In this talk, we will discuss integrated correlators of four superconformal primaries in N=4 super Yang-Mills, that are defined by integrating over spacetime coordinates of the four-point correlator with certain integration measures. The integrated correlators can be computed using supersymmetric localisation, which are expressed as N-dimensional matrix-model integrals. We will mostly focus on one of the integrated correlators. We find that this integrated correlator can be presented as a lattice sum, which makes manifest the SL(2, Z) modular invariance of N=4 SYM. Furthermore, the integrated correlator obeys a remarkable Laplace-difference equation, which relates the correlator of SU(N) theory with those of SU(N-1) and SU(N+1) theories. The expression allows us to obtain exact results of the integrated correlator in various limits. For instance, in perturbation, the expression is checked to be consistent with known results in the literature; in the large-N limit, it is shown to match with the expected results from string theory due to AdS/CFT duality.
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