Conformality Lost

Abstract

We consider zero-temperature transitions from conformal to non-conformal phases in quantum theories. We argue that there are three generic mechanisms for the loss of conformality in any number of dimensions: (i) fixed point goes to zero coupling, (ii) fixed point runs off to infinite coupling, or (iii) an IR fixed point annihilates with a UV fixed point and they both disappear into the complex plane. We give both relativistic and non-relativistic examples of the last case in various dimensions and show that the critical behavior of the mass gap behaves similarly to the correlation length in the finite temperature Berezinskii-Kosterlitz-Thouless (BKT) phase transition in two dimensions, xi ~ exp(c/|T-T_c|^{1/2}). We speculate that the chiral phase transition in QCD at large number of fermion flavors belongs to this universality class, and attempt to identify the UV fixed point that annihilates with the Banks-Zaks fixed point at the lower end of the conformal window.

30 pages, 6 figures; v2: typos fixed, references added

References in corpus (7)

• Nonrelativistic conformal field theories
• Supersymmetry Inspired QCD Beta Function
• Zero of the discrete beta function in SU(3) lattice gauge theory with color sextet fermions
• Spectrum of SU(2) lattice gauge theory with two adjoint Dirac flavours
• Phase structure of SU(3) gauge theory with two flavors of symmetric-representation fermions
• Universal Fermi Gas with Two- and Three-Body Resonances
• A Model Study of Discrete Scale Invariance and Long-Range Interactions

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