Renormalization group limit-cycles and field theories for elliptic S-matrices

Abstract

The renormalization group for maximally anisotropic su(2) current interactions in 2d is shown to be cyclic at one loop. The fermionized version of the model exhibits spin-charge separation of the 4-fermion interactions and has Z_4 symmetry. It is proposed that the S-matrices for these theories are the elliptic S-matrices of Zamolodchikov and Mussardo-Penati. The S-matrix parameters are related to lagrangian parameters by matching the period of the renormalization group. All models exhibit two characteristic signatures of an RG limit cycle: periodicity of the S-matrix as a function of energy and the existence of an infinite number of resonance poles satisfying Russian doll scaling.

version 2: only some additional references version 3: a reason for why the c-theorem is violated is proposed. published version

References in corpus (4)

• Log-periodic behavior of finite size effects in field theories with RG limit cycles
• K_{e3} decays and CKM unitarity
• Search for Chargino and Neutralino Production at sqrt(s) = 192-209 GeV at LEP
• Small x Phenomenology: Summary and status 2002

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