Confluentes Mathematici

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“…In order to determine a formula for the Euler characteristic of Kronecker moduli space, it is useful to reduce it to a sum of Euler characteristics of simpler spaces. This is achieved with the MPS degeneration formula [38] (see also [39]).…”

Section: The Degeneration Formula and Star Quiversmentioning

confidence: 99%

Counting trees in supersymmetric quantum mechanics

Córdova

Shao

2018

Ann. Inst. Henri Poincaré Comb. Phys. Interact.

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We study the supersymmetric ground states of the Kronecker model of quiver quantum mechanics. This is the simplest quiver with two gauge groups and bifundamental matter fields, and appears universally in four-dimensional N = 2 systems. The ground state degeneracy may be written as a multi-dimensional contour integral, and the enumeration of poles can be simply phrased as counting bipartite trees. We solve this combinatorics problem, thereby obtaining exact formulas for the degeneracies of an infinite class of models. We also develop an algorithm to compute the angular momentum of the ground states, and present explicit expressions for the refined indices of theories where one rank is small.

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“…In order to compare the exact answer (4.8) with the prediction from the Coulomb branch formula (3.6), a crucial fact is that the stack invariants (4.9) with arbitrary dimensions {M } can all be computed in terms of stack invariants of Abelian quivers, a property known as the Abelianization (or MPS) formula [15,17] …”

Section: Quivers Without Loopsmentioning

confidence: 99%

“…While being equivalent to the original wall-crossing formulae of [8,9], its structure is completely different and has already led to a number of new mathematical insights on DT invariants [17,18] (see [19] for an earlier review of wall-crossing, with a different emphasis).…”

Section: Introductionmentioning

confidence: 99%

Wall-crossing, Black holes, and Quivers

Pioline¹

2013

Proceedings of Proceedings of the Corfu Summer Institute 2012 — PoS(Corfu2012)

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The BPS state spectrum in four-dimensional gauge theories or string vacua with N = 2 supersymmetries is well known to depend on the values of the parameters or moduli at spatial infinity. The BPS index is locally constant, but discontinuous across real codimension-one walls where some of the BPS states decay. By postulating that BPS states are bound states of more elementary constituents carrying their own degrees of freedom and interacting via supersymmetric quantum mechanics, we provide a physically transparent derivation of the universal wall-crossing formula which governs the jump of the index. The same physical picture suggests that at any point in moduli space, the total index can be written as a sum of contributions from all possible bound states of elementary, absolutely stable constituents with the same total charge. For D-brane bound states described by quivers, this 'Coulomb branch formula' predicts that the cohomology of quiver moduli spaces is uniquely determined by certain 'pure-Higgs' invariants, which are the microscopic analogues of single-centered black holes. These lectures are based on joint work with J. Manschot and A. Sen.

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MPS degeneration formula for quiver moduli and refined GW/Kronecker correspondence

Cited by 24 publications

References 21 publications

The Coulomb Branch Formula for Quiver Moduli Spaces

The Coulomb Branch Formula for Quiver Moduli Spaces

Counting trees in supersymmetric quantum mechanics

Wall-crossing, Black holes, and Quivers

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