Wilson loop OPE, analytic continuation and multi-Regge limit

We explore a direct connection between the collinear limit and the multi-Regge limit for scattering amplitudes in the N $$\mathcal{N}$$ = 4 super Yang-Mills theory. Starting with the collinear expansion for the six-gluon amplitude in the Euclidean kinematic region, we perform an analytic continuation term by term to the so-called Mandelstam region. We find that the result coincides with the collinear expansion of the analytically continued amplitude. We then take the multi-Regge limit, and conjecture that the final result precisely reproduces the one from the BFKL approach. Combining this procedure with the OPE for null polygonal Wilson loops, we explicitly compute the leading contribution in the “collinear-Regge” limit up to five loops. Our results agree with all the known results up to four loops. At five-loop, our results up to the next-to-next-to-leading logarithmic approximation (NNLLA) also reproduce the known results, and for the N 3 LLA and the N 4 LLA give non-trivial predictions. We further present an all-loop prediction for the imaginary part of the next-to-double-leading logarithmic approximation. Our procedure has a possibility of an interpolation from weak to strong coupling in the multi-Regge limit with the help of the OPE

Resummations and non-perturbative corrections

We consider a generalization of the Borel resummation, which turns out to be equivalent to the standard Borel resummation. We apply it to the simplest large N duality between the pure Chern-Simons theory and the topological string on the resolved conifold, and obtain a simple integral formula for the free energy. Expanding this integral representation around the large radius point at finite string coupling g s , we find that it includes not only the M-theoretic resummation à la Gopakumar and Vafa, but also a non-perturbative correction in g s . Remarkably, the obtained non-perturbative correction is in perfect agreement with a proposal for membrane instanton corrections in arXiv:1306.1734 . Various other examples are also presented

Probing non-perturbative effects in M-theory

The AdS/CFT correspondence enables us to probe M-theory on various backgrounds from the corresponding dual gauge theories. Here we investigate in detail a three-dimensional U N N = 4 $$U(N)\mathcal{N}=4$$ super Yang-Mills theory coupled to one adjoint hypermultiplet and N f fundamental hypermultiplets, which is large N dual to M-theory on Ad S 4 × S 7 / ℤ N f $$Ad{S}_4\times {S}^7/{\mathrm{\mathbb{Z}}}_{N_f}$$ . Using the localization and the Fermi-gas formulation, we explore non-perturbative corrections to the partition function. As in the ABJM theory, we find that there exists a non-trivial pole cancellation mechanism, which guarantees the theory to be well-defined, between worldsheet instantons and membrane instantons for all rational (in particular, physical or integral) values of N f

Large N non-perturbative effects in N = 4 N=4 \mathcal{N}=4 superconformal Chern-Simons theories

We investigate the large N instanton effects of partition functions in a class of N = 4 $$\mathcal{N}=4$$ circular quiver Chern-Simons theories on a three-sphere. Our analysis is based on the supersymmetry localization and the Fermi-gas formalism. The resulting matrix model can be regarded as a two-parameter deformation of the ABJM matrix model, and has richer non-perturbative structures. Based on a systematic semi-classical analysis, we find analytic expressions of membrane instanton corrections. We also exactly compute the partition function for various cases and find some exact forms of worldsheet instanton corrections, which appear as quantum mechanical non-perturbative corrections in the Fermi-gas system