Massive Scaling Limit of beta-Deformed Matrix Model of Selberg Type

Abstract

We consider a series of massive scaling limits m_1 -> infty, q -> 0, lim m_1 q = Lambda_{3} followed by m_4 -> infty, Lambda_{3} -> 0, lim m_4 Lambda_{3} = (Lambda_2)^2 of the beta-deformed matrix model of Selberg type (N_c=2, N_f=4) which reduce the number of flavours to N_f=3 and subsequently to N_f=2. This keeps the other parameters of the model finite, which include n=N_L and N=n+N_R, namely, the size of the matrix and the "filling fraction". Exploiting the method developed before, we generate instanton expansion with finite g_s, epsilon_{1,2} to check the Nekrasov coefficients (N_f =3,2 cases) to the lowest order. The limiting expressions provide integral representation of irregular conformal blocks which contains a 2d operator lim frac{1}{C(q)} : e^{(1/2) α_1 ϕ(0)}: (int_0^q dz : e^{b_E phi(z)}:)^n : e^{(1/2) alpha_2 phi(q)}: and is subsequently analytically continued.

arXiv commentLaTeX, 21 pages; v2: a reference added

References in corpus (38)

• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• N=2 dualities
• Solutions Of Four-Dimensional Field Theories Via M Theory
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• The Coulomb Phase of N=2 Supersymmetric QCD
• On AGT relation in the case of U(3)
• On the Quantum Moduli Space of Vacua of $N=2$ Supersymmetric $SU(N_c)$ Gauge Theories
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• On non-conformal limit of the AGT relations
• Asymptotically free N=2 theories and irregular conformal blocks
• Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
• On AGT conjecture
• The Quiver Matrix Model and 2d-4d Conformal Connection
• Conformal blocks as Dotsenko-Fateev Integral Discriminants
• A & B model approaches to surface operators and Toda theories
• Hitchin systems, N=2 gauge theories and W-gravity
• Method of Generating q-Expansion Coefficients for Conformal Block and N=2 Nekrasov Function by beta-Deformed Matrix Model
• The Effective Prepotential of N=2 Supersymmetric SU(N_c) Gauge Theories
• The Power of Nekrasov Functions
• Penner Type Matrix Model and Seiberg-Witten Theory
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Seiberg-Witten theory, matrix model and AGT relation
• On Combinatorial Expansions of Conformal Blocks
• Proving the AGT relation for N_f = 0,1,2 antifundamentals
• Zamolodchikov asymptotic formula and instanton expansion in N=2 SUSY N_f=2N_c QCD
• On N=2 Supersymmetric QCD with 4 Flavors
• The matrix model version of AGT conjecture and CIV-DV prepotential
• The Renormalization Group Equation in N=2 Supersymmetric Gauge Theories
• Non-conformal limit of AGT relation from the 1-point torus conformal block
• Prepotential of N=2 SU(2) Yang-Mills gauge theory coupled with a massive matter multiplet
• Analysis of correlation functions in Toda theory and AGT-W relation for SU(3) quiver
• N=2 Generalized Superconformal Quiver Gauge Theory
• Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories
• Prepotentials of N=2 SU(2) Yang-Mills theories coupled with massive matter multiplets
• Periods and Prepotential of N=2 SU(2) Supersymmetric Yang-Mills Theory with Massive Hypermultiplets
• Triality in SU(2) Seiberg-Witten theory and Gauss hypergeometric function
• On a Selberg-Schur integral

Cited by in corpus (30)

• Proving AGT conjecture as HS duality: extension to five dimensions
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• A direct proof of AGT conjecture at beta = 1
• Towards a proof of AGT conjecture by methods of matrix models
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• A slow review of the AGT correspondence
• 2d-4d Connection between q-Virasoro/W Block at Root of Unity Limit and Instanton Partition Function on ALE Space
• Quantum Hitchin Systems via beta-deformed Matrix Models
• Matrix model from N = 2 orbifold partition function
• $q$-Virasoro/W Algebra at Root of Unity and Parafermions
• W(1+infinity) algebra as a symmetry behind AGT relation
• β-deformed matrix model and Nekrasov partition function
• Discrete Painleve system and the double scaling limit of the matrix model for irregular conformal block and gauge theory
• ε-Corrected Seiberg-Witten Prepotential Obtained From Half Genus Expansion in beta-Deformed Matrix Model
• Argyres-Douglas theories and Liouville Irregular States
• Discrete Painleve system for the partition function of $N_f=2$ $SU(2)$ supersymmetric gauge theory and its double scaling limit
• q-Vertex Operator from 5D Nekrasov Function
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• The integral representation of solutions of KZ equation and a modification by $\mathcal{K}$ operator insertion
• Multicritical points of unitary matrix model with logarithmic potential identified with Argyres-Douglas points
• Unitary matrix with a Penner-like potential also yields N_f=2
• Perturbation of multi-critical unitary matrix models, double scaling limits, and Argyres-Douglas theories
• An(1) Affine Quiver Matrix Model
• Genus one correction to Seiberg-Witten prepotential from β-deformed matrix model
• Cubic constraints for the resolvents of the ABJM matrix model and its cousins
• Construction of irregular conformal/W block and flavor mass relations of $\mathcal{N}=2$ SUSY gauge theory from the $A_{n-1}$ quiver matrix model
• A-D hypersurface of $su(n)$ $\mathcal{N}=2$ supersymmetric gauge theory with $N_f=2n-2$ flavors
• Asymptotics of the determinant of the modified Bessel functions and the second Painlevé equation
• Asymptotics of the partition function of the perturbed Gross-Witten-Wadia unitary matrix model
• Theory space of one unitary matrix model and its critical behavior associated with Argyres-Douglas theory