Does Conformal Quantum Field Theory Describe the Continuum Limits of 2D Spin Models with Continuous Symmetry?

Details Does Conformal Quantum Field Theory Describe the Continuum Limits of 2D Spin Models with Continuous Symmetry? Does Conformal Quantum Field Theory Describe the Continuum Limits of 2D Spin Models with Continuous Symmetry?

1997-03-24

arxiv.org/abs/hep-lat/9703015v1

Phys.Lett. B417 (1998) 123-128

Physics

High Energy Physics

High Energy Physics - Lattice

9 pages

Scientific paper

10.1016/S0370-2693(97)01366-X

It is generally taken for granted that two-dimensional critical phenomena can be fully classified by the well known two-dimensional (rational) conformal quantum field theories (CQFTs). In particular it is believed that in models with a continuous symmetry characterized by a Lie group $G$ the continuum theory enjoys an enhanced symmetry $G\times G$ due to the decoupling of right and left movers. In this letter we review the conventional arguments leading to this conclusion, point out two gaps and provide a conterexample. Nevertheless we justify in the end the conventional conclusions by additional arguments.

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