Related papers: A Note on Self-Dual Yang-Mills Theory

We show that the physical degrees of freedom of the critical open string with N=2 superconformal symmetry on the worldsheet are described by a self-dual Yang-Mills field on a hyperspace parametrised by the coordinates of the target space…

The relation between two--dimensional integrable systems and four--dimen\-sional self--dual Yang--Mills equations is considered. Within the twistor description and the zero--curvature representation a method is given to associate self--dual…

We derive and test a novel holographic duality in the B-model topological string theory. The duality relates the B-model on certain Calabi-Yau three-folds to two-dimensional chiral algebras defined as gauged $\beta\gamma\,$ systems. The…

We formulate a precise holographic duality between an ensemble of 4d $U(1)^g$ Maxwell theories living on a spin four-manifold $M_4$ and an Abelian BF-type 2-form gauge theory of level $N$, summed over all five-manifolds with boundary $M_4$.…

We summarise some of our recent works on $L_\infty$-algebras and quasi-groups with regard to higher principal bundles and their applications in twistor theory and gauge theory. In particular, after a lightning review of $L_\infty$-algebras,…

There exist many four dimensional integrable theories. They include self-dual gauge and gravity theories, all their extended supersymmetric generalisations, as well the full (non-self-dual) N=3 super Yang-Mills equations. We review the…

Self-dual Yang-Mills theory admits an underlying infinite dimensional symmetry algebra, which has been obtained from mode expansion of Mellin transformed 4d scattering amplitudes and separately, Koszul duality on twistor space. In this…

By using the Atiyah-Singer theorem through some similarities with the instanton and the anti-instanton moduli spaces, the dimension of the moduli space for two and four-dimensional BF theories valued in different background manifolds and…

This paper studies novel four-dimensional integrable field theories that are deformations of self-dual Yang-Mills. They are engineered by considering holomorphic Chern-Simons and BF type theories on covers of twistor space obtained by…

With the help of the Penrose-Ward transform, which relates certain holomorphic vector bundles over the supertwistor space to the equations of motion of self-dual SYM theory in four dimensions, we construct hidden infinite-dimensional…

A self-dual algebras is one isomorphic as a module to the opposite of its dual; a quasi self-dual algebra is one whose cohomology with coefficients in itself is isomorphic to that with coefficients in the opposite of its dual. For these…

These are expository lectures reviewing (1) recent developments in two-dimensional Yang-Mills theory, and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of…

Through a self-dual mapping of the geometry AdS5 x S5, fermionic T-duality provides a beautiful geometric interpretation of hidden symmetries for scattering amplitudes in N=4 super-Yang-Mills. Starting with Green-Schwarz sigma-models, we…

After a short introduction on the theory of homogeneous algebras we describe the application of this theory to the analysis of the cubic Yang-Mills algebra, the quadratic self-duality algebras, their "super" versions as well as to some…

This work is a continuation of our previous paper arXiv:1812.06473 where we have constructed ${\cal N}=2$ supersymmetric Yang-Mills theory on 4D manifolds with a Killing vector field with isolated fixed points. In this work we expand on the…

Using (partial) curvature flows and the transitive action of subgroups of O(d,Z) on the indices {1,...,d} of the components of the Yang-Mills curvature in an orthonormal basis, we obtain a nested system of equations in successively higher…

To any manifold equipped with a higher degree closed form, one can associate an L-infinity algebra of local observables that generalizes the Poisson algebra of a symplectic manifold. Here, by means of an explicit homotopy equivalence, we…

This paper presents a $q$-analogue of an extension of the tensor algebra given by the same author. This new algebra naturally contains the ordinary tensor algebra and the Iwahori-Hecke algebra type $A$ of infinite degree. Namely this…

Consider a pair $(X,L)$, of a Weinstein manifold $X$ with an exact Lagrangian submanifold $L$, with ideal contact boundary $(Y,\Lambda)$, where $Y$ is a contact manifold and $\Lambda\subset Y$ is a Legendrian submanifold. We introduce the…

We have recently introduced the notion of a q-quaternion bialgebra and shown its strict link with the SO_q(4)-covariant quantum Euclidean space R_q^4. Adopting the available differential geometric tools on the latter and the quaternion…