Related papers: Convergent Yang-Mills Matrix Theories
In this paper we consider IIA and IIB matrix string theories which are defined by two-dimensional and three-dimensional super Yang-Mills theory with the maximal supersymmetry, respectively. We exactly compute the partition function of both…
We propose a nonperturbative framework to study general correlation functions of single-trace operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory at large $N$. The basic strategy is to decompose them into fundamental building…
On any simply connected Sasaki-Einstein five dimensional manifold one can construct a super Yang-Mills theory which preserves at least two supersymmetries. We study the special case of toric Sasaki-Einstein manifolds known as $Y^{p,q}$…
We show that ${\cal N} = 4$ supersymmetric-Yang-Mills (SYM) theory on $\mathbb{R} \times S^3$ with gauge group $\text{SU}(N)$ is described in a near-BPS limit by a simple lower-dimensional nonrelativistic field theory with $\text{SU}(1,1)…
Quantum correlators of pure supersymmetric Yang-Mills theories in D=3,4,6 and 10 dimensions can be reformulated via the non-linear and non-local transformation (`Nicolai map') that maps the full functional measure of the interacting theory…
We attempt to determine the partition function of ${\cal N}=4$ super Yang-Mills theory for $ADE$ gauge groups on $K3$ and investigate the relation with affine Lie algebras. In particular we describe eta functions, which compose SU(N)…
We perform a systematic study of integrated four-point functions of half-BPS operators in four-dimensional $\mathcal{N}=4$ super Yang-Mills theory with gauge group $SU(N)$. These observables, defined by a certain spacetime integral of…
In this paper we summarise the localisation calculation of 5D super Yang-Mills on simply connected toric Sasaki-Einstein (SE) manifolds. We show how various aspects of the computation, including the equivariant index, the asymptotic…
Based on the construction by Hosomichi, Seong and Terashima we consider N=1 supersymmetric 5D Yang-Mills theory with matter on a five-sphere with radius r. This theory can be thought of as a deformation of the theory in flat space with…
Recently there was a substantial progress in understanding of supersymmetric theories (in particular, their BPS spectrum) in space-times of different dimensions due to the exact computation of superconformal indices and partition functions…
We test the conjectured relationship between N=4 super Yang-Mills theory in four dimensions and IIB supergravity compactified on $AdS_5\times S_5$ by computing the two- and three-point functions of R-symmetry currents. We observe that the…
The connection of maximally supersymmetric Yang-Mills theory to the (2,0) theory in six dimensions has raised the possibility that it might be perturbatively ultraviolet finite in five dimensions. We test this hypothesis by computing the…
Certain integrable models are described by pairs (X,Y) of ADET Dynkin diagrams. At high energy these models are expected to have a conformally invariant limit. The S-matrix of the model determines algebraic equations, whose solutions are…
Noncommutative ${\cal N}=1$ and ${\cal N}=2$ supersymmetric Yang-Mills theories with gauge group U(N) are studied here using the background field method and superspace background covariant D-algebra in perturbation theory. At one loop…
We investigate the spontaneous breaking of the SO(D) symmetry in matrix models, which can be obtained by the zero-volume limit of pure SU(N) super Yang-Mills theory in D = 6, 10 dimensions. The D = 10 case corresponds to the IIB matrix…
This is a pedagogical review on the integrability-based approach to the three-point function in N=4 supersymmetric Yang-Mills theory. We first discuss the computation of the structure constant at weak coupling and show that the result can…
We study particular integrated correlation functions of two superconformal primary operators of the stress tensor multiplet in the presence of a half-BPS line defect labelled by electromagnetic charges $(p,q)$ in $\mathcal{N}=4$…
We perform the calculation of the partition function of the Poisson-sigma model on the world sheet with the topology of a two-dimensional disc. Considering the special case of a linear Poisson structure we recover the partition function of…
This talk is an overview of our recent investigations of supersymmetric and near conformal gauge theories. We have studied extensively $\mathcal{N}=1$ super Yang-Mills theory, most recently with the gauge group SU(3). In addition we have…
We solve exactly the Dyson-Schwinger equations for Yang-Mills theory in 3 and 4 dimensions. This permits us to obtain the exact correlation functions till order 2. In this way, the spectrum of the theory is straightforwardly obtained and…