Journal of High Energy Physics, ISSN 1126-6708, 2/2010, Volume 2010, Issue 2, pp. 1 - 26

We give a concise summary of the impressive recent development unifying a number of different fundamental subjects. The quiver Nekrasov functions (generalized...

Integrable Hierarchies | Supersymmetric gauge theory | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Matrix Models | Physics | Elementary Particles, Quantum Field Theory | Conformal and W symmetry | Matrix models | Integrable hierarchies | SUPERSYMMETRIC GAUGE-THEORIES | 1ST SPECIAL-FUNCTIONS | TOPOLOGICAL STRINGS | CONFORMAL SYMMETRY | INTEGRABLE SYSTEMS | SUPER YANG-MILLS | SEIBERG-WITTEN THEORY | PARTITION-FUNCTIONS | VIRASORO CONSTRAINTS | FREE-FIELD REPRESENTATION | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Integrable Hierarchies | Supersymmetric gauge theory | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Matrix Models | Physics | Elementary Particles, Quantum Field Theory | Conformal and W symmetry | Matrix models | Integrable hierarchies | SUPERSYMMETRIC GAUGE-THEORIES | 1ST SPECIAL-FUNCTIONS | TOPOLOGICAL STRINGS | CONFORMAL SYMMETRY | INTEGRABLE SYSTEMS | SUPER YANG-MILLS | SEIBERG-WITTEN THEORY | PARTITION-FUNCTIONS | VIRASORO CONSTRAINTS | FREE-FIELD REPRESENTATION | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Journal Article

Physics Letters B, ISSN 0370-2693, 09/2018, Volume 784, pp. 342 - 344

The recently discovered general formulas for perturbative correlators in basic matrix models can be interpreted as the Schur-preservation property of Gaussian...

POLYNOMIALS | SYMMETRY | ASTRONOMY & ASTROPHYSICS | REPRESENTATION | PHYSICS, NUCLEAR | TENSOR-MODELS | GRAVITY | PHYSICS, PARTICLES & FIELDS | Analysis | Information management | Subatomic Physics | Mathematical Physics | Subatomär fysik | Mathematics | High Energy Physics - Theory | Physics | Representation Theory | Fysik | Physical Sciences | Naturvetenskap | Natural Sciences

POLYNOMIALS | SYMMETRY | ASTRONOMY & ASTROPHYSICS | REPRESENTATION | PHYSICS, NUCLEAR | TENSOR-MODELS | GRAVITY | PHYSICS, PARTICLES & FIELDS | Analysis | Information management | Subatomic Physics | Mathematical Physics | Subatomär fysik | Mathematics | High Energy Physics - Theory | Physics | Representation Theory | Fysik | Physical Sciences | Naturvetenskap | Natural Sciences

Journal Article

Selecta Mathematica, ISSN 1022-1824, 6/2019, Volume 25, Issue 2, pp. 1 - 29

We consider a system of three commuting difference operators in three variables $$x_{12},x_{13},x_{23}$$ x12,x13,x23 with two generic complex parameters q, t....

20G42 | 57M60 | 16T20 | 57M27 | 81R12 | Mathematics, general | Mathematics | 12H10

20G42 | 57M60 | 16T20 | 57M27 | 81R12 | Mathematics, general | Mathematics | 12H10

Journal Article

Physics Letters A, ISSN 0375-9601, 02/2011, Volume 375, Issue 6, p. 984

Using the replica method, we calculate the mean Coulomb energy of two-dimensional (2d) Dyson gas (in quadratic potential and for particular value of Coulomb...

Journal Article

Physics Letters A, ISSN 0375-9601, 02/2011, Volume 375, Issue 6, pp. 984 - 989

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 2009, Volume 2009, Issue 4, pp. 64 - 64

JHEP 0904:064,2009 We show that partition functions of various matrix models can be obtained by acting on elementary functions with exponents of W-operators. A...

Matrix models | Conformal and w symmetry | Integrable hierarchies | Physics - High Energy Physics - Theory

Matrix models | Conformal and w symmetry | Integrable hierarchies | Physics - High Energy Physics - Theory

Journal Article

04/2017

We consider a system of three commuting difference operators in three variables $x_{12},x_{13},x_{23}$ with two generic complex parameters $q,t$. This system...

Journal Article

Physics Letters A, ISSN 0375-9601, 02/2011, Volume 375, Issue 6, pp. 984 - 989

Using the replica method, we calculate the mean Coulomb energy of two-dimensional (2d) Dyson gas (in quadratic potential and for particular value of Coulomb...

PHYSICS, MULTIDISCIPLINARY | Coulomb friction | Energy use | Asymptotic properties | Mathematical analysis | Exact solutions | Images | Solid state physics | Recursive | Energy of solution

PHYSICS, MULTIDISCIPLINARY | Coulomb friction | Energy use | Asymptotic properties | Mathematical analysis | Exact solutions | Images | Solid state physics | Recursive | Energy of solution

Journal Article

Nuclear Physics, Section B, ISSN 0550-3213, 2012, Volume 855, Issue 1, pp. 128 - 151

We extend the proof from Mironov et al. (2011) [25], which interprets the AGT relation as the Hubbard–Stratonovich duality relation to the case of 5 d gauge...

