Self-dual effective action of N = 4 super-Yang-Mills

The full low-energy effective action of N = 4 SYM is believed to be self-dual. Starting with the first two leading terms in a momentum expansion of this effective action, we perform a duality transformation and find the conditions for self-duality. These determine some of the higher-order terms. We compare the effective action of N = 4 SYM with the probe-source description of type IIB D3-branes in the AdS5 × S5 background. We find agreement up to six derivative terms if we identify the separation of the 3-branes with a redefinition of the gauge scalar that involves the gauge field strength.