Related papers: Some Non-Renormalization Theorems for Higher Deriv…

In this short note we review the interpretation of the spectral action for the Yang-Mills system in noncommutative geometry as a higher-derivative gauge theory, adopting an asymptotic expansion in a cutoff parameter. We recall our previous…

It is known that the supermultiplet of beta-deformations of ${\cal N}=4$ supersymmetric Yang-Mills theory can be described in terms of the exterior product of two adjoint representations of the superconformal algebra. We present a…

We examine a double trace deformation of SU(N) Yang-Mills theory which, for large $N$ and large volume, is equivalent to unmodified Yang-Mills theory up to $O(1/N^2)$ corrections. In contrast to the unmodified theory, large $N$ volume…

We study the mixing of operators under renormalization group flow in quantum theories, and prove a non-renormalization theorem at non-linear order. It dictates zeros up to a certain number of loops in anomalous dimension tensors that…

We formulate a method of performing non-perturbative calculations in quantum field theory, based upon a derivative expansion of the exact renormalization group. We then proceed to apply this method to the calculation of critical exponents…

I revisit a basic question about the noncommutative Yang-Mills theory: if it exists or not, or more precisely, whether a nonperturbative formulation exists. As the most promising approach, I consider a formulation based on matrix models. It…

We construct lattice action for five-dimensional maximally supersymmetric Yang-Mills theory. This supersymmetric lattice formulation can be used to explore the non-perturbative regime of the continuum target theory, which has a known…

We consider the dimensional reduction of N = 1 SYM_{2+1} to 1+1 dimensions, which has (1,1) supersymmetry. The gauge groups we consider are U(N) and SU(N), where N is a finite variable. We implement Discrete Light-Cone Quantization to…

Discretization of supersymmetric theories is an old problem in lattice field theory. It has resisted solution until quite recently when new ideas drawn from orbifold constructions and topological field theory have been brought to bear on…

We study the effective action of quantum mechanical SU(N) Yang-Mills theories with sixteen supersymmetries and N>2. We show that supersymmetry requires that the eight fermion terms in the supersymmetric completion of the $v^4$ terms be…

We raise the issue whether gauge theories, that are not renormalizable in the usual power-counting sense, are nevertheless renormalizable in the modern sense that all divergences can be cancelled by renormalization of the infinite number of…

Exact expressions for certain integrated correlators of four half-BPS operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory with gauge group $SU(N)$ have been recently obtained thanks to a beautiful interplay between supersymmetric…

We show that the Yang-Mills quantum field theory with momentum and spacetime cutoffs in four Euclidean dimensions is equivalent, term by term in an appropriately resummed perturbation theory, to a Fermionic theory with nonlocal interaction…

Massive renormalizable Yang-Mills theories in three dimensions are analysed within the algebraic renormalization in the Landau gauge. In analogy with the four dimensional case, the renormalization of the mass operator A^2 turns out to be…

We describe a simple method for determining the strong-coupling BPS spectrum of four dimensional N=2 supersymmetric Yang-Mills theory. The idea is to represent the magnetic monopoles and dyons in terms of D-brane boundary states of a…

We formulate noncommutative self-dual N=4 supersymmetric Yang-Mills theory in D=2+2 dimensions. As in the corresponding commutative case, this theory can serve as the possible master theory of all the noncommutative supersymmetric…

Perturbative renormalization provides the bedrock of understanding quantum field theories. In this work, I point out an alternative way of renormalizing quantum field theories, which is naturally encountered and well known for the case of…

It is shown that the beta functions for four dimensional N=2 supersymmetric Yang-Mills theory without matter give integral curves on the moduli space some of which are geodesics of the natural metric on the moduli space. In particular the…

We examine the renormalization of the first order formulation of Yang-Mills theory, by using the BRST idenities. These preserve the gauge invariance of the theory and enable a recursive proof of renormalizability to higher orders in…

We study correlation functions in (0+1)-dimensional maximally supersymmetric U(N) Yang-Mills theory, which was proposed by Banks et al. as a non-perturbative definition of 11-dimensional M-theory in the infinite-momentum frame. We perform…