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

2010/08/31 by H. Itoyama, T. Oota, N. Yonezawa · 2 citations
Physics and Astronomy · #hep-th

paper · pdf · doi:10.1103/physrevd.82.085031

published as Phys.Rev.D82:085031,2010 · LaTeX, 21 pages; v2: a reference added

arxiv created 2010/09/08 · arxiv updated 2010/11/11

Abstract

We consider a series of massive scaling limits m₁ -> infty, q -> 0, lim m₁ q = Lambda₃ followed by m₄ -> infty, Lambda₃ -> 0, lim m₄ Lambda₃ = (Lambda₂)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 frac1C(q) : e^{(1/2) α₁ ϕ(0)}: (int₀^q dz : e^{b_E phi(z)}:)ⁿ : e^{(1/2) alpha₂ phi(q)}: and is subsequently analytically continued.

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• Discrete Painlevé system and the double scaling limit of the matrix model for irregular conformal block and gauge theory
• Notes on phase structure and non-vanishing β functions of one-unitary matrix model

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