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Tremendous ongoing theory efforts are dedicated to developing new methods for QCD calculations. Qualitative rather than incremental advances are needed to fully exploit data still to be collected at the LHC. The maximally supersymmetric Yang-Mills theory (${mathcal N}=4$ sYM) shares with QCD the gluon sector, which contains the most complicated Feynman graphs, but at the same time has many special properties, and is believed to be solvable exactly. It is natural to ask what we can learn from advances in ${mathcal N}=4$ sYM for addressing difficult problems in QCD. With this in mind, we review here several remarkable developments and highlights of recent results in ${mathcal N}=4$ sYM. This includes all-order results for certain scattering amplitudes, novel symmetries, surprising geometrical structures of loop integrands, novel tools for the calculation of Feynman integrals, and bootstrap methods. While several insights and tools have already been carried over to QCD and have contributed to state-of-the-art calculations for LHC physics, we argue that there is a host of further fascinating ideas waiting to be explored.
Precision studies at electron-positron colliders with center-of-mass energies in the charm-tau region and below have strongly contributed to our understanding of light-meson interactions at low energies. We focus on the processes involving two or thr
Different from other multiple top-quark productions, triple top-quark production requires the presence of both flavor violating neutral interaction and flavor conserving neutral interaction. We describe the interaction of triple top-quarks and up-qua
We study event shapes in N=4 SYM describing the angular distribution of energy and R-charge in the final states created by the simplest half-BPS scalar operator. Applying the approach developed in the companion paper arXiv:1309.0769, we compute these
Ultra-relativistic electromagnetic plasmas can be used for improving our understanding of the quark-gluon plasma. In the weakly coupled regime both plasmas can be described by transport theoretical and quantum field theoretical methods leading to sim
We study the domain walls in hot $4$-D $SU(N)$ super Yang-Mills theory and QCD(adj), with $n_f$ Weyl flavors. We find that the $k$-wall worldvolume theory is $2$-D QCD with gauge group $SU(N-k)times SU(k) times U(1)$ and Dirac fermions charged under