The Next-to-Simplest Quantum Field Theories

          @misc{ pirsa_PIRSA:10030039,
            doi = {10.48660/10030039},
            url = {https://pirsa.org/10030039},
            author = {Raju, Suvrat},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {The Next-to-Simplest Quantum Field Theories},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {mar},
            note = {PIRSA:10030039 see, \url{https://pirsa.org}}
          }
          

Abstract

We apply newly-developed techniques for studying perturbative scattering amplitudes to gauge theories with matter. It is well known that the N=4 SYM theory has a very simple S-matrix; do other gauge theories see similar simplifications in their S-matrices? It turns out the one-loop gluon S-matrix simplifies if the matter representations satisfy some group theoretic constraints. In particular, these constraints can be expressed as linear Diophantine equations involving the higher order Indices (or higher-order Casimirs) of these representations. We solve these constraints to find examples of theories whose gluon scattering amplitudes are as simple as those of the N=4 theory. This class includes the N=2, SU(K) theory with a symmetric and anti-symmetric tensor hypermultiplet. Non-supersymmetric theories with appropriately tuned matter content can also see remarkable simplifications. We find an infinite class of non-supersymmetric amplitudes that are cut-constructible even though naive power counting would suggest the presence of rational remainders.