pith. sign in

arxiv: 1907.02771 · v1 · pith:4JOTJ55Unew · submitted 2019-07-05 · ✦ hep-th · math-ph· math.AG· math.MP

Defects, nested instantons and comet shaped quivers

Giulio Bonelli , Nadir Fasola , Alessandro Tanzini This is my paper

Pith reviewed 2026-05-25 02:15 UTC · model grok-4.3

classification ✦ hep-th math-phmath.AGmath.MP
keywords surface defectsnested instantonsquiver gauge theorieselliptic genusnested Hilbert schemesD-branesCalabi-Yau threefoldsparabolic reduction
0
0 comments X

The pith

D3/D7-branes on T² × T*C_{g,k} engineer comet-shaped quiver theories whose elliptic genera count nested instantons on surface defects.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes that a surface defect supporting nested instantons, defined via parabolic reduction of the gauge group, arises from a D3/D7-brane configuration on a non-compact Calabi-Yau threefold. When the threefold is T² times the cotangent bundle of a marked Riemann surface C_{g,k}, the low-volume limit on C_{g,k} yields an effective description as a comet-shaped quiver gauge theory living on T². The tails of the comet are flag quivers, one per marked point, while the head encodes the genus-g degrees of freedom. For a single D7-brane this produces explicit conjectural expressions for the virtual equivariant elliptic genus of a bundle over the moduli space of the nested Hilbert scheme of points on the affine plane, together with links to elliptic cohomology of character varieties and elliptic analogues of modified Macdonald polynomials.

Core claim

A D3/D7-brane system on the non-compact Calabi-Yau threefold X = T² × T*C_{g,k} engineers a surface defect whose effective dynamics, in the small-volume limit of C_{g,k}, is captured by a comet-shaped quiver gauge theory on T²; the mathematical counterpart for one D7-brane supplies conjectural closed-form expressions for the virtual equivariant elliptic genus of an associated bundle on the nested Hilbert scheme of points in the plane.

What carries the argument

The comet-shaped quiver gauge theory on T², whose tails are flag quivers attached at each marked point of C_{g,k} and whose head encodes the genus-g contribution, which realizes the nested instanton moduli problem with parabolic reduction.

If this is right

  • The elliptic genus formulae give a concrete way to compute the partition function of the surface defect for any number of marked points.
  • The same quiver construction extends the ordinary instanton counting to the nested, parabolic case.
  • The resulting expressions connect the gauge-theory partition function to elliptic cohomology of character varieties.
  • An elliptic deformation of modified Macdonald polynomials appears naturally as the generating function for these counts.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The comet-quiver description may furnish a uniform combinatorial model for parabolic reductions at multiple points simultaneously.
  • Specializing the elliptic parameter to roots of unity could recover known K-theoretic or cohomological invariants of the nested Hilbert scheme.
  • The construction suggests a route to define elliptic versions of more general flag varieties attached to higher-rank parabolic structures.

Load-bearing premise

The D3/D7-brane configuration on the non-compact Calabi-Yau threefold directly engineers the surface defect that supports nested instantons with respect to the parabolic reduction of the gauge group.

What would settle it

An explicit computation, for small numbers of points, of the virtual equivariant elliptic genus of the bundle over the nested Hilbert scheme that fails to match the conjectural formula supplied by the comet quiver would falsify the claim.

read the original abstract

We introduce and study a surface defect in four dimensional gauge theories supporting nested instantons with respect to the parabolic reduction of the gauge group at the defect. This is engineered from a D3/D7-branes system on a non compact Calabi-Yau threefold $X$. For $X=T^2\times T^*{\mathcal C}_{g,k}$, the product of a two torus $T^2$ times the cotangent bundle over a Riemann surface ${\mathcal C}_{g,k}$ with marked points, we propose an effective theory in the limit of small volume of ${\mathcal C}_{g,k}$ given as a comet shaped quiver gauge theory on $T^2$, the tail of the comet being made of a flag quiver for each marked point and the head describing the degrees of freedom due to the genus $g$. Mathematically, we obtain for a single D7-brane conjectural explicit formulae for the virtual equivariant elliptic genus of a certain bundle over the moduli space of the nested Hilbert scheme of points on the affine plane. A connection with elliptic cohomology of character varieties and an elliptic version of modified Macdonald polynomials naturally arises.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 4 minor

Summary. The manuscript introduces surface defects in four-dimensional gauge theories supporting nested instantons with respect to a parabolic reduction of the gauge group at the defect. These are engineered via a D3/D7-brane system on the non-compact Calabi-Yau threefold X = T² × T^*C_{g,k}. In the small-volume limit of C_{g,k}, the authors propose an effective description as a comet-shaped quiver gauge theory on T², with tails given by flag quivers for each marked point and the head capturing genus-g degrees of freedom. For a single D7-brane, they provide conjectural explicit formulae for the virtual equivariant elliptic genus of a certain bundle over the moduli space of the nested Hilbert scheme of points on the affine plane, and note a natural connection to elliptic cohomology of character varieties and an elliptic version of modified Macdonald polynomials.

