Title: Sigma models on fiber bundles with a Grassmannian base space

Abstract

Some magnetic phenomena in correlated electron systems were recently shown to be described in the continuum limit by a class of sigma models with a target space interpolating between $S^3$ and $CP^1$. In this paper we study a generalization of such models with a target space given by a fiber bundle with a Grassmannian base space. The metric of our target space is shown to be left-symmetric which implies that it is fully parametrized by two constants: the first one—the conventional coupling constant—is responsible for the overall scale of the target space while the second constant $$\mathcal{κ}$$ parametrizes the size of the fibers. In two dimensions these sigma models are perturbatively renormalizable. We calculate their β functions to two loops and find the RG flow of the coupling constants. We calculate the two-point function in the UV limit, which has a power law dependence with an exponent dependent on the RG trajectory.

Authors:

Schubring, Daniel; Shifman, Mikhail

Publication Date:

2020-02-06

Research Org.:

Univ. of Minnesota, Minneapolis, MN (United States)

Sponsoring Org.:

USDOE Office of Science (SC)

OSTI Identifier:

1598081

Alternate Identifier(s):

OSTI ID: 1802275

Grant/Contract Number:  

SC0011842

Resource Type:

Published Article

Journal Name:

Physical Review D

Additional Journal Information:

Journal Name: Physical Review D Journal Volume: 101 Journal Issue: 4; Journal ID: ISSN 2470-0010

Publisher:

American Physical Society

Country of Publication:

United States

Language:

English

Subject:

79 ASTRONOMY AND ASTROPHYSICS; Astronomy & Astrophysics; Physics