Physics letters. B, ISSN 0370-2693, 2010, Volume 691, Issue 2, pp. 111 - 115

We propose some arguments supporting an M-theory derivation of the duality recently discovered by Alday, Gaiotto and Tachikawa between two-dimensional...

[formula omitted][formula omitted] gauge theories | [formula omitted] Toda theory | Hitchin systems | D=2 Toda theory | N=2 D=4 gauge theories Hitchin systems | PHYSICS, NUCLEAR | N=2 D=4 gauge theories | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS

[formula omitted][formula omitted] gauge theories | [formula omitted] Toda theory | Hitchin systems | D=2 Toda theory | N=2 D=4 gauge theories Hitchin systems | PHYSICS, NUCLEAR | N=2 D=4 gauge theories | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS

Journal Article

Advances in mathematics (New York. 1965), ISSN 0001-8708, 2013, Volume 234, pp. 239 - 403

.... In the case where the Higgs bundles have rank 2, we construct canonical Darboux coordinate systems on their moduli spaces...

Wall-crossing | Donaldson–Thomas invariants | Hyperkähler geometry | Fock–Goncharov coordinates | Hitchin systems | Supersymmetric gauge theory | Fock-Goncharov coordinates | Donaldson-Thomas invariants | N=2 | BPS STATES | MONOPOLES | SELF-DUAL STRINGS | PROBING F-THEORY | SUPERCONFORMAL FIELD-THEORIES | MATHEMATICS | GAUGE-THEORIES | Hyperkahler geometry | MODULI SPACE | SPECTRA | COMPACTIFICATION

Wall-crossing | Donaldson–Thomas invariants | Hyperkähler geometry | Fock–Goncharov coordinates | Hitchin systems | Supersymmetric gauge theory | Fock-Goncharov coordinates | Donaldson-Thomas invariants | N=2 | BPS STATES | MONOPOLES | SELF-DUAL STRINGS | PROBING F-THEORY | SUPERCONFORMAL FIELD-THEORIES | MATHEMATICS | GAUGE-THEORIES | Hyperkahler geometry | MODULI SPACE | SPECTRA | COMPACTIFICATION

Journal Article

Advances in mathematics (New York. 1965), ISSN 0001-8708, 2018, Volume 327, pp. 225 - 348

.... It gives rise to a moduli space XPGLm,S, closely related to the moduli space of PGLm-local systems on S, which carries a canonical cluster Poisson variety structure [13...

Cluster varieties | Motivic Donaldson–Thomas invariants | Canonical bases | REPRESENTATIONS | QUIVERS | Motivic Donaldson-Thomas invariants | POTENTIALS | QUANTUM DILOGARITHM | CATEGORIES | HITCHIN SYSTEMS | MATHEMATICS | DOUBLE BRUHAT CELLS | SPECTRAL NETWORKS | CLUSTER ALGEBRAS

Cluster varieties | Motivic Donaldson–Thomas invariants | Canonical bases | REPRESENTATIONS | QUIVERS | Motivic Donaldson-Thomas invariants | POTENTIALS | QUANTUM DILOGARITHM | CATEGORIES | HITCHIN SYSTEMS | MATHEMATICS | DOUBLE BRUHAT CELLS | SPECTRAL NETWORKS | CLUSTER ALGEBRAS

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 2016, Volume 165, Issue 15, pp. 2991 - 3042

.... Next, we show that every algebraically integrable system gives rise to a degenerate abelian scheme and discuss applications to Hitchin systems.

