Attractor invariants, brane tilings and crystals

Mozgovoy, Sergey; Pioline, Boris

doi:10.48550/arxiv.2012.14358

Cited by 13 publications

(37 citation statements)

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“…The above compatibility means that it is enough to know stability data A Q,W Z for some Z in order to determine stability data A σ for all special geometric stability conditions σ. A complete (conjectural) description of stability data A Q,W Z exists for P 2 and other surfaces [8,55]. It is fully verified for small dimension vectors.…”

Section: Scattering Diagrammentioning

confidence: 64%

“…This implies that knowing stability data on D b (mod J W ), we can reconstruct stability data on D b (Coh X). A complete (but still conjectural except for low dimension vectors) description of stability data on D b (mod J W ) was given in [8,55]. A partial description of stability data on D b (Coh X) was given in [12] (the scattering diagram used there captures a significant, but incomplete information about the stability data).…”

Section: Stability Conditions On Surfacesmentioning

confidence: 99%

“…It should be not difficult to generalize our results to other del Pezzo surfaces. A complete (conjectural) description of stability data for D b (mod J W ) is also available in this case [8,55].…”

Section: Stability Conditions On Surfacesmentioning

confidence: 99%

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Wall-crossing structures on surfaces

Mozgovoy¹

2022

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Families of Bridgeland stability conditions induce families of stability data, wall-crossing structures and scattering diagrams on the motivic Hall algebra. These structures can be transferred to the quantum torus if the stability conditions of the family have global dimension at most 2. We show that geometric stability conditions on surfaces with nef anticanonical bundle have global dimension 2 and we study the resulting family of stability data. We formulate a conjecture relating this family to the family of stability data associated with a quiver with potential and we verify this conjecture for the projective plane. SERGEY MOZGOVOY MotivicHall algebra of an exact category 5.3. Wall-crossing in the Hall algebra 5.4. Wall-crossing in the quantum torus 5.5. Stability data associated to a stability condition 5.6. Families of stability data and stability conditions 6. Stability conditions on surfaces 6.1. Some conventions 6.2. Construction of stability conditions 6.3. Cone of positive planes 6.4. Geometric stability conditions 6.5. Gieseker and twisted stability 6.6. Large volume limit 6.7. Bogomolov-type inequalities 6.8. Alternative parametrization of stability conditions 7. Stability data associated to geometric stability conditions 7.1. Vanishing results 7.2. Geometric stability data 7.3. Relation to intersection cohomology 8. Relation to quivers with potentials 8.1. Exceptional collections and tilting objects 8.2. Local surfaces 8.3. Relation to quiver representations 8.4. Quivers with potential and their motivic invariants 8.5. Relating stability data 8.6. Gluing families of stability data References

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Section: Scattering Diagrammentioning

confidence: 64%

Section: Stability Conditions On Surfacesmentioning

confidence: 99%

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Wall-crossing structures on surfaces

Mozgovoy¹

2022

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“…Interestingly our partition function agrees with a theorem of [23] according to which the MacMahon factor in front is not a square of the same refinement; and also agrees with the result physical expectation that such partition functions should have coefficients which are linear combinations of SU (N ) characters. Note however that the differences between the partition functions can all be traced to the ambiguity of defining the MacMahon, arising from the non-compactness of the moduli space, see [25] for a recent discussion. Furthermore our result depends explicitly on the torus chosen to take the refined limit.…”

Section: Refined and Unrefined Limitsmentioning

confidence: 99%

“…In this note we study K-theoretic Donaldson-Thomas theory defined on noncommutative crepant resolutions of Calabi-Yau singularities as a model for the M2-brane index in M-theory. Recent progress in K-theoretic countings of BPS states have been made in the contest of smooth geometries and fourfolds [2,3,12,13,16,19,25,29,31,34] as well as defects in quantum field theory [5].…”

Section: Introductionmentioning

confidence: 99%

On the M2-Brane Index on Noncommutative Crepant Resolutions

Cirafici¹

2021

Preprint

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On certain M-theory backgrounds which are a circle fibration over a smooth Calabi-Yau the quantum theory of M2 branes can be studied in terms of the K-theoretic Donaldson-Thomas theory on the threefold. We extend this relation to noncommutative crepant resolutions. In this case the threefold develops a singularity and classical smooth geometry is replaced by the algebra of paths of a certain quiver. K-theoretic quantities on the quiver representation moduli space can be computed via toric localization and result in certain rational functions of the toric parameters. We discuss in particular the case of the conifold and certain orbifold singularities.

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Seiberg-Witten geometry, modular rational elliptic surfaces and BPS quivers

Magureanu

2022

J. High Energ. Phys.

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We study the Coulomb branches of four-dimensional supersymmetric quantum field theories with $$ \mathcal{N} $$ N = 2 supersymmetry, including the KK theories obtained from the circle compactification of the 5d $$ \mathcal{N} $$ N = 1 En Seiberg theories, with particular focus on the relation between their Seiberg-Witten geometries and rational elliptic surfaces. More attention is given to the modular surfaces, which we completely classify using the classification of subgroups of the modular group PSL(2, ℤ), deriving closed-form expressions for the modular functions for all congruence and some of the non-congruence subgroups. Moreover, in such cases, we give a prescription for determining the BPS quivers from the fundamental domains of the monodromy groups and study how changes of these domains can be interpreted as quiver mutations. This prescription can be also generalized to theories whose Coulomb branches contain ‘undeformable’ singularities, leading to known quivers of such theories.

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Attractor invariants, brane tilings and crystals

Cited by 13 publications

References 0 publications

Wall-crossing structures on surfaces

Wall-crossing structures on surfaces

On the M2-Brane Index on Noncommutative Crepant Resolutions

Seiberg-Witten geometry, modular rational elliptic surfaces and BPS quivers

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