Abstract
It is shown that a unitary translationally invariant field theory in 1+1 dimensions, satisfying isotropic scale invariance, standard assumptions about the spectrum of states and operators, and the requirement that signals propagate with finite velocity, possesses an infinite dimensional symmetry given by one or a product of several copies of conformal algebra. In particular, this implies the presence of one or several Lorentz groups acting on the operator algebra of the theory.
Highlights
It is shown that a unitary translationally invariant field theory in 1 þ 1 dimensions, satisfying isotropic scale invariance, standard assumptions about the spectrum of states and operators, and the requirement that signals propagate with finite velocity, possesses an infinite dimensional symmetry given by one or a product of several copies of conformal algebra
This is the only possible form of scale invariance in relativistic field theories, where it is believed to imply the larger conformal symmetry. This assertion has been rigorously proved in the case of two space-time dimensions, where the symmetry (1) combined with unitarity and some technical assumptions about the energy-momentum tensor (EMT), leads to conformal invariance [1,2]
There is a large amount of theoretical evidence that the renormalization group fixed points characterized by (1) exhibit emergent Lorentz symmetry
Summary
The theory is invariant under translations in time and space which correspond to local conserved currents. DxT t t ðt; xÞ; Px 1⁄4 − dxTtxðt; xÞ; commute with each other and define the evolution of local operators in time and space
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