MATHEMATICS | DUALITY | COMPACTIFIED JACOBIANS | Mathematics - Algebraic Geometry

MATHEMATICS | DUALITY | COMPACTIFIED JACOBIANS | Mathematics - Algebraic Geometry

Journal Article

Annals of mathematics, ISSN 0003-486X, 2012, Volume 175, Issue 3, pp. 1329 - 1407

Journal Article

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, ISSN 1815-0659, 2019, Volume 15

the present notes we explain the relationship between Calabi-Yau integrable systems and Hitchin systems based on work by Diaconescu-Donagi-Pantev and the author...

variations of Hodge structures | Hitchin systems | complex integrable systems | LANGLANDS DUALITY | Calabi-Yau threefolds | PHYSICS, MATHEMATICAL | MODULI

variations of Hodge structures | Hitchin systems | complex integrable systems | LANGLANDS DUALITY | Calabi-Yau threefolds | PHYSICS, MATHEMATICAL | MODULI

Journal Article

Functional Analysis and Its Applications, ISSN 0016-2663, 10/2018, Volume 52, Issue 4, pp. 316 - 320

... 4 –98, 2018 Original Russian Text Copyright c by O. K. Sheinman Integrable Systems of Algebraic Origin and Separation of V ariables ∗ O. K. Sheinman Received...

integrable system | Functional Analysis | Analysis | the method of separation of variables | quantum analogue | plane algebraic curve | Poisson bracket | Mathematics | Lagrange interpolation polynomial | hyperelliptic Hitchin systems | MATHEMATICS | MATHEMATICS, APPLIED

integrable system | Functional Analysis | Analysis | the method of separation of variables | quantum analogue | plane algebraic curve | Poisson bracket | Mathematics | Lagrange interpolation polynomial | hyperelliptic Hitchin systems | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 04/2019, Volume 99, Issue 2, pp. 340 - 341

Journal Article

Theoretical and Mathematical Physics, ISSN 0040-5779, 8/2016, Volume 188, Issue 2, pp. 1121 - 1154

We construct twisted Calogero–Moser systems with spins as Hitchin systems derived from the Higgs bundles over elliptic curves, where the transition operators...

Knizhnik–Zamolodchikov–Bernard equation | Theoretical, Mathematical and Computational Physics | Higgs bundle | Applications of Mathematics | finite-order Lie algebra automorphism | Physics | elliptic integrable system | HITCHIN SYSTEMS | PHYSICS, MULTIDISCIPLINARY | DYNAMICAL R-MATRICES | ZUMINO-WITTEN MODELS | Knizhnik-Zamolodchikov-Bernard equation | PHYSICS, MATHEMATICAL | OPERATORS | Algebra

Knizhnik–Zamolodchikov–Bernard equation | Theoretical, Mathematical and Computational Physics | Higgs bundle | Applications of Mathematics | finite-order Lie algebra automorphism | Physics | elliptic integrable system | HITCHIN SYSTEMS | PHYSICS, MULTIDISCIPLINARY | DYNAMICAL R-MATRICES | ZUMINO-WITTEN MODELS | Knizhnik-Zamolodchikov-Bernard equation | PHYSICS, MATHEMATICAL | OPERATORS | Algebra

Journal Article

Theoretical and Mathematical Physics, ISSN 0040-5779, 10/2013, Volume 177, Issue 1, pp. 1281 - 1338

We describe a construction of elliptic integrable systems based on bundles with nontrivial characteristic classes, especially attending to the bundle-modification procedure, which relates models...

integrable system | Theoretical, Mathematical and Computational Physics | Painlevé equation | Hitchin system | Applications of Mathematics | modification of bundles | Physics | INVERSE SCATTERING METHOD | 2ND-ORDER | PHYSICS, MULTIDISCIPLINARY | MOMENT MAPS | MODEL | PHYSICS, MATHEMATICAL | DEFORMATION | CURVES | Painleve equation | PAINLEVE-EQUATION | TOPS | HOLOMORPHIC BUNDLES | ORDINARY DIFFERENTIAL-EQUATIONS

integrable system | Theoretical, Mathematical and Computational Physics | Painlevé equation | Hitchin system | Applications of Mathematics | modification of bundles | Physics | INVERSE SCATTERING METHOD | 2ND-ORDER | PHYSICS, MULTIDISCIPLINARY | MOMENT MAPS | MODEL | PHYSICS, MATHEMATICAL | DEFORMATION | CURVES | Painleve equation | PAINLEVE-EQUATION | TOPS | HOLOMORPHIC BUNDLES | ORDINARY DIFFERENTIAL-EQUATIONS

Journal Article

International Journal of Mathematics, ISSN 0129-167X, 02/2014, Volume 25, Issue 2, pp. 1450016 - 1-1450016-20

Donagi and Markman (1993) have shown that the infinitesimal period map for an algebraic completely integrable Hamiltonian system (ACIHS...