Significance. If the conjectures hold, the work would supply a brane-engineering route to nested instantons and surface defects, together with explicit formulae linking quiver gauge theories to elliptic genera and modified Macdonald polynomials. The explicit emergence of elliptic cohomology structures is a notable strength that could stimulate further study at the interface of supersymmetric gauge theory and algebraic geometry.

minor comments (4)
  1. [§3] The abstract states the effective theory is 'given as' a comet-shaped quiver but the transition from the D3/D7 system to the specific quiver data (ranks, superpotential, etc.) is presented only heuristically; a short table or diagram in §3 or §4 explicitly matching the brane charges to the quiver nodes would improve readability.
  2. [Mathematical results] The conjectural formulae for the virtual equivariant elliptic genus are stated without an accompanying low-rank numerical check or comparison to known cases (e.g., ordinary instantons when the nesting depth is 1); adding such a consistency test, even if brief, would help readers assess the proposal.
  3. [Introduction] Notation for the 'head' and 'tail' of the comet quiver is introduced without a global diagram; a single figure showing the full quiver for small g and k would clarify the construction.
  4. [References] A few references to prior work on flag quivers and parabolic reductions appear to be missing or cited only indirectly; adding explicit citations to the relevant literature on elliptic genera of Hilbert schemes would strengthen the context.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript and the recommendation for minor revision. The referee's summary accurately captures the main results on comet-shaped quivers, nested instantons, and the conjectural formulae for the virtual equivariant elliptic genus.

Circularity Check

0 steps flagged

No significant circularity; results framed as conjectures from heuristics

full rationale

The paper presents its main results explicitly as proposals and conjectures derived from standard brane-engineering heuristics on D3/D7 systems. The comet quiver construction and virtual elliptic genus formulae are introduced as effective descriptions in a stated small-volume limit, without any claimed rigorous derivation chain. No equations or steps reduce by construction to self-definitions, fitted inputs renamed as predictions, or self-citation load-bearing arguments. The derivation remains self-contained against external benchmarks in the field.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 2 invented entities

Based on abstract only. Main assumptions are the brane engineering of the defect and the small volume limit yielding the quiver description. No explicit free parameters or invented entities with independent evidence are detailed.

axioms (2)
  • domain assumption The D3/D7-branes system on X engineers the surface defect supporting nested instantons with parabolic reduction
    Stated as the engineering method in the abstract.
  • domain assumption In the small volume limit of C_{g,k} the effective theory is the comet shaped quiver gauge theory
    Proposed directly in the abstract for the specific X.
invented entities (2)
  • nested instantons no independent evidence
    purpose: Gauge field configurations supported on the surface defect
    Introduced as the central object of study.
  • comet shaped quiver no independent evidence
    purpose: Effective description of degrees of freedom on T^2
    New gauge theory model proposed for the defect.

pith-pipeline@v0.9.0 · 5735 in / 1665 out tokens · 33077 ms · 2026-05-25T02:15:03.486262+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

75 extracted references · 60 canonical work pages · 52 internal anchors

  1. [1]

    ’t Hooft,A Property of Electric and Magnetic Flux in Nonabelian Gauge Theories, Nucl

    G. ’t Hooft,A Property of Electric and Magnetic Flux in Nonabelian Gauge Theories, Nucl. Phys. B153 (1979) 141

    1979

  2. [2]

    P. B. Kronheimer and T. S. Mrowka,Gauge theory for embedded surfaces, I, Topology 32 (1993) 773

    1993

  3. [3]

    Gauge theory for embedded surfaces, ii

    P. B. Kronheimer and T. S. Mrowka, “Gauge theory for embedded surfaces, ii.”

  4. [4]

    Gauge Theory, Ramification, And The Geometric Langlands Program

    S. Gukov and E. Witten,Gauge Theory, Ramification, And The Geometric Langlands Program, hep-th/0612073

    work page internal anchor Pith review Pith/arXiv arXiv

  5. [5]

