Lattice perturbation theory for the null cusp string
Gabriel Bliard (Institut für Physik, Humboldt-Universität zu Berlin, IRIS Adlershof, Zum Großen Windkanal 2, 12489 Berlin, Germany, Dipartimento di Fisica, Università di Parma, Viale G.P. Usberti 7/A, 43100 Parma, Italy); Ilaria Costa (Institut für Physik, Humboldt-Universität zu Berlin, IRIS Adlershof, Zum Großen Windkanal 2, 12489 Berlin, Germany); Valentina Forini (Institut für Physik, Humboldt-Universität zu Berlin, IRIS Adlershof, Zum Großen Windkanal 2, 12489 Berlin, Germany, Department of Mathematics, City, University of London Northampton Square, EC1V 0HB London, United Kingdom); Agostino Patella (Institut für Physik, Humboldt-Universität zu Berlin, IRIS Adlershof, Zum Großen Windkanal 2, 12489 Berlin, Germany)
We reconsider the problem of discretizing the worldsheet for the gauge-fixed Green-Schwarz superstring on a null cusp background, and present a setup which fully preserves its global symmetry. We discuss divergences by power counting on the lattice, and study renormalizability at one loop with the example of one-point functions and one bosonic correlator of the worldsheet excitations. In order to remove UV divergences at one loop, it is necessary to introduce two extra parameters in the action, which need to be either fine-tuned at tree level or renormalized at one loop.