Hitchin system | Higgs bundles | Donagi-Markman cubic | algebraic completely integrable systems | SPECTRAL-CURVES | RIEMANN SURFACE | BUNDLES | VARIETIES | MODULI | ALGEBRAIC MANIFOLDS | MATHEMATICS | INTEGRABLE SYSTEMS | JACOBIANS | DUALITY | GEOMETRY | Bundling | Mathematical analysis | Algebra

Hitchin system | Higgs bundles | Donagi-Markman cubic | algebraic completely integrable systems | SPECTRAL-CURVES | RIEMANN SURFACE | BUNDLES | VARIETIES | MODULI | ALGEBRAIC MANIFOLDS | MATHEMATICS | INTEGRABLE SYSTEMS | JACOBIANS | DUALITY | GEOMETRY | Bundling | Mathematical analysis | Algebra

Journal Article

International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 04/2017, Volume 14, Issue 4

This paper is about geometric quantization of the Hitchin system. We quantize a Kahler form on the Hitchin moduli space...

geometric quantization | Hitchin system | Quillen bundle | RIEMANN SURFACE | BUNDLES | PHYSICS, MATHEMATICAL

geometric quantization | Hitchin system | Quillen bundle | RIEMANN SURFACE | BUNDLES | PHYSICS, MATHEMATICAL

Journal Article

International Mathematics Research Notices, ISSN 1073-7928, 2007, Volume 2007

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 05/2014, Volume 79, pp. 1 - 13

We will generalize the Treibich–Verdier theory about elliptic solitons to a Hitchin system by constructing a particular ruled surface and we will propose a generalization of a tangency condition associated with elliptic solitons...

Elementary transformation | Hitchin system | Elliptic soliton | Tangential cover | Residue section | Ruled surface | MATHEMATICS, APPLIED | SOLITONS | EQUATIONS | PHYSICS, MATHEMATICAL

Elementary transformation | Hitchin system | Elliptic soliton | Tangential cover | Residue section | Ruled surface | MATHEMATICS, APPLIED | SOLITONS | EQUATIONS | PHYSICS, MATHEMATICAL

Journal Article

Russian mathematical surveys, ISSN 1468-4829, 2014, Volume 69, Issue 1, pp. 35 - 118

This paper describes isomonodromy problems in terms of flat G-bundles over punctured elliptic curves Sigma(tau) and connections with regular singularities at...

Painlevé equations | Higgs bundles | Monodromy-preserving deformations | Flat connections | Schlesinger systems | monodromy-preserving deformations | DEFORMATION | MODULI SPACES | R-MATRICES | HITCHIN SYSTEMS | MATHEMATICS | Painleve equations | PAINLEVE-VI | ALGEBRAS | INTEGRABLE SYSTEMS | flat connections | HOLOMORPHIC BUNDLES | ORDINARY DIFFERENTIAL-EQUATIONS | Mathematical analysis | Flats | Classification | Lie groups | Transformations | Representations | Joints | Bundles

Painlevé equations | Higgs bundles | Monodromy-preserving deformations | Flat connections | Schlesinger systems | monodromy-preserving deformations | DEFORMATION | MODULI SPACES | R-MATRICES | HITCHIN SYSTEMS | MATHEMATICS | Painleve equations | PAINLEVE-VI | ALGEBRAS | INTEGRABLE SYSTEMS | flat connections | HOLOMORPHIC BUNDLES | ORDINARY DIFFERENTIAL-EQUATIONS | Mathematical analysis | Flats | Classification | Lie groups | Transformations | Representations | Joints | Bundles

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 10/2018, Volume 59, Issue 10, p. 102301

...) system is obtained in this article. Starting from the known solutions of the original equations, some solutions to these deformed equations are obtained...