    L. F. Alday, D. Gaiotto and Y. Tachikawa,Liouville Correlation Functions from Four-dimensional Gauge Theories, Lett. Math. Phys.91 (2010) 167 [0906.3219]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  6. [6]

    L. F. Alday, D. Gaiotto, S. Gukov, Y. Tachikawa and H. Verlinde,Loop and surface operators in N=2 gauge theory and Liouville modular geometry, JHEP 01 (2010) 113 [0909.0945]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  7. [7]

    BPS/CFT correspondence IV: sigma models and defects in gauge theory

    N. Nekrasov,BPS/CFT correspondence IV: sigma models and defects in gauge theory, Lett. Math. Phys.109 (2019) 579 [1711.11011]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  8. [8]

    Conformal field theory of Painlev\'e VI

    O. Gamayun, N. Iorgov and O. Lisovyy,Conformal field theory of Painlevé VI, JHEP 10 (2012) 038 [1207.0787]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  9. [9]

    On Painlev\'e/gauge theory correspondence

    G. Bonelli, O. Lisovyy, K. Maruyoshi, A. Sciarappa and A. Tanzini,On Painlevé/gauge theory correspondence, 1612.06235

    work page internal anchor Pith review Pith/arXiv arXiv

  10. [10]

    Bonelli, F

    G. Bonelli, F. Del Monte, P. Gavrylenko and A. Tanzini,N = 2∗ gauge theory, free fermions on the torus and Painlevé VI, 1901.10497

    work page arXiv 1901

  11. [11]

    A Strong Coupling Test of S-Duality

    C. Vafa and E. Witten,A Strong coupling test of S duality, Nucl. Phys. B431 (1994) 3 [hep-th/9408074]

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  12. [12]

    S. K. Donaldson and R. P. Thomas,Gauge theory in higher dimensions, inThe geometric universe: Science, geometry, and the work of Roger Penrose. Proceedings, Symposium, Geometric Issues in the Foundations of Science, Oxford, UK, June 25-29, 1996, pp. 31–47, 1996

    1996

  13. [13]

    Multi-Instanton Calculus and Equivariant Cohomology

    U. Bruzzo, F. Fucito, J. F. Morales and A. Tanzini,Multiinstanton calculus and equivariant cohomology, JHEP 05 (2003) 054 [hep-th/0211108]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  14. [14]

    G. W. Moore, N. Nekrasov and S. Shatashvili,D particle bound states and generalized instantons, Commun. Math. Phys.209 (2000) 77 [hep-th/9803265]. – 49 –

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  15. [15]

    Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups

    F. Benini, R. Eager, K. Hori and Y. Tachikawa,Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups, Lett. Math. Phys.104 (2014) 465 [1305.0533]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  16. [16]

    Elliptic genera of 2d N=2 gauge theories

    F. Benini, R. Eager, K. Hori and Y. Tachikawa,Elliptic Genera of 2dN = 2 Gauge Theories, Commun. Math. Phys.333 (2015) 1241 [1308.4896]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  17. [17]

    Benini, G

    F. Benini, G. Bonelli, M. Poggi and A. Tanzini,Elliptic non-Abelian Donaldson-Thomas invariants ofC3, 1807.08482

    work page arXiv

  18. [18]

    Bonelli, A

    G. Bonelli, A. Sciarappa, A. Tanzini and P. Vasko,Vortex partition functions, wall crossing and equivariant Gromov-Witten invariants, Commun. Math. Phys.333 (2015) 717 [1307.5997]

    work page arXiv 2015

  19. [19]

    S. K. Ashok, S. Ballav, M. Billó, E. Dell’Aquila, M. Frau, V. Gupta et al.,Surface operators, dual quivers and contours, Eur. Phys. J.C79 (2019) 278 [1807.06316]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  20. [20]

    Hausel, E

    T. Hausel, E. Letellier and F. Rodriguez-Villegas,Arithmetic harmonic analysis on character and quiver varieties, Duke Math. J.160 (2011) 323

    2011

  21. [21]

    Parabolic refined invariants and Macdonald polynomials

    W.-y. Chuang, D.-E. Diaconescu, R. Donagi and T. Pantev,Parabolic refined invariants and Macdonald polynomials, Commun. Math. Phys.335 (2015) 1323 [1311.3624]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  22. [22]

