From scale invariance to Lorentz symmetry


Sibiryakov, S. (2014). From scale invariance to Lorentz symmetry. Perimeter Institute. https://pirsa.org/14050136


Sibiryakov, Sergey. From scale invariance to Lorentz symmetry. Perimeter Institute, May. 28, 2014, https://pirsa.org/14050136


          @misc{ pirsa_14050136,
            doi = {10.48660/14050136},
            url = {https://pirsa.org/14050136},
            author = {Sibiryakov, Sergey},
            keywords = {},
            language = {en},
            title = {From scale invariance to Lorentz symmetry},
            publisher = {Perimeter Institute},
            year = {2014},
            month = {may},
            note = {PIRSA:14050136 see, \url{https://pirsa.org}}

Sergey Sibiryakov McMaster University


I will discuss the enhancement of space-time symmetries to Lorentz (rotation) invariance at the renormalization group fixed points of non-relativistic (anisotropic) field theories. Upon describing examples from the condensed matter physics, I will review the general argument for the stability of the infrared fixed points with the enhanced symmetry. Then I will focus on unitary field theories in (1+1) space-time dimensions which are invariant under translations, isotropic scale transformations and satisfy the requirement that the velocity of signal propagation is bounded from above. No a priori Lorentz invariance will be assumed. Still, I will prove that above properties are sufficient to ensure the existence of an infinite dimensional symmetry given by one or a product of several copies of conformal algebra. In particular, this implies presence of one or several Lorentz groups acting on the operator algebra of the theory. I will conclude by discussing the challenges in extending this result to higher space-time dimensions.