Integrability and Exact Results in N = 2 gauge theories

Any N=2 gauge theory in four dimensions contains a set of localoperators made only out of fields in the N=2 vector multiplet that isclosed under renormalization to all loops, with SU(2,1|2) symmetry. Wepresent a diagrammatic argument that for any planar N=2 theory theSU(2,1|2) Hamiltonian acting on infinite spin chains is identical toall loops to that of N=4 SYM, up to a redefinition of the couplingconstant g^2 → f(g^2). Thus, this sector is integrable and anomalousdimensions can be read off from the N=4 ones up to this redefinition.The functions f(g^2) dubbed as effective couplings encode therelative, finite renormalization between the N=2 and the N=4 gluonpropagator and thus can be computed in perturbation theory usingFeynman diagrams. For each N=2 theory exact effective couplings can beobtained by computing different exact results for localizableobservables such as Wilson loops and the Bremsstrahlung function andby comparing them with their N = 4 counterparts