Sigma models with $A_k$ singularities in Euclidean spacetime of dimension 0<=D<4 and in the limit N->infinity

Abstract

For the case of the single-O($N$)-vector linear sigma models the critical behaviour following from any $A_k$ singularity in the action is worked out in the double scaling limit $N\to \infty$, $f_r\to f_r^c$, $2\le r\le k$. After an exact elimination of Gaussian degrees of freedom, the critical objects such as coupling constants, indices and susceptibility matrix are derived for all $A_k$ and spacetime dimensions $0\le D<4$. There appear exceptional spacetime dimensions where the degree $k$ of the singularity $A_k$ is more strongly constrained than by the renormalizability requirement.

arXiv commentLaTeX, 25 pages, no figures

References in corpus (1)

• $O(N)$ Vector Field Theories in the Double Scaling Limit