    Topological Reduction of 4D SYM to 2D $\sigma$--Models

    M. Bershadsky, A. Johansen, V. Sadov and C. Vafa,Topological reduction of 4-d SYM to 2-d sigma models, Nucl. Phys. B448 (1995) 166 [hep-th/9501096]

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  23. [23]

    C. T. Simpson,Harmonic bundles on noncompact curves, Journal of the American Mathematical Society 3 (1990) 713

    1990

  24. [24]

    Donaldson-Thomas theory for Calabi-Yau 4-folds

    Y. Cao and N. Conan Leung,Donaldson-Thomas theory for Calabi-Yau 4-folds, arXiv e-prints (2014) arXiv:1407.7659 [1407.7659]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  25. [25]

    Zero-dimensional Donaldson-Thomas invariants of Calabi-Yau 4-folds

    Y. Cao and M. Kool,Zero-dimensional Donaldson-Thomas invariants of Calabi-Yau 4-folds, Adv. Math. 338 (2018) 601 [1712.07347]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  26. [26]

    A. Sen,String field theory and self-dual forms, talk at ggi conference string field theory and string perturbation theory, https://agenda.infn.it/event/18134/contributions/88472/attachments/62847/75516/ggisft.pdf, 2019

    2019

  27. [27]

    Tachyon Condensation on the Brane Antibrane System

    A. Sen,Tachyon condensation on the brane anti-brane system, JHEP 08 (1998) 012 [hep-th/9805170]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  28. [28]

    Nekrasov,Localizing gauge theories,

    N. Nekrasov,Localizing gauge theories,

  29. [29]

    Exact results for ${\cal N}=2$ supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants

    M. Bershtein, G. Bonelli, M. Ronzani and A. Tanzini,Exact results forN = 2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants, JHEP 07 (2016) 023 [1509.00267]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  30. [30]

    Gauge theories on compact toric surfaces, conformal field theories and equivariant Donaldson invariants

    M. Bershtein, G. Bonelli, M. Ronzani and A. Tanzini,Gauge theories on compact toric surfaces, conformal field theories and equivariant Donaldson invariants, J. Geom. Phys. 118 (2017) 40 [1606.07148]. – 50 –

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  31. [31]

    The Donaldson-Witten function for gauge groups of rank larger than one

    M. Marino and G. W. Moore,The Donaldson-Witten function for gauge groups of rank larger than one, Commun. Math. Phys.199 (1998) 25 [hep-th/9802185]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  32. [32]

    Donaldson invariants of product ruled surfaces and two-dimensional gauge theories

    C. Lozano and M. Marino,Donaldson invariants of product ruled surfaces and two-dimensional gauge theories, Commun. Math. Phys.220 (2001) 231 [hep-th/9907165]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  33. [33]

    Vafa-Witten theory and iterated integrals of modular forms

    J. Manschot,Vafa-Witten theory and iterated integrals of modular forms, 1709.10098

    work page internal anchor Pith review Pith/arXiv arXiv

  34. [34]

    Wild Quiver Gauge Theories

    G. Bonelli, K. Maruyoshi and A. Tanzini,Wild Quiver Gauge Theories, JHEP 02 (2012) 031 [1112.1691]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  35. [35]

    G. W. Moore and I. Nidaiev,The Partition Function Of Argyres-Douglas Theory On A Four-Manifold, 1711.09257

    work page internal anchor Pith review Pith/arXiv arXiv

  36. [36]

    Nakajima,Instantons on ale spaces, quiver varieties, and kac-moody algebras, Duke Math

    H. Nakajima,Instantons on ale spaces, quiver varieties, and kac-moody algebras, Duke Math. J.76 (1994) 365

    1994

  37. [37]

    Schiffmann and E

    O. Schiffmann and E. Vasserot,Cherednik algebras, w-algebras and the equivariant cohomology of the moduli space of instantons on a2, Publications mathématiques de l’IHÉS 118 (2013) 213

    2013

  38. [38]

    Quantum Groups and Quantum Cohomology

    D. Maulik and A. Okounkov,Quantum Groups and Quantum Cohomology, arXiv e-prints (2012) arXiv:1211.1287 [1211.1287]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  39. [39]

    Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics

    G. Bonelli, A. Sciarappa, A. Tanzini and P. Vasko,Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics, JHEP 07 (2014) 141 [1403.6454]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  40. [40]

    Quantum Cohomology and Quantum Hydrodynamics from Supersymmetric Quiver Gauge Theories

