Related papers: Higher Nahm transform in non commutative geometry

We show how the linear special conformal transformation in four-dimensional N=4 super Yang-Mills theory is metamorphosed into the nonlinear and field-dependent transformation for the collective coordinates of Dirichlet 3-branes, which…

To any spectral triple (A,D,H) a dimension d is associated, in analogy with the Hausdorff dimension for metric spaces. Indeed d is the unique number, if any, such that |D|^-d has non trivial logarithmic Dixmier trace. Moreover, when d is…

We continue the study of the relationship between Dixmier traces and noncommutative residues initiated by A. Connes. The utility of the residue approach to Dixmier traces is shown by a characterisation of the noncommutative integral in…

Given a Hopf algebra H, we study modules and bimodules over an algebra A that carry an H-action, as well as their morphisms and connections. Bimodules naturally arise when considering noncommutative analogues of tensor bundles. For…

In ${\cal N}=4$ super Yang-Mills theory on a four-manifold $M$, one can specify a discrete magnetic flux valued in $H^2(M,\Z_N)$. This flux is encoded in the AdS/CFT correspondence in terms of a five-dimensional topological field theory…

We study correlation functions in topologically twisted $\mathcal{N}=2, d=4$ supersymmetric Yang-Mills theory for gauge groups of rank larger than one on compact four-manifolds $X$. We find that the topological invariance of the generator…

The Yang-Baxter $\sigma$-model is a systematic way to generate integrable deformations of AdS$_5\times$S$^5$. We recast the deformations as seen by open strings, where the metric is undeformed AdS$_5\times$S$^5$ with constant string…

We consider SU($N$) Yang-Mills theory on ${\mathbb R}^{2,1}\times S^1$, where $S^1$ is a spatial circle. In the infrared limit of a small-circle radius the Yang-Mills action reduces to the action of a sigma model on ${\mathbb R}^{2,1}$…

We provide a simple non-perturbative formulation for non-commutative four-dimensional N = 2 supersymmetric Yang-Mills theories. The formulation is constructed by a combination of deconstruction (orbifold projection), momentum cut-off and…

It is shown that classical nonsupersymmetric Yang-Mills theory in 4 dimensions is symmetric under a generalized dual transform which reduces to the usual dual *-operation for electromagnetism. The parallel phase transport $\tilde{A}_\mu(x)$…

We show that dual conformal symmetry, mainly studied in planar $\mathcal N = 4$ super-Yang-Mills theory, has interesting consequences for Feynman integrals in nonsupersymmetric theories such as QCD, including the nonplanar sector. A simple…

We construct a mathematical framework for twisted N=2 supersymmetric topological quantum field theory on a 4-manifold. Supersymmetry in flat space is defined and the twist homomorphism is constructed, giving us a supermanifold that is the…

We observe that the main feature of the Randall-Sundrum model, used to solve the hierarchy problem, is already present in a class of Yang-Mills plus gravity theories inspired by noncommutative geometry. Strikingly the same expression for…

Fundamental group of a manifold gives a deep effect on its underlying smooth structure. In this paper we introduce a new variant of the Donaldson invariant in Yang-Mills gauge theory from twisting by the Picard group of a four manifold in…

We study numerically the geometric properties of reduced supersymmetric non-compact SU(N) Yang-Mills integrals in D=4 dimensions, for N = 2,3, ..., 8. We show that in the range of large eigenvalues of the matrices A^mu, the original…

We provide a systematic way of dimensional reduction for $(4+2n)$-dimensional $U(N)$ supersymmetric Yang-Mills (SYM) theories ($n=0,1,2,3$) and their mixtures compactified on two-dimensional tori with background magnetic fluxes, which…

A recent paper proposes a way of constructing infinite dimensional symmetries of the non-supersymmetric self-dual Yang-Mills action using isometries of the space-time. We review the Lagrangian formulation of N = 4 super Yang-Mills MHV rules…

We aim to connect the non commutative geometry ``quotient space'' viewpoint with the standard super Yang Mills theory approach in the spirit of Connes-Douglas-Schwartz and Douglas-Hull description of application of noncommutative geometry…

We exploit the $6D, {\cal N}=(1,0)$ and ${\cal N}=(1,1)$ harmonic superspace approaches to construct the full set of the maximally supersymmetric on-shell invariants of the canonical dimension ${\bf d=12}$ in $6D, \,{\cal N}=(1,1)$…

We show that the self-dual Yang-Mills equations afford supersymmetrisation to systems of equations invariant under global N-extended super-Poincar\'e transformations for arbitrary values of N, without the limitation (N\le 4) applicable to…