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.

LaTeX, 21 pages; v2: a reference added

References in corpus (7)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• On AGT relation in the case of U(3)
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• Asymptotically free N=2 theories and irregular conformal blocks
• The Power of Nekrasov Functions
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories

Cited by in corpus (12)

• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• A direct proof of AGT conjecture at beta = 1
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• Quantum Hitchin Systems via beta-deformed Matrix Models
• $q$-Virasoro/W Algebra at Root of Unity and Parafermions
• W(1+infinity) algebra as a symmetry behind AGT relation
• An(1) Affine Quiver Matrix Model
• Perturbation of multi-critical unitary matrix models, double scaling limits, and Argyres-Douglas theories
• A-D hypersurface of $su(n)$ $\mathcal{N}=2$ supersymmetric gauge theory with $N_f=2n-2$ flavors
• 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
• 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