    G. Bonelli, A. Sciarappa, A. Tanzini and P. Vasko,Quantum Cohomology and Quantum Hydrodynamics from Supersymmetric Quiver Gauge Theories, J. Geom. Phys. 109 (2016) 3 [1505.07116]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  41. [41]

    D-Branes and Topological Field Theories

    M. Bershadsky, C. Vafa and V. Sadov,D-branes and topological field theories, Nucl. Phys. B463 (1996) 420 [hep-th/9511222]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  42. [42]

    M. R. Douglas and G. W. Moore,D-branes, quivers, and ALE instantons, hep-th/9603167

    work page internal anchor Pith review Pith/arXiv arXiv

  43. [43]

    Poincare polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces

    U. Bruzzo, R. Poghossian and A. Tanzini,Poincare polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces, Commun. Math. Phys.304 (2011) 395 [0909.1458]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  44. [44]

    D-instanton probes of N=2 non-conformal geometries

    F. Fucito, J. F. Morales and A. Tanzini,D instanton probes of non conformal geometries, JHEP 07 (2001) 012 [hep-th/0106061]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  45. [45]

    D-instantons on orbifolds and gauge/gravity correspondence

    A. Tanzini,D instantons on orbifolds and gauge / gravity correspondence, Fortsch. Phys. 50 (2002) 992 [hep-th/0201102]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  46. [46]

    Instanton counting with a surface operator and the chain-saw quiver

    H. Kanno and Y. Tachikawa,Instanton counting with a surface operator and the chain-saw quiver, JHEP 06 (2011) 119 [1105.0357]. – 51 –

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  47. [47]

    Jeong and N

    S. Jeong and N. Nekrasov,Opers, surface defects, and Yang-Yang functional, 1806.08270

    work page arXiv

  48. [48]

    D-branes, surface operators, and ADHM quiver representations

    U. Bruzzo, W. y. Chuang, D. E. Diaconescu, M. Jardim, G. Pan and Y. Zhang, D-branes, surface operators, and ADHM quiver representations, Adv. Theor. Math. Phys. 15 (2011) 849 [1012.1826]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  49. [49]

    Vertices, Vortices & Interacting Surface Operators

    G. Bonelli, A. Tanzini and J. Zhao,Vertices, Vortices and Interacting Surface Operators, JHEP 06 (2012) 178 [1102.0184]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  50. [50]

    The Liouville side of the Vortex

    G. Bonelli, A. Tanzini and J. Zhao,The Liouville side of the Vortex, JHEP 09 (2011) 096 [1107.2787]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  51. [51]

    T[U(N)] duality webs: mirror symmetry, spectral duality and gauge/CFT correspondences

    A. Nedelin, S. Pasquetti and Y. Zenkevich,T[SU(N)] duality webs: mirror symmetry, spectral duality and gauge/CFT correspondences, JHEP 02 (2019) 176 [1712.08140]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  52. [52]

    On Framed Quivers, BPS Invariants and Defects

    M. Cirafici, On Framed Quivers, BPS Invariants and Defects, 1801.03778

    work page internal anchor Pith review Pith/arXiv arXiv

  53. [53]

    Foda and M

    O. Foda and M. Manabe,Nested coordinate Bethe wavefunctions from the Bethe/gauge correspondence, 1907.00493

    work page arXiv 1907

  54. [54]

    R. A. von Flach and M. Jardim,Moduli spaces of framed flags of sheaves on the projective plane, Journal of Geometry and Physics118 (2017) 138 [1607.01169]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  55. [55]

    Five-dimensional Chern-Simons terms and Nekrasov's instanton counting

    Y. Tachikawa,Five-dimensional Chern-Simons terms and Nekrasov’s instanton counting, JHEP 02 (2004) 050 [hep-th/0401184]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  56. [56]

    Localization techniques in quantum field theories

    V. Pestun et al.,Localization techniques in quantum field theories, J. Phys. A50 (2017) 440301 [1608.02952]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  57. [57]

    Magnificent Four

    N. Nekrasov,Magnificent Four, 1712.08128

    work page internal anchor Pith review Pith/arXiv arXiv

  58. [58]

    The Stringy Instanton Partition Function

    G. Bonelli, A. Sciarappa, A. Tanzini and P. Vasko,The Stringy Instanton Partition Function, JHEP 01 (2014) 038 [1306.0432]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  59. [59]

    N. A. Nekrasov,Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2003) 831 [hep-th/0206161]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  60. [60]

