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We study a special class of four-point correlation functions of infinitely heavy half-BPS operators in planar N=4 SYM which admit factorization into a product of two octagon form factors. We demonstrate that these functions satisfy a system of nonlinear integro-differential equations which are powerful enough to fully determine their dependence on the 't Hooft coupling and two cross ratios. At weak coupling, solution to these equations yields a known series representation of the octagon in terms of ladder integrals. At strong coupling, we develop a systematic expansion of the octagon in the inverse powers of the coupling constant and calculate accompanying expansion coefficients analytically. We examine the strong coupling expansion of the correlation function in various kinematical regions and observe a perfect agreement both with the expected asymptotic behavior dictated by the OPE and with results of numerical evaluation. We find that, surprisingly enough, the strong coupling expansion is Borel summable. Applying the Borel-Pade summation method, we show that the strong coupling expansion correctly describes the correlation function over a wide region of the 't Hooft coupling., Comment: 43 pages, 5 figures, 2 ancillary files; references updated, typos fixed

Journal of high energy physics 1908(8), 162 (2019). doi:10.1007/JHEP08(2019)162, We explain how the ’t Hooft expansion of correlators of half-BPS operators can be resummed in a large-charge limit in $ \mathcal{N} $ = 4 super Yang-Mills theory. The full correlator in the limit is given by a non-trivial function of two variables: One variable is the charge of the BPS operators divided by the square root of the number N$_{c}$ of colors, the other variable is the octagon that contains all the ’t Hooft coupling and spacetime dependence. At each genus g in the large N$_{c}$ expansion, this function is a polynomial of degree 2g + 2 in the octagon. We find several dual matrix model representations of the correlators in the large-charge limit. Amusingly, the number of colors in these matrix models is formally taken to zero in the relevant limit., Published by SISSA, [Trieste]

We propose a method for calculating dynamical correlation functions at finite temperature in integrable lattice models of Yang-Baxter type. The method is based on an expansion of the correlation functions as a series over matrix elements of a time-dependent quantum transfer matrix rather than the Hamiltonian. In the infinite Trotter-number limit the matrix elements become time independent and turn into the thermal form factors studied previously in the context of static correlation functions. We make this explicit with the example of the XXZ model. We show how the form factors can be summed utilizing certain auxiliary functions solving finite sets of nonlinear integral equations. The case of the XX model is worked out in more detail leading to a novel form-factor series representation of the dynamical transverse two-point function., 42 pages, LaTeX, v2: minor corrections, references added, published version, v3: typos corrected