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This is a talk delivered at the Workshop on Quantum Fields and Strings of the 2014 Corfu Summer Institute. We discuss how giant magnons emerge in the context of the AdS5/CFT4 correspondence as the gravity duals of N = 4 super Yang-Mills magnon excitations. Then we present a new analytic expression for the dispersion relation of classical finite-size giant magnons with Lamberts W-function.
Perturbations of giant magnons and single spikes in a $2+1$ dimensional $mathbb R times S^2$ background spacetime are analysed. Using the form of the giant magnon solution in the Jevicki-Jin gauge,the well-known Jacobi equation for small normal defor
We consider conformal field theories around points of large twist degeneracy. Examples of this are theories with weakly broken higher spin symmetry and perturbations around generalised free fields. At the degenerate point we introduce twist conformal
We propose a set of novel expansions of Nekrasovs instanton partition functions. Focusing on 5d supersymmetric pure Yang-Mills theory with unitary gauge group on $mathbb{C}^2_{q,t^{-1}} times mathbb{S}^1$, we show that the instanton partition functio
A central object in any axionic theory is its periodic potential, which is typically generated by instantons. The goal of this paper is to understand what physically happens to the theory when we lose control of the potentials instanton expansion. We
Usually the asymptotic behavior for large orders of the perturbation theory is reached rather slowly. However, in the case of the N-component $phi^4$ model in D=4 dimensions one can find a special quantity that exhibits an extremely fast convergence