相关论文: A direct proof of AGT conjecture at beta = 1

We observe that, at beta-deformed matrix models for the four-point conformal block, the point q=0 is the point where the three-Penner type model becomes a pair of decoupled two-Penner type models and where, in the planar limit, (an array…

We consider the half-genus expansion of the resolvent function in the $\beta$-deformed matrix model with three-Penner potential under the AGT conjecture and the $0d-4d$ dictionary. The partition function of the model, after the…

Extending recent work of Kachru and Silverstein, we consider ``orbifolds'' of 4-dimensional $\mathcal{N}=4$ SU(n) super-Yang-Mills theories with respect to discrete subgroups of the SU(4) $R$-symmetry which act nontrivially on the gauge…

We consider Alday-Gaiotto-Tachikawa (AGT) realization of the Nekrasov partition function of N=2 SCFT. We focus our attention on the SU(2) theory with N_f=4 flavor symmetry, whose partition function, according to AGT, is given by the…

An attempt is made to formulate Gaiotto's S-duality relations in an explicit quantitative form. Formally the problem is that of evaluation of the Racah coefficients for the Virasoro algebra, and we approach it with the help of the matrix…

The Nekrasov instanton partition function of the 4d $\mathcal{N}=2^*$ $U(N)$ gauge theory (a mass deformation of 4d $\mathcal{N}=4$ super-Yang-Mills theory), which is a generating series of equivariant integrals over instanton moduli…

We apply Schroedinger functional methods to two gauge theories with fermions in two-index representations: the SU(3) theory with Nf=2 adjoint fermions, and the SU(4) theory with Nf=6 fermions in the two-index antisymmetric representation.…

The Penner type beta-ensemble for Omega-deformed N=2 SU(2) gauge theory with two massless flavors arising as a limiting case from the AGT conjecture is considered. The partition function can be calculated perturbatively in a saddle-point…

We calculate the quantum corrections to the two-point function of four dimensional topologically massive non-Abelian vector fields at one loop order for $SU(N)$ gauge theory in Feynman-'t Hooft gauge. We calculate the beta function of the…

The purpose of the article is to provide partial proofs for two conjectures given by Witte and Forrester in "Moments of the Gaussian $\beta$ Ensembles and the large $N$ expansion of the densities" with the use of the topological recursion…

Recently Alday, Gaiotto and Tachikawa have proposed relation between 2- and 4-dimensional conformal field theories. The relation implies that the Nekrasov partition functions of N=2 superconformal gauge theories are equal to conformal…

We report new results on the conformal properties of an important strongly coupled gauge theory, a building block of composite Higgs models beyond the Standard Model. With twelve massless fermions in the fundamental representation of the…

For a general ${\cal N}=1$ supersymmetric gauge theory regularized by higher covariant derivatives we prove in all orders that the $\beta$-function defined in terms of the bare couplings is given by integrals of double total derivatives…

We give some evidences of the AGT-W relation between SU(3) quiver gauge theories and A_2 Toda theory. In particular, we derive the explicit form of 5-point correlation functions in the lower orders and confirm the agreement with Nekrasov's…

We propose a Nekrasov-type formula for the instanton partition functions of four-dimensional N=2 U(2) gauge theories coupled to (A_1,D_{2n}) Argyres-Douglas theories. This is carried out by extending the generalized AGT correspondence to…

Noncommutative U(1) gauge theory in 4-dimensions is shown to be equivalent in some scaling limit to an ordinary non-linear sigma model in 2-dimensions . The model in this regime is solvable and the corresponding exact beta function is…

In this article I first give an abbreviated history of string theory and then describe the recently-conjectured field-string duality. This suggests a class of nonsupersymmetric gauge theories which are conformal (CGT) to leading order of…

The problem of finding good approximations of arbitrary 1-qubit gates is identical to that of finding a dense group generated by a universal subset of $SU(2)$ to approximate an arbitrary element of $SU(2)$. The Solovay-Kitaev Theorem is a…

We show that the dual partition function of the pure $\mathcal N=2$ $SU(2)$ gauge theory in the self-dual $\Omega$-background (a) is given by Fredholm determinant of a generalized Bessel kernel and (b) coincides with the tau function…

We study $SU(2)$ gauge theories coupled to $(A_1,D_N)$ theories with or without a fundamental hypermultiplet. For even $N$, a formula for the contribution of $(A_1,D_N)$ to the Nekrasov partition function was recently obtained by us with…