Perturbative Anomalies of the Massless Free Fermion and Formal Moduli Problems

          @misc{ pirsa_PIRSA:18080047,
            doi = {10.48660/18080047},
            url = {https://pirsa.org/18080047},
            author = {Rabinovich, Eugene},
            keywords = {Mathematical physics},
            language = {en},
            title = {Perturbative Anomalies of the Massless Free Fermion and Formal Moduli Problems},
            publisher = {Perimeter Institute},
            year = {2018},
            month = {aug},
            note = {PIRSA:18080047 see, \url{https://pirsa.org}}
          }
          

Abstract

It is conventional wisdom among physicists that anomalies of fermionic theories measure an obstruction to the existence of a well-defined (gauge-invariant) partition function. The aim of this talk is to use the formalism of Costello and Gwilliam to show how this wisdom is instantiated for perturbative anomalies of the massless free fermion. We will show how an action of a dg Lie algebra L on the massless free fermion theory gives rise to a line bundle over the formal moduli problem corresponding to L; the anomaly is precisely the failure of this line bundle to be trivial. Our running example will be the axial symmetry of the massless free fermion.