$C{P}^{N-1}$ Models at a Lifshitz Point

Abstract

We consider $C{P}^{N-1}$ models in $d+1$ dimensions around Lifshitz fixed points with dynamical critical exponent $z$, in the large-N expansion. It is shown that these models are asymptotically free and dynamically generate a mass for the $C{P}^{N-1}$ fields for all $d=z$. We demonstrate that, for $z=d=2$, the initially nondynamical gauge field acquires kinetic terms in a way similar to usual $C{P}^{N-1}$ models in 1+1 dimensions. Lorentz invariance emerges generically in the low-energy electrodynamics, with a nontrivial dielectric constant given by the inverse mass gap and a magnetic permeability which has a logarithmic dependence on scale. At a special multicritical point, the low-energy electrodynamics also has $z=2$, and an essentially singular dependence of the effective action on $B={\epsilon }_{ij}{\partial }_i{A}_j$.

LaTeX 13 pages; added a comment about constant field effective action. version published in Physical Review D

References in corpus (8)

• Quantum Gravity at a Lifshitz Point
• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Topological Order and Conformal Quantum Critical Points
• Lorentz symmetry breaking as a quantum field theory regulator
• Three dimensional resonating valence bond liquids and their excitations
• On bipartite Rokhsar-Kivelson points and Cantor deconfinement