PIRSA:12050071

Scale Without Conformal Invariance in Relativistic Quantum Field Theory

APA

Grinstein, B. (2012). Scale Without Conformal Invariance in Relativistic Quantum Field Theory. Perimeter Institute. https://pirsa.org/12050071

MLA

Grinstein, Benjamin. Scale Without Conformal Invariance in Relativistic Quantum Field Theory. Perimeter Institute, May. 10, 2012, https://pirsa.org/12050071

BibTex

          @misc{ pirsa_12050071,
            doi = {},
            url = {https://pirsa.org/12050071},
            author = {Grinstein, Benjamin},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Scale Without Conformal Invariance in Relativistic Quantum Field Theory},
            publisher = {Perimeter Institute},
            year = {2012},
            month = {may},
            note = {PIRSA:12050071 see, \url{https://pirsa.org}}
          }
          

Abstract

In 2-dim it is known that a unitary, well defined quantum field theory, if scale invariant must also be invariant under conformal transformations. Whether this is also true in dimensions higher than two has been an open question for decades. We have discovered renomalization group flows in 4-epsilon dimensions corresponding to scale but not conformal invariant theories. The flows correspond to limit cycles or ergodic behavior,  neither of which had been reported in relativistic quantum field theories either.   There seems to be a deep connection between scale without conformal invariance and this type of renormalization group  behavior. We will present these results and list some of open questions, including the possibility of such behavior in integral dimensions.