Related papers: Pure N=2 Super Yang-Mills and Exact WKB
Let $\mathfrak{g}$ be a simple Lie algebra. We study 1/2-BPS Wilson loops of supersymmetric 5d $\mathfrak{g}$-type quiver gauge theories on a circle, in a non-trivial instanton background. The Wilson loops are codimension 4 defects of the…
We evaluate quasi-classically the Ramond partition function of Euclidean D=10 U(N) super-Yang--Mills theory reduced to a two-dimensional torus. The result can be interpreted in terms of free strings wrapping the space-time torus, as…
We consider the $T\bar{T}$ deformation of two dimensional Yang--Mills theory on general curved backgrounds. We compute the deformed partition function through an integral transformation over frame fields weighted by a Gaussian kernel. We…
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…
The instanton contributions to the partition function and to homologically trivial Wilson loops for a U(N) Yang-Mills theory on a torus $T^2$ are analyzed. An exact expression for the partition function is obtained as a sum of contributions…
We use supersymmetric localization to study probes of four dimensional Lagrangian N=2 superconformal field theories. We first derive a unique equation for the eigenvalue density of these theories. We observe that these theories have a…
This is the third article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J. Teschner. It is explained how to compute the instanton partition functions. The results can be written as sums over bases…
We find exact solutions for N=2 supersymmetric SO(N), N=7,9,10,11,12 gauge theories with matter in the fundamental and spinor representation. These theories, with specific numbers of vectors and spinors, arise naturally in the…
In this contribution we describe how to obtain instanton effects in four dimensional gauge theories by computing string scattering amplitudes in D3/D(-1) brane systems. In particular we study a system of fractional D3/D(-1) branes in a Z_2…
Exact results in supersymmetric Chern-Simons and N=2 Yang-Mills theories can be used to examine the quantum behavior of observables and the structure of the perturbative series. For the U(2) x U(2) ABJM model, we determine the asymptotic…
The partition function of a 3d $\mathcal{N}=4$ gauge theory with rank $N$ can be computed using supersymmetric localization in terms of a matrix model, which often can be formulated as an ideal Fermi gas with a non-trivial one-particle…
We argue the connection of Nekrasov's partition function in the \Omega background and the moduli space of D-branes, suggested by the idea of geometric engineering and Gopakumar-Vafa invariants. In the instanton expansion of N=2 SU(2)…
Generalizations of the AGT correspondence between 4D $\mathcal{N}=2$ $SU(2)$ supersymmetric gauge theory on ${\mathbb {C}}^2$ with $\Omega$-deformation and 2D Liouville conformal field theory include a correspondence between 4D…
The free field partition function for a generic U(N) gauge theory, where the fundamental fields transform in the adjoint representation, is analysed in terms of symmetric polynomial techniques. It is shown by these means how this is related…
We present a string theory construction of Omega-deformed four-dimensional gauge theories with generic values of \epsilon_1 and \epsilon_2. Our solution gives an explicit description of the geometry in the core of Nekrasov and Witten's…
We formulate a `master' partition function in three-dimensional $\mathcal{N}=2$ superspace that realises, upon integrating out complementary superfields, both the electric Maxwell--Chern--Simons (MCS) theory and its magnetic $S$-dual: a…
We study a Gaussian measure with parameter $q\in(0,1)$ on the dual of the unitary group of size $N$: we prove that a random highest weight under this measure is the coupling of two independent $q$-uniform random partitions $\alpha,\beta$…
The partition function of general N = 2 supersymmetric SU(2) Yang-Mills theories on a four-sphere localizes to a matrix integral. We show that in the decompactification limit, and in a certain regime, the integral is dominated by a saddle…
We show that noncommutative gauge theory in two dimensions is an exactly solvable model. A cohomological formulation of gauge theory defined on the noncommutative torus is used to show that its quantum partition function can be written as a…
The low energy effective couplings of a four-dimensional $\mathcal{N}=2$ supersymmetric gauge theory to topological invariants of the background gravitational field are described by two functions $A$ and $B$. These two functions play an…