FIELDS | HITCHIN EQUATIONS | EINSTEIN EQUATIONS | INTEGRABLE SYSTEMS | SU(INFINITY) NAHM EQUATIONS | HEAVENLY SPACES | DUALITY | PHYSICS, MATHEMATICAL | GRAVITY | KNOTS | GEOMETRY

FIELDS | HITCHIN EQUATIONS | EINSTEIN EQUATIONS | INTEGRABLE SYSTEMS | SU(INFINITY) NAHM EQUATIONS | HEAVENLY SPACES | DUALITY | PHYSICS, MATHEMATICAL | GRAVITY | KNOTS | GEOMETRY

Journal Article

FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, ISSN 0016-2663, 10/2019, Volume 53, Issue 4, pp. 291 - 303

This paper describes a class of spectral curves and gives explicit formulas for the Darboux coordinates of the Hitchin systems of types A(l...

MATHEMATICS | MATHEMATICS, APPLIED | BUNDLES | spectral curve | Darboux coordinates | Hitchin system | VARIABLES | SEPARATION | separation of variables

MATHEMATICS | MATHEMATICS, APPLIED | BUNDLES | spectral curve | Darboux coordinates | Hitchin system | VARIABLES | SEPARATION | separation of variables

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 2012, Volume 8, p. 095

We describe new families of the Knizhnik-Zamolodchikov-Bernard (KZB) equations related to the WZW-theory corresponding to the adjoint G-bundles of different...

Integrable system | Hitchin system | KZB equation | Characteristic class | ELLIPTIC-CURVES | integrable system | characteristic class | GEOMETRIC-QUANTIZATION | ZUMINO-WITTEN MODELS | CALOGERO-MOSER SYSTEMS | PHYSICS, MATHEMATICAL | R-MATRICES | PAINLEVE-VI | INTEGRABLE SYSTEMS | ZAMOLODCHIKOV-BERNARD EQUATIONS | MANY-BODY SYSTEMS | HOLOMORPHIC BUNDLES

Integrable system | Hitchin system | KZB equation | Characteristic class | ELLIPTIC-CURVES | integrable system | characteristic class | GEOMETRIC-QUANTIZATION | ZUMINO-WITTEN MODELS | CALOGERO-MOSER SYSTEMS | PHYSICS, MATHEMATICAL | R-MATRICES | PAINLEVE-VI | INTEGRABLE SYSTEMS | ZAMOLODCHIKOV-BERNARD EQUATIONS | MANY-BODY SYSTEMS | HOLOMORPHIC BUNDLES

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 02/2019, Volume 136, pp. 14 - 30

...–Yau orbifolds, over the same base. Their intermediate Jacobian fibration, constructed in terms of equivariant cohomology, is isomorphic to the Hitchin system...

Calabi–Yau threefolds | Hodge theory | Global quotient stacks | Integrable systems | Hitchin systems | MATHEMATICS | DUALITY | Calabi-Yau threefolds | PHYSICS, MATHEMATICAL

Calabi–Yau threefolds | Hodge theory | Global quotient stacks | Integrable systems | Hitchin systems | MATHEMATICS | DUALITY | Calabi-Yau threefolds | PHYSICS, MATHEMATICAL

Journal Article

Physics of Particles and Nuclei, ISSN 1063-7796, 1/2009, Volume 40, Issue 1, pp. 93 - 114

In this review we consider the Hitchin integrable systems and their relations with the self-duality equations and twisted super-symmetric Yang-Mills theory in four dimensions...

Elementary Particles and Nuclei | Physics | HITCHIN SYSTEM | BODY PROBLEMS | PAINLEVE-VI | ALGEBRAS | BUNDLES | SYMMETRY | METRICS | EQUATIONS | DUALITY | MODEL | PHYSICS, PARTICLES & FIELDS

Elementary Particles and Nuclei | Physics | HITCHIN SYSTEM | BODY PROBLEMS | PAINLEVE-VI | ALGEBRAS | BUNDLES | SYMMETRY | METRICS | EQUATIONS | DUALITY | MODEL | PHYSICS, PARTICLES & FIELDS

Journal Article

No results were found for your search.

Cannot display more than 1000 results, please narrow the terms of your search.