Sigma models on fiber bundles with a Grassmannian base space
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.
- Research Organization:
- Univ. of Minnesota, Minneapolis, MN (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- Grant/Contract Number:
- SC0011842
- OSTI ID:
- 1598081
- Alternate ID(s):
- OSTI ID: 1802275
- Journal Information:
- Physical Review D, Journal Name: Physical Review D Vol. 101 Journal Issue: 4; ISSN 2470-0010
- Publisher:
- American Physical SocietyCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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