Related papers: Virasoro constraint for Nekrasov instanton partiti…
We give a mathematically rigorous proof of Nekrasov's conjecture: the integration in the equivariant cohomology over the moduli spaces of instantons on $\mathbb R^4$ gives a deformation of the Seiberg-Witten prepotential for N=2 SUSY…
AGT conjecture reveals a connection between 4D $\mathcal{N}=2$ gauge theory and 2D conformal field theory. Though some special instances have been proven, others remain elusive and the attempts on its full proof never stop. When the…
We investigate a relation between the super topological recursion and Gaiotto vectors for $\mathcal{N}=1$ superconformal blocks. Concretely, we introduce the notion of the untwisted and $\mu$-twisted super topological recursion, and…
We present in this paper a differential version of Mirzakhani's recursion relation for the Weil-Petersson volumes of the moduli spaces of bordered Riemann surfaces. We discover that the differential relation, which is equivalent to the…
It is pointed out that the sine law for the k-string tension emerges as the critical threshold below which the spatial Z_N symmetry of the static baryon potential is spontaneously broken. This result applies not only to SU(N) gauge…
String representation of the $[U(1)]^{N-1}$ gauge-invariant dual Abelian-Higgs-type theory, which is relevant to the SU(N)-QCD with the $\Theta$-term and provides confinement of quarks, is derived. The N-dependence of the Higgs vacuum…
For a valuation ring $V$, a smooth $V$-algebra $A$, and a reductive $V$-group scheme $G$ satisfying a certain natural isotropicity condition, we prove that every Nisnevich $G$-torsor on $\mathbb{A}^N_A$ descends to a $G$-torsor on $A$. As a…
We give a proof of the recursive formula on the norm of Whittaker vector of the deformed Virasoro algebra, which is an analog of the one for the Virasoro Lie algebra proposed by Al. Zamolodchikov. Our formula gives a proof of the pure SU(2)…
We study the U(1) and U(2) instanton solutions of gauge theory on general noncommutative $\bf{R}^4$. In all cases considered we obtain explicit results for the projection operators. In some cases we computed numerically the instanton charge…
We provide a formula for the partition function of five-dimensional $\mathcal{N}=1$ gauge theories on $\mathcal{M}_4 \times S^1$, topologically twisted along $\mathcal{M}_4$ in the presence of general background magnetic fluxes, where…
We investigate the Abelian projection with respect to the Polyakov loop operator for SU(N) gauge theories on the four torus. The gauge fixed $A_0$ is time-independent and diagonal. We construct fundamental domains for $A_0$. In sectors with…
In earlier work, we constructed invariants of irreducible representations of the Kauffman skein algebra of a surface. We introduce here an inverse construction, which to a set of possible invariants associates an irreducible representation…
We investigate the viability of predictive schemes for quark-lepton Yukawa ratios and nucleon decay in non-supersymmetric SU(5) Grand Unified Theories (GUTs) where neutrino masses are generated by a type II seesaw mechanism. The scalar…
We provide evidence that the conformal blocks of N=1 super Liouville conformal field theory are described in terms of the SU(2) Nekrasov partition function on the ALE space O_{P^1}(-2).
We summarize recent studies of realistic nonsupersymmetric Grand Unified Theories (GUTs) extended with a global $U(1)_{\rm PQ}$ symmetry, so as to accommodate the axion solution to the strong CP problem. Aside from solving the CP problem…
We consider the topological string partition function, including the Nekrasov deformation, for type IIB geometries with an A_{n-1} singularity over a Riemann surface. These models realize the N=2 SU(n) superconformal gauge systems recently…
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 give some evidences which imply that W(1+infinity) algebra describes the symmetry behind AGT(-W) conjecture: a correspondence between the partition function of N=2 supersymmetric quiver gauge theories and the correlators of Liouville…
In a recent paper (arXiv:0906.3219) the representation of Nekrasov partition function in terms of nontrivial two-dimensional conformal field theory has been suggested. For non-vanishing value of the deformation parameter…
We describe how an SU(N) chiral gauge theory can be put on the lattice using non-perturbative gauge fixing. In particular, we explain how the Gribov problem is dealt with. Our construction is local, avoids doublers, and weak-coupling…