相关论文: Yang-Mills detour complexes and conformal geometry

This paper recalls the development of gauge theory culminating in Yang-Mills theory, and the application of differential geometry including connections on fiber bundles to field theory. Finally, we see how the preceding is used to explain…

We associate geometric partial differential equations on holomorphic vector bundles to Bridgeland stability conditions. We call solutions to these equations $Z$-critical connections, with $Z$ a central charge. Deformed Hermitian Yang--Mills…

In the first part of this thesis, we study form factors of general gauge-invariant local composite operators in $\mathcal{N}=4$ super Yang-Mills theory at various loop orders and for various numbers of external legs. We show how to use…

We generalize to topologically non-trivial gauge configurations the description of the Einstein-Yang-Mills system in terms of a noncommutative manifold, as was done previously by Chamseddine and Connes. Starting with an algebra bundle and a…

A Riemannian or pseudo-Riemannian (or conformal) structure is conformally Einstein if and only if there is a suitably generic parallel section of a certain vector bundle -- the so-called standard conformal tractor bundle. We show that this…

We provide an explicit construction of a manifestly duality invariant, interacting deformation of Maxwell theory in four dimensions in terms of mutually local, but interacting 1- and 3-forms. Interestingly, our theory is formulated directly…

The deformed Hermitian Yang-Mills (dHYM) equation is a special Lagrangian type condition in complex geometry. It requires the complex analogue of the Lagrangian phase, defined for Chern connections on holomorphic line bundles using a…

We construct a minitwistor action for Yang--Mills--Higgs theory in three dimensions. The Feynman diagrams of this action will construct perturbation theory around solutions of the Bogomolny equations in much the same way that MHV diagrams…

On conformally compact manifolds we study Yang-Mills equations, their boundary conditions, formal asymptotics, and Dirichlet-to-Neumann maps. We find that smooth solutions with "magnetic" Dirichlet boundary data are obstructed by a…

We lay the foundations of a Morse homology on the space of connections on a principal $G$-bundle over a compact manifold $Y$, based on a newly defined gauge-invariant functional $\mathcal J$. While the critical points of $\mathcal J$…

Centre-stabilised $SU(N)$ Yang-Mills theories on $\mathbb{R}^3 \times S^1$ are QCD-like theories that can be engineered to remain weakly-coupled at all energy scales by taking the $S^1$ circle length $L$ to be sufficiently small. In this…

By using the self-dual Yang-Mills (SDYM) equation as an example, we study a method for relating symmetries and recursion operators of two partial differential equations connected to each other by a non-auto-Backlund transformation. We prove…

Geometry of the solution space of the self-dual Yang-Mills (SDYM) equations in Euclidean four-dimensional space is studied. Combining the twistor and group-theoretic approaches, we describe the full infinite-dimensional symmetry group of…

Let $\Sigma$ be a closed surface, $G$ a compact Lie group, not necessarily connected, with Lie algebra $g$, endowed with an adjoint action invariant scalar product, let $\xi \colon P \to \Sigma$ be a principal $G$-bundle, and pick a…

The symmetry operator $Q=Y^2$ is introduced to re-describe the Heisenberg spin triangles in the \{V6\} molecule, where $\mathbf{Y}$ stands for the Yangian operator which can be viewed as special form of Dzyaloshiky-Moriya (DM) interaction…

The first and shorter part of this thesis deals with the structural assumption of invertibility in a Lie groupoid. When this assumption is dropped, we obtain the notion of a Lie category: a small category, endowed with a compatible…

Yangian symmetry of amplitudes in $\mathcal{N}=4$ super Yang-Mills theory is formulated in terms of eigenvalue relations for monodromy matrix operators. The Quantum Inverse Scattering Method provides the appropriate tools to treat the…

We define a natural generalized symmetry of the Yang-Mills equations as an infinitesimal transformation of the Yang-Mills field, built in a local, gauge invariant, and Poincar\'e invariant fashion from the Yang-Mills field strength and its…

Herein, we consider a topologically twisted version of maximally supersymmetric Yang-Mills theory in five dimensions which was introduced by Witten in 2011. We consider this theory on a five manifold of the form M_4 x I for M_4 an oriented…

We study an angular dipole deformation of maximally supersymmetric Yang-Mills theory (SYM) that preserves its classical scale invariance. We show that two-point functions of suitable single trace operators, restricted to an invariant plane,…