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Following a remark advanced by Feynman,we study the connection between the form of the nonlinear vertices involving gauge particles and the Abelian gauge invariance of physical tree amplitudes. We show that this requirement, together with…
Supersymmetric gauge theories in four dimensions have taught us many important physics lessons. These can both inform and be informed by future work on the lattice. I focus on three issues: the properties of supersymmetric Yang-Mills theory…
We give a self-contained introduction into the metric-affine gauge theory of gravity. Starting from the equivalence of reference frames, the prototype of a gauge theory is presented and illustrated by the example of Yang-Mills theory. Along…
It has been noticed that the k-string observables can be expressed in terms of the fundamental string ones. We identify a sufficient condition for a generic gravity dual background which when satisfied the mapping can be done. The condition…
The local symmetry transformations of the quantum effective action for general gauge theory are found. Additional symmetries arise under consideration of background gauges. Together with "trivial" gauge transformations, vanishing on mass…
The Kerr-Schild double copy relates exact solutions of gauge and gravity theories. In all previous examples, the gravity solution is associated with an abelian-like gauge theory object, which linearises the Yang-Mills equations. This…
We suggest that four dimensional massive gauge vectors could be described by coupling ordinary Yang-Mills theory to a topological gauge theory. For this the coupling should excite a nontrivial degree of freedom from the topological theory,…
A framework for constructing new kinds of gauge theories is suggested. Essentially it consists in replacing Lie algebras by Lie or Courant algebroids. Besides presenting novel topological theories defined in arbitrary spacetime dimensions,…
We show that a spinless theory of gravity is also allowed by the kinematics of general relativity. In the absence of fermions the spinless theory of gravity and the theories in the standard model of particle physics are the same Yang-Mills…
We argue that the non gauge invariant coupling between torsion and the Maxwell or Yang-Mills fields in Einstein-Cartan theory can not be ignored. Arguments based in the existence of normal frames in neighbourhoods, and an approximation to a…
Previous investigations on the renormalizability properties of Lorentz-violating Yang-Mills (LVYM) theories in the Landau gauge have pointed out the necessity of the inclusion of a mass-like term for the gauge fields. If one aims at…
Finding solutions to non-linear field theories, such as Yang-Mills theories or general relativity, is usually difficult. The field equations of Yang-Mills theories and general relativity are known to share some mathematical similarities,…
After reviewing how Albert Einstein's general relativity (GR) can be viewed as a gauge theory of the Poincar\'e algebra, we show how \'Elie Cartan's geometric formulation of Newtonian gravity (Newton-Cartan gravity) can be viewed as a gauge…
We describe a ten dimensional supergravity geometry which is dual to a gauge theory that is non-supersymmetric Yang Mills in the infra-red but reverts to $N$=4 super Yang Mills in the ultra-violet. A brane probe of the geometry shows that…
We discuss the relation between spacetime diffeomorphisms and gauge transformations in theories of the Yang-Mills type coupled with Einstein's General Relativity. We show that local symmetries of the Hamiltonian and Lagrangian formalisms of…
We generalize the gradient flow equation for field theories with nonlinearly realized symmetry. Applying the formalism to super Yang-Mills theory, we construct a supersymmetric extension of the gradient flow equation. It can be shown that…
The three fundamental geometric components of Yang-Mills theory -gauge field, gauge fixing and ghost field- are unified in a new object: an extended connection in a properly chosen principal fiber bundle. To do this, it is necessary to…
We study double copy relations for loop integrands in gauge theories and gravity based on their constructions from single cuts, which are in turn obtained from forward limits of lower-loop cases. While such a construction from forward…
We introduce and study a new class of power-counting non-renormalisable gauge theories in four space-time dimensions. The Lagrangian is an arbitrary function of the self-dual part of the field strength. The resulting perturbation theory has…
The canonical formulation of general relativity is based on decomposition space--time manifold $M$ into $ R\times \Sigma$, this decomposition has to preserve the invariance of general relativity, invariance under general coordinates, and…