Related papers: Locally Finite Observables in sYM
We examine the relation between supersymmetric localization on $\mathbb{S}^4$ and standard QFT results for non-conformal theories in flat space. Specifically, we consider 1/2 BPS circular Wilson loops in four-dimensional SU($N$)…
Discretization of supersymmetric Yang--Mills (SYM) theories is an old problem in lattice field theory. It has resisted solution until recently when new ideas drawn from orbifold constructions and topological field theories have been brought…
A power-counting renormalizable model into which massive Yang-Mills theory is embedded is analyzed. The model is invariant under a nilpotent BRST differential s. The physical observables of the embedding theory, defined by the cohomology…
In planar ${\cal N}=4$ supersymmetric Yang-Mills theory we have studied supersymmetric Wilson loops composed of a large number of light-like segments, i.e., null zig-zags. These contours oscillate around smooth underlying spacelike paths.…
We provide two derivations of the one-loop dual conformal anomaly of generic n-point superamplitudes in maximally supersymmetric Yang-Mills theory. Our proofs are based on simple applications of unitarity, and the known analytic properties…
We uncover a method of calculation that proceeds at every step without fixing the gauge or specifying details of the regularisation scheme. Results are obtained by iterated use of integration by parts and gauge invariance identities. The…
We propose an integrability approach for planar three-point functions at finite coupling in $\mathcal{N}=2$ superconformal field theories obtained as $\mathbb{Z}_K$ orbifolds of $\mathcal{N}=4$ super Yang-Mills (SYM). Generalizing the…
Extending and unifying a number of well-known conjectures and open questions, we conjecture that locally elliptic (that is, every element has a bounded orbit) actions by automorphisms of finitely generated groups on finite dimensional…
We show that if $f$ is locally in $L\log\log L$ then the lacunary spherical means converge almost everywhere. The argument given here is a model case for more general results on singular maximal functions and Radon transforms (see ref. 6).
A formulation of $\mathcal{N} = 2$ supersymmetric Yang-Mills theory with a spacetime-dependent gauge coupling allows to study the breaking of conformal symmetry at the quantum level. The theory has an energy-momentum tensor that is only…
Let (R,m) be a complete local ring, a an ideal of R and M a finitely generated R-module. The aim of this paper is to show that for any non-negative integer n, the least integer i such that the i-th local cohomology with respect to a is not…
We describe local mirror symmetry from a mathematical point of view and make several A-model calculations using the mirror principle (localization). Our results agree with B-model computations from solutions of Picard-Fuchs differential…
We show that an action of a group on a set $X$ is locally finite if and only if $X$ is not equidecomposable with a proper subset of itself. As a consequence, a group is locally finite if and only if its uniform Roe algebra is finite.
A modified generally covariant Yang-Mills action, which depends on the complex structure of spacetime and not its metric, is proved to be renormalizable. This proof makes this Lagrangian model the unique known generally covariant four…
A manifestly gauge invariant exact renormalization group for pure SU(N) Yang-Mills theory is proposed, along with the necessary gauge invariant regularisation which implements the effective cutoff. The latter is naturally incorporated by…
We investigate the structure of locally finite profinite rings. We classify (Jacobson-) semisimple locally finite profinite rings as products of complete matrix rings of bounded cardinality over finite fields, and we prove that the Jacobson…
The large-N limit of the two-dimensional non-local U$(N)$ Yang-Mills theory on an orientable and non-orientable surface with boundaries is studied. For the case which the holonomies of the gauge group on the boundaries are near the…
In both mathematics and physics, topological field theories and holomorphic field theories appear naturally, but there are interesting theories that are hybrids -- looking topological in some directions and holomorphic in others -- such as…
We explicitly compute the one-loop exact beta function for a nonlocal extension of the standard gauge theory, in particular Yang-Mills and QED. The theory, made of a weakly nonlocal kinetic term and a local potential of the gauge field, is…
In this note we study supersymmetric Wilson loops restricted to an S^2 submanifold of four-dimensional space in N=4 super Yang-Mills. We provide evidence from both perturbation theory and the AdS dual that those loops are equal to the…