Related papers: Large N techniques for Nekrasov partition function…
We use solvable two-dimensional gauge theories to illustrate the issues in relating large N gauge theory to string theory. We also give an introduction to recent mathematical work which allows constructing master fields for higher…
The recent AGT suggestion to use the set of Nekrasov functions as a basis for a linear decomposition of generic conformal blocks works very well not only in the case of Virasoro symmetry, but also for conformal theories with extended chiral…
We study the large $N$ limit of twisted partition functions on $\mathcal{M}_{g,p}$, the $S^1$ bundle of degree $p$ over a Riemann surface of genus $g$, for 3D $\mathcal{N}=2$ superconformal field theories arising as low-energy limit of…
A slice of AdS_5 is used to provide a 5D gravitational description of 4D strongly-coupled Seiberg dual gauge theories. An (electric) SU(N) gauge theory in the conformal window at large N is described by the 5D bulk, while its weakly coupled…
We study the single site SU(N) lattice gauge theory with N_f=2 adjoint Wilson fermions for values of N up to 53. We determine the phase diagram of the theory as a function of the hopping parameter kappa and the inverse 't Hooft coupling b,…
We prove the connection between the Nekrasov partition function of N=2 super-symmetric U(2) gauge theory with adjoint matter and conformal blocks for the Virasoro algebra, as predicted by the Alday-Gaiotto-Tachikawa relations.…
We examine the partition function of N=2* supersymmetric SU(N) Yang-Mills theory on the four-sphere in the large radius limit. We point out that the large radius partition function, at fixed N, is computed by saddle points lying on…
An intriguing coincidence between the partition function of super Yang-Mills theory and correlation functions of 2d Toda system has been heavily studied recently. While the partition function of gauge theory was explored by Nekrasov, the…
Recently it was shown that an asymptotic behaviour of $SU(N)$ gauge theory for large $N$ is described by q-deformed quantum field. The master fields for large N theories satisfy to standard equations of relativistic field theory but fields…
We derive the partition function for the Vafa-Witten twist of the $\mathcal{N}=4$ supersymmetric gauge theory with gauge group SU(N) (for prime $N$) and arbitrary values of the 't Hooft fluxes $v\in H^{2}(X,\mathbb{Z}_{N})$ on K\"ahler…
In these lecture notes prepared for the 11th Taiwan Spring School, Taipei 1997}, and updated for the Saalburg summer school 1998, we review the solutions of O(N) or U(N) models in the large N limit and as 1/N expansions, in the case of…
Phenomenological analysis of the covariant theta-exact noncommutative (NC) gauge field theory (GFT), inspired by high energy cosmic rays experiments, is performed in the framework of the inelastic neutrino-nucleon scatterings, plasmon and…
A sequence of massive scaling limits of the $\beta$-deformed $A_{n-1}$ quiver matrix model that keeps the size of the matrices finite and that corresponds to the $N_{f} =2n \rightarrow 2n-1, 2n-2$ limits on the number of flavors at 4d…
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…
In theories without known Lagrangian descriptions, knowledge of the global symmetries is often one of the few pieces of information we have at our disposal. Gauging (part of) such global symmetries can then lead to interesting new theories,…
We relate Liouville/Toda CFT correlators on Riemann surfaces with boundaries and cross-cap states to supersymmetric observables in four-dimensional N=2 gauge theories. Our construction naturally involves four-dimensional theories with…
We consider N=3 supersymmetric Chern-Simons (CS) theories that contain product U(N) gauge groups and bifundamental matter fields. Using the matrix model of Kapustin, Willett and Yaakov, we examine the Euclidean partition function of these…
We present a summary of current knowledge about the AGT relations for conformal blocks with additional insertion of the simplest degenerate operator, and a special choice of the corresponding intermediate dimension, when the conformal…
An explicit check of the AGT relation between the W_N-symmetry controlled conformal blocks and U(N) Nekrasov functions requires knowledge of the Shapovalov matrix and various triple correlators for W-algebra descendants. We collect simplest…
We analyze the conjectured duality between a class of double-scaling limits of a one-matrix model and the topological twist of non-critical superstring backgrounds that contain the N=2 Kazama-Suzuki SL(2)/U(1) supercoset model. The…