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We study four-dimensional $\mathcal{N}=2$ supersymmetric $U(N)$ gauge theory with $2N$ fundamental hypermultiplets in the self-dual $\Omega$-background. The partition function simplifies at special points of the parameter space and is…
By studying the partition function of $N=4$ topologically twisted supersymmetric Yang-Mills on four-manifolds, we make an exact strong coupling test of the Montonen-Olive strong-weak duality conjecture. Unexpected and exciting links are…
Scattering amplitudes in superconformal field theories do not enjoy this symmetry, because the definition of asymptotic states involve a notion of infinity. Concentrating on planar $\mathcal{N}=4$ Yang-Mills, we consider a generalization of…
We propose new formulae for the two-loop n-point D-dimensional integrands of scattering amplitudes in Yang-Mills theory and gravity. The loop integrands are written as a double-forward limit of tree-level trivalent diagrams, and are…
The vacuum structure of N=2 (and N=4) SUSY Yang-Mills theory is analyzed in detail by considering the effective potential for constant background scalar- magnetic fields within different approximations. We compare the one-loop approximation…
We show how to give the expression for periods, Higgs field and its dual of N=2 supersymmetric Yang-Mills theory around the conformal point. This is achieved by evaluating the integral representation in the weak coupling region, and by…
We confirm by explicit computation the conjectured all-orders iteration of planar maximally supersymmetric N=4 Yang-Mills theory in the nontrivial case of five-point two-loop amplitudes. We compute the required unitarity cuts of the…
A new set of gauge invariant variables is defined to describe the physical Hilbert space of $d = 3 + 1$ $SU(2)$ Yang-Mills theory in the fixed-time canonical formalism. A natural geometric interpretation arises due to the $GL(3)$ covariance…
The use of supersymmetric localisation has recently led to modular covariant expressions for certain integrated correlators of half-BPS operators in $\mathcal{N} = 4$ supersymmetric Yang-Mills theory with a general classical gauge group…
Self-dual perturbiner in the Yang-Mills theory is constructed by the twistor methods both in topologically trivial and topologically nontrivial cases. Maximally helicity violating amplitudes and their instanton induced analogies are briefly…
We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity…
We review some recent additions to the tool-chest of techniques for finding compact integrand representations of multiloop gauge-theory amplitudes - including non-planar contributions - applicable for N=4 super-Yang-Mills in four and higher…
We construct a prescriptive, bubble power-counting basis of one-loop integrands suitable for representing amplitude integrands in less-supersymmetric Yang-Mills theory. With the exception of massless bubbles, all integrands have…
One of the simplest examples of non-invertible symmetries in higher dimensions appears in 4d Maxwell theory, where its $SL(2,\mathbb{Z})$ duality group can be combined with gauging subgroups of its electric and magnetic 1-form symmetries to…
We construct a four dimensional Yang-Mills theory with ${\cal N}=4$ twisted supersymmetry whose classical vacua correspond to four dimensional anti-de Sitter space. The theory utilizes a complex gauge field whose real part is a spin…
We propose a new version of SU(N) Yang-Mills theory reformulated in terms of new field variables which are obtained by a nonlinear change of variables from the original Yang-Mills gauge field. The reformulated Yang-Mills theory enables us…
In these lectures we present a detailed description of various aspects of gauge theories with extended N=2 and N=4 supersymmetry that are at the basis of recently found exact results. These results include the exact calculation of the low…
In generalized Yang-Mills theories scalar fields can be gauged just as vector fields in a usual Yang-Mills theory, albeit it is done in the spinorial representation. The presentation of these theories is aesthetic in the following sense: A…
We compute B-type Weyl anomaly coefficients for the two non-supersymmetric codimension-1 domain wall versions of N = 4 super Yang-Mills theory which are holographically dual to the D3-D7 probe-brane system. We compute the two-point function…
Supersymmetric integrands for the two-loop five-point amplitudes in ten-dimensional super Yang--Mills and type II supergravity are proposed. The kinematic numerators are manifestly local and satisfy the duality between color and kinematics…