    Fantechi and L

    B. Fantechi and L. Göttsche,Riemann–roch theorems and elliptic genus for virtually smooth schemes, Geom. Topol.14 (2010) 83

    2010

  61. [61]

    Rimányi, A

    R. Rimányi, A. Smirnov, A. Varchenko and Z. Zhou,Three dimensional mirror self-symmetry of the contangent bundle of the full flag variety, 1906.00134

    work page arXiv 1906

  62. [62]

    Zero Modes and the Atiyah-Singer Index in Noncommutative Instantons

    K.-Y. Kim, B.-H. Lee and H. S. Yang,Zero modes and Atiyah-Singer index in noncommutative instantons, Phys. Rev. D66 (2002) 025034 [hep-th/0205010]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  63. [63]

    Lectures on Instanton Counting

    H. Nakajima and K. Yoshioka,Lectures on instanton counting, inCRM Workshop on Algebraic Structures and Moduli Spaces Montreal, Canada, July 14-20, 2003, 2003, math/0311058

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  64. [64]

    Hausel, E

    T. Hausel, E. Letellier and F. Rodriguez-Villegas,Arithmetic harmonic analysis on character and quiver varieties, arXiv e-prints (2008) arXiv:0810.2076 [0810.2076]. – 52 –

    work page arXiv 2008

  65. [65]

    Quantum Hydrodynamics from Large-n Supersymmetric Gauge Theories

    P. Koroteev and A. Sciarappa,Quantum Hydrodynamics from Large-n Supersymmetric Gauge Theories, Lett. Math. Phys.108 (2018) 45 [1510.00972]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  66. [66]

    A. M. Garsia and J. Haglund,A positivity result in the theory of macdonald polynomials, Proceedings of the National Academy of Sciences98 (2001) 4313 [https://www.pnas.org/content/98/8/4313.full.pdf]

    2001

  67. [67]

    Haiman,Notes on macdonald polynomials and the geometry of hilbert schemes, in Symmetric Functions 2001: Surveys of Developments and Perspectives(S

    M. Haiman,Notes on macdonald polynomials and the geometry of hilbert schemes, in Symmetric Functions 2001: Surveys of Developments and Perspectives(S. Fomin, ed.), (Dordrecht), pp. 1–64, Springer Netherlands, 2002

    2001

  68. [68]

    W. Y. Chuang, D. E. Diaconescu and G. Pan,BPS states and the P=W conjecture, Lond. Math. Soc. Lect. Note Ser.411 (2014) 132 [1202.2039]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  69. [69]

    Bruzzo, W.-Y

    U. Bruzzo, W.-Y. Chuang, D.-E. Diaconescu, M. Jardim, G. Pan and Y. Zhang, D-branes, surface operators, and adhm quiver representations, Adv. Theor. Math. Phys. 15 (2011) 849

    2011

  70. [70]

    Wallcrossing and Cohomology of The Moduli Space of Hitchin Pairs

    W.-y. Chuang, D.-E. Diaconescu and G. Pan,Wallcrossing and Cohomology of The Moduli Space of Hitchin Pairs, Commun. Num. Theor. Phys.5 (2011) 1 [1004.4195]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  71. [71]

    Hilbert schemes, polygraphs, and the Macdonald positivity conjecture

    M. Haiman,Hilbert schemes, polygraphs, and the Macdonald positivity conjecture, arXiv Mathematics e-prints(2000) math/0010246 [math/0010246]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  72. [72]

    Cheah,Cellular decompositions for nested hilbert schemes of points, Pacific Journal of Mathematics 183 (1998)

    J. Cheah,Cellular decompositions for nested hilbert schemes of points, Pacific Journal of Mathematics 183 (1998)

    1998

  73. [73]

    Computing equivariant characteristic classes of singular varieties

    A. Weber,Computing equivariant characteristic classes of singular varieties, arXiv e-prints (2013) arXiv:1308.0787 [1308.0787]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  74. [74]

    Equivariant Hirzebruch class for singular varieties

    A. Weber,Equivariant Hirzebruch class for singular varieties, arXiv e-prints (2013) arXiv:1308.0788 [1308.0788]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  75. [75]

    Gholampour, A

    A. Gholampour, A. Sheshmani and S.-T. Yau,Nested Hilbert schemes on surfaces: Virtual fundamental class, arXiv e-prints (2017) arXiv:1701.08899 [1701.08899]. – 53 –

    work page arXiv 2017