Scattering on the Moduli Space of N=4 Super Yang-Mills
Robert M. Schabinger
TL;DR
The paper investigates the S-matrix of N=4 SYM away from the conformal origin by studying the Coulomb branch of the theory with SU(2) broken to U(1). Using $R_\xi$ quantization and a unitary-gauge focus, it computes several one-loop four-point amplitudes with both massless and massive external states, showing that amplitudes remain extremely simple and are governed by pure scalar-box integrals with mass-independent coefficients in the massless sector. It also provides explicit results for amplitudes with massive external states, and demonstrates a consistent coefficient structure across cases, consistent with SUSY Ward identities. Moreover, the work draws a connection to Alday–Maldacena's strong-coupling IR-regulator idea by interpreting the four-photon amplitude as a weak-coupling analog of a mass-regulated, planar amplitude, suggesting avenues to compare weak and strong coupling in a controlled setting and to extend the analysis to higher points and loops.
Abstract
We calculate one-loop scattering amplitudes in N=4 super Yang-Mills theory away from the origin of the moduli space and demonstrate that the results are extremely simple, in much the same way as in the conformally invariant theory. Specifically, we consider the model where an SU(2) gauge group is spontaneously broken down to U(1). The complete component Lagrange density of the model is given in a form useful for perturbative calculations. We argue that the scattering amplitudes with massive external states deserve further study. Finally, our work shows that loop corrections can be readily computed in a mass-regulated N=4 theory, which may be relevant in trying to connect weak-coupling results with those at strong coupling, as discussed recently by Alday and Maldacena.