BPS Hall algebra of scattering Hall states

Galakhov, Dmitry

doi:10.1016/j.nuclphysb.2019.114693

Cited by 15 publications

(17 citation statements)

References 141 publications

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“…While cohomological Hall algebras for JHEP11(2020)035 C 3 are known [28], it seems to be difficult to generalize the discussion to a larger class of Calabi-Yau threefolds, and we hope that our work will shed some light on this problem (see [75][76][77][78] for examples of recent studies of cohomological Hall algebras). Note also that the cohomological Hall algebra was recently discussed in the language of supersymmetric quiver quantum mechanics, which is closely related to the approach of this paper [79].…”

Section: Jhep11(2020)035mentioning

confidence: 81%

Quiver Yangian from crystal melting

Yamazaki

2020

J. High Energ. Phys.

200

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We find a new infinite class of infinite-dimensional algebras acting on BPS states for non-compact toric Calabi-Yau threefolds. In Type IIA superstring compactification on a toric Calabi-Yau threefold, the D-branes wrapping holomorphic cycles represent the BPS states, and the fixed points of the moduli spaces of BPS states are described by statistical configurations of crystal melting. Our algebras are “bootstrapped” from the molten crystal configurations, hence they act on the BPS states. We discuss the truncation of the algebra and its relation with D4-branes. We illustrate our results in many examples, with and without compact 4-cycles.

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Section: Jhep11(2020)035mentioning

confidence: 81%

Quiver Yangian from crystal melting

Yamazaki

2020

J. High Energ. Phys.

200

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“…It would be very interesting to work out the details and understand the relation with the cohomological Hall algebra of [29]. In this respect an intermediate step would be to understand the relation between our construction and [26].…”

Section: Discussionmentioning

confidence: 99%

Quantum line defects and refined BPS spectra

Cirafici

2019

Lett Math Phys

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In this note we study refined BPS invariants associated with certain quantum line defects in quantum field theories of class S. Such defects can be specified via geometric engineering in the UV by assigning a path on a certain curve. In the IR they are described by framed BPS quivers. We study the associated BPS spectral problem, including the spin content. The relevant BPS invariants arise from the K-theoretic enumerative geometry of the moduli spaces of quiver representations, adapting a construction by Nekrasov and Okounkov. In particular refined framed BPS states are described via Euler characteristics of certain complexes of sheaves.

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“…In what follows we will construct a shuffle algebra Sh(Q) associated to a quiver Q following [69]. It will be natural to identify this algebra with an algebra of the Coulomb branch, similar to the one constructed in [70], whereas the BPS algebra constructed in section 4.2 can be called an algebra of the Higgs branch (since we performed the localization with respect to the Higgs branch of our quantum field theory). A generic approach to localization dictates that both ways of localization are expected to give isomorphic Hilbert spaces of BPS states, and this observation is referred to as the Higgs-Coulomb duality in the literature.…”

Section: Jhep02(2022)024mentioning

confidence: 99%

Toroidal and elliptic quiver BPS algebras and beyond

Galakhov

Yamazaki

2022

J. High Energ. Phys.

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The quiver Yangian, an infinite-dimensional algebra introduced recently in [1], is the algebra underlying BPS state counting problems for toric Calabi-Yau three-folds. We introduce trigonometric and elliptic analogues of quiver Yangians, which we call toroidal quiver algebras and elliptic quiver algebras, respectively. We construct the representations of the shifted toroidal and elliptic algebras in terms of the statistical model of crystal melting. We also derive the algebras and their representations from equivariant localization of three-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric quiver gauge theories, and their dimensionally-reduced counterparts. The analysis of supersymmetric gauge theories suggests that there exist even richer classes of algebras associated with higher-genus Riemann surfaces and generalized cohomology theories.

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BPS Hall algebra of scattering Hall states

Cited by 15 publications

References 141 publications

Quiver Yangian from crystal melting

Quiver Yangian from crystal melting

Quantum line defects and refined BPS spectra

Toroidal and elliptic quiver BPS algebras and beyond

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