RG equations from Whitham hierarchy

DOI10.1016/S0550-3213(98)00315-0zbMath0951.37022arXivhep-th/9802007OpenAlexW3100107401MaRDI QIDQ1570559

Andrei Mironov, A. Yu. Morozov, Andrei Marshakov, Alexander Gorsky

Publication date: 11 July 2000

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9802007

zbMATH Keywords

renormalization group Seiberg-Witten theory Riemann theta-functions

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Supersymmetric field theories in quantum mechanics (81T60) Yang-Mills and other gauge theories in quantum field theory (81T13) Renormalization group methods applied to problems in quantum field theory (81T17) Theta functions and abelian varieties (14K25) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants) (14J80)

Related Items (47)

Check-operators and quantum spectral curves ⋮ Angular momentum and gravimagnetization of the ${\mathcal N=2}$ supersymmetric vacuum ⋮ Seiberg-Witten/Whitham Equations and Instanton Corrections in ${\mathscr{N}}=2$ Supersymmetric Yang-Mills Theory ⋮ Matrix model conjecture for exact BS periods and Nekrasov functions ⋮ Whitham prepotential and superpotential ⋮ WDVV equation and triple-product relation ⋮ Rainbow tensor model with enhanced symmetry and extreme melonic dominance ⋮ On Painlevé/gauge theory correspondence ⋮ Generalized Picard-Fuchs operators from Whitham hierarchy in $\mathcal{N} = 2$ supersymmetric gauge theory with massless hypermultiplets ⋮ Check of AGT relation for conformal blocks on sphere ⋮ RG-Whitham dynamics and complex Hamiltonian systems ⋮ On $n$-point amplitudes in $N = 4$ SYM ⋮ Random ballistic growth and diffusion in symmetric spaces ⋮ On AGT relation in the case of $U(3)$ ⋮ Cubic curves from instanton counting ⋮ Relation between Nekrasov functions and Bohr-Sommerfeld periods in the pure $\mathrm{SU}(N)$ case ⋮ WHITHAM DEFORMATIONS OF SEIBERG–WITTEN CURVES FOR CLASSICAL GAUGE GROUPS ⋮ Direct derivation of scaling relation of prepotential in N=2 supersymmetric G2 Yang–Mills theory ⋮ Bands and gaps in Nekrasov partition function ⋮ On the microscopic origin of integrability in the Seiberg-Witten theory ⋮ The matrix model version of AGT conjecture and CIV-DV prepotential ⋮ Commuting Hamiltonians from Seiberg-Witten $\Theta$-functions. ⋮ Strings, SUSY gauge theories, and integrable systems ⋮ Seiberg-Witten theory for a non-trivial compactification from five to four dimensions. ⋮ Strong coupling expansion and the Seiberg-Witten-Whitham equations. ⋮ Perverse coherent sheaves on blowup. III: Blow-up formula from wall-crossing ⋮ $\mathcal N=2$ supersymmetric gauge theories with massive hypermultiplets and the Whitham hierarchy. ⋮ CONFORMAL BLOCKS AS DOTSENKO–FATEEV INTEGRAL DISCRIMINANTS ⋮ Integrability properties of Hurwitz partition functions. II. Multiplication of cut-and-join operators and WDVV equations ⋮ The Toda system and solution to the N = 2 SUSY Yang–Mills theory ⋮ ON THE SHAPES OF ELEMENTARY DOMAINS OR WHY MANDELBROT SET IS MADE FROM ALMOST IDEAL CIRCLES? ⋮ Counting exceptional instantons ⋮ Tau-functions for quiver gauge theories ⋮ Whitham hierarchy and generalized Picard-Fuchs operators in the $\mathcal{N}=2$ susy Yang-Mills theory for classical gauge groups ⋮ DV and WDVV ⋮ ON EQUIVALENCE OF TWO HURWITZ MATRIX MODELS ⋮ PARTITION FUNCTIONS OF MATRIX MODELS AS THE FIRST SPECIAL FUNCTIONS OF STRING THEORY II: KONTSEVICH MODEL ⋮ Duality symmetry in softly broken $\mathcal N=2$ gauge theories. ⋮ Donaldson-Witten functions of massless $N=2$ supersymmetric QCD ⋮ Whitham hierarchies, instanton corrections and soft supersymmetry breaking in $N=2$ $\text{SU}(N)$ super Yang-Mills theory ⋮ The Ruijsenaars-Schneider model in the context of Seiberg-Witten theory. ⋮ Instanton corrections in $N=2$ supersymmetric theories with classical gauge groups and fundamental matter hypermultiplets ⋮ Instanton counting on blowup. I: 4-dimensional pure gauge theory ⋮ Matrix models vs. Seiberg-Witten/Whitham theories ⋮ Picard–Fuchs equations and Whitham hierarchy in N=2 supersymmetric SU(r+1) Yang–Mills theory ⋮ Experiments with the WDVV equations for the gluino-condensate prepotential: the cubic (two-cut) case ⋮ The Dijkgraaf-Vafa prepotential in the context of general Seiberg-Witten theory

Cites Work

This page was built for publication: RG equations from Whitham hierarchy