Seiberg–Witten theory | Matrix models | AGT conjecture | (5 d) [formula omitted] SUSY gauge theory | ( q-)Virasoro algebra | (5d) N=2 SUSY gauge theory | Seiberg-Witten theory | (q-)Virasoro algebra | HAMILTONIAN REDUCTION | ZUMINO-WITTEN MODEL | PARAFERMIONS | GAUGE-THEORIES | SYMMETRY | INTEGRABLE SYSTEMS | POINT-OF-VIEW | CONFORMAL BLOCKS | FREE-FIELD REPRESENTATION | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Seiberg–Witten theory | Matrix models | AGT conjecture | (5 d) [formula omitted] SUSY gauge theory | ( q-)Virasoro algebra | (5d) N=2 SUSY gauge theory | Seiberg-Witten theory | (q-)Virasoro algebra | HAMILTONIAN REDUCTION | ZUMINO-WITTEN MODEL | PARAFERMIONS | GAUGE-THEORIES | SYMMETRY | INTEGRABLE SYSTEMS | POINT-OF-VIEW | CONFORMAL BLOCKS | FREE-FIELD REPRESENTATION | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Journal Article

International Journal of Modern Physics A, ISSN 0217-751X, 06/2018, Volume 33, Issue 17, p. 1850105

Quantum ℛ -matrices are the building blocks for the colored HOMFLY polynomials. In the case of three-strand braids with an identical finite-dimensional...

representation theory | knot theory | Racah matrices | Chern-Simons theory | quantum groups | topological field theory | COLORED KNOT POLYNOMIALS | REPRESENTATIONS | FIELD-THEORIES | INVARIANTS | LINKS | PHYSICS, NUCLEAR | PRETZEL KNOTS | ALGEBRAS | EVOLUTION | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

representation theory | knot theory | Racah matrices | Chern-Simons theory | quantum groups | topological field theory | COLORED KNOT POLYNOMIALS | REPRESENTATIONS | FIELD-THEORIES | INVARIANTS | LINKS | PHYSICS, NUCLEAR | PRETZEL KNOTS | ALGEBRAS | EVOLUTION | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Journal Article

International Journal of Modern Physics A, ISSN 0217-751X, 06/2010, Volume 25, Issue 16, pp. 3173 - 3207

Journal Article

SELECTA MATHEMATICA-NEW SERIES, ISSN 1022-1824, 06/2019, Volume 25, Issue 2, p. 1

We consider a system of three commuting difference operators in three variables x12,x13,x23 with two generic complex parameters q,t. This system and its...

POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | INVARIANTS | QUANTUM | Analysis | Algebra | Resveratrol

POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | INVARIANTS | QUANTUM | Analysis | Algebra | Resveratrol

Journal Article

International Journal of Modern Physics A, ISSN 0217-751X, 06/2010, Volume 25, Issue 16, pp. 3173 - 3207

As anticipated in Ref. 1, elaborated in Refs. 2–4, and explicitly formulated in Ref. 5, the Dotsenko–Fateev integral discriminant coincides with conformal...

STRINGS | 2D conformal theories | HAMILTONIAN REDUCTION | EQUATIONS | matrix models | PHYSICS, NUCLEAR | ZUMINO-WITTEN MODEL | PARAFERMIONS | SYMMETRY | Dotsenko-Fateev representation | POINT-OF-VIEW | DUALITY | FREE-FIELD REPRESENTATION | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

STRINGS | 2D conformal theories | HAMILTONIAN REDUCTION | EQUATIONS | matrix models | PHYSICS, NUCLEAR | ZUMINO-WITTEN MODEL | PARAFERMIONS | SYMMETRY | Dotsenko-Fateev representation | POINT-OF-VIEW | DUALITY | FREE-FIELD REPRESENTATION | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 8/2010, Volume 2010, Issue 8, pp. 1 - 37

Recently exact formulas were provided for partition function of conformal (multi-Penner) β-ensemble in the Dijkgraaf-Vafa phase, which, if interpreted as...

Supersymmetric gauge theory | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Matrix Models | Physics | Elementary Particles, Quantum Field Theory | 1ST SPECIAL-FUNCTIONS | INTEGRABILITY | VOLUME | GAUGE-THEORIES | SYMMETRY | WDVV EQUATIONS | DUALITY | SEIBERG-WITTEN THEORY | PARTITION-FUNCTIONS | QUANTUM MODULI | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Supersymmetric gauge theory | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Matrix Models | Physics | Elementary Particles, Quantum Field Theory | 1ST SPECIAL-FUNCTIONS | INTEGRABILITY | VOLUME | GAUGE-THEORIES | SYMMETRY | WDVV EQUATIONS | DUALITY | SEIBERG-WITTEN THEORY | PARTITION-FUNCTIONS | QUANTUM MODULI | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 2/2011, Volume 2011, Issue 2, pp. 1 - 41

The AGT conjecture claims an equivalence of conformal blocks in 2d CFT and sums of Nekrasov functions (instantonic sums in 4d SUSY gauge theory). The conformal...

