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

Sumit R. Das; Ganpathy Murthy

doi:10.1103/PhysRevD.80.065006

paper

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

arXiv:0906.3261 · doi:10.1103/PhysRevD.80.065006

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 $B = ε_{ij} \partial_{i} A_{j}$ .

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

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

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