Supersymmetric gauge theory | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Matrix Models | Physics | Elementary Particles, Quantum Field Theory | Conformal and W symmetry | Matrix models | 1ST SPECIAL-FUNCTIONS | HAMILTONIAN REDUCTION | SUPERSYMMETRIC GAUGE | GAUGE-THEORIES | INTEGRABLE SYSTEMS | POINT-OF-VIEW | SUSY FIELD-THEORIES | SEIBERG-WITTEN THEORY | CONFORMAL BLOCKS | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Supersymmetric gauge theory | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Matrix Models | Physics | Elementary Particles, Quantum Field Theory | Conformal and W symmetry | Matrix models | 1ST SPECIAL-FUNCTIONS | HAMILTONIAN REDUCTION | SUPERSYMMETRIC GAUGE | GAUGE-THEORIES | INTEGRABLE SYSTEMS | POINT-OF-VIEW | SUSY FIELD-THEORIES | SEIBERG-WITTEN THEORY | CONFORMAL BLOCKS | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 5/2012, Volume 2012, Issue 5, pp. 1 - 12

In [1] extended superpolynomials were introduced for the torus links T [m, mk + r], which are functions on the entire space of time variables and, at expense...

Topological Field Theories | Quantum Physics | Quantum Field Theories, String Theory | Chern-Simons Theories | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | Topological field theories | Chern-Simons theories | ALGEBRAS | MATRIX FACTORIZATIONS | LINK HOMOLOGY | SYSTEMS | HAMILTONIANS | KNOT | OPERATORS | PHYSICS, PARTICLES & FIELDS | Analysis | Universities and colleges

Topological Field Theories | Quantum Physics | Quantum Field Theories, String Theory | Chern-Simons Theories | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | Topological field theories | Chern-Simons theories | ALGEBRAS | MATRIX FACTORIZATIONS | LINK HOMOLOGY | SYSTEMS | HAMILTONIANS | KNOT | OPERATORS | PHYSICS, PARTICLES & FIELDS | Analysis | Universities and colleges

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 3/2011, Volume 2011, Issue 3, pp. 1 - 25

The AGT relation identifies the Nekrasov functions for various $$ \mathcal{N} = 2 $$ SUSY gauge theories with the 2d conformal blocks, which possess explicit...

Supersymmetric gauge theory | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Matrix Models | Physics | Elementary Particles, Quantum Field Theory | Conformal and W symmetry | Matrix models | 1ST SPECIAL-FUNCTIONS | INTEGRABILITY | YANG-MILLS | EXPANSIONS | AGT RELATION | SUSY FIELD-THEORIES | DUALITY | PARTITION-FUNCTIONS | CONFORMAL BLOCKS | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Supersymmetric gauge theory | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Matrix Models | Physics | Elementary Particles, Quantum Field Theory | Conformal and W symmetry | Matrix models | 1ST SPECIAL-FUNCTIONS | INTEGRABILITY | YANG-MILLS | EXPANSIONS | AGT RELATION | SUSY FIELD-THEORIES | DUALITY | PARTITION-FUNCTIONS | CONFORMAL BLOCKS | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Journal Article

International Journal of Modern Physics A, ISSN 0217-751X, 01/2012, Volume 27, Issue 1, p. 1230001

A matrix model approach to proof of the AGT relation is briefly reviewed. It starts from the substitution of conformal blocks by the Dotsenko–Fateev β-ensemble...

matrix model | Nekrasov functions | conformal theories | Seiberg-Witten theory | 1ST SPECIAL-FUNCTIONS | TODA HIERARCHY | SUPERSYMMETRIC GAUGE | PHYSICS, NUCLEAR | INTEGRABLE SYSTEMS | CONFORMAL SYMMETRY | WDVV EQUATIONS | SUSY FIELD-THEORIES | PARTITION-FUNCTIONS | VIRASORO CONSTRAINTS | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

matrix model | Nekrasov functions | conformal theories | Seiberg-Witten theory | 1ST SPECIAL-FUNCTIONS | TODA HIERARCHY | SUPERSYMMETRIC GAUGE | PHYSICS, NUCLEAR | INTEGRABLE SYSTEMS | CONFORMAL SYMMETRY | WDVV EQUATIONS | SUSY FIELD-THEORIES | PARTITION-FUNCTIONS | VIRASORO CONSTRAINTS | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 2012, Volume 45, Issue 35, pp. 355202 - 1-355202-11

We show that the HOMFLYPT polynomials for the torus knots T[m, n] in all fundamental representations are equal to the Hall-Littlewood polynomials in a...

KNOT | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | OPERATORS | ALGEBRA | Mathematical analysis | Braiding | Strands | Polynomials | Representations | Knots | Symmetry

KNOT | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | OPERATORS | ALGEBRA | Mathematical analysis | Braiding | Strands | Polynomials | Representations | Knots | Symmetry

Journal Article