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 leftsymmetric 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 twopoint function in the UV limit, which has a power law dependence with an exponent dependent on the RG trajectory.
 Authors:

 Univ. of Minnesota, Minneapolis, MN (United States)
 Publication Date:
 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 Volume: 101; Journal Issue: 4; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTRONOMY AND ASTROPHYSICS; Astronomy & Astrophysics; Physics
Citation Formats
Schubring, Daniel, and Shifman, Mikhail. Sigma models on fiber bundles with a Grassmannian base space. United States: N. p., 2020.
Web. doi:10.1103/physrevd.101.045003.
Schubring, Daniel, & Shifman, Mikhail. Sigma models on fiber bundles with a Grassmannian base space. United States. https://doi.org/10.1103/physrevd.101.045003
Schubring, Daniel, and Shifman, Mikhail. Thu .
"Sigma models on fiber bundles with a Grassmannian base space". United States. https://doi.org/10.1103/physrevd.101.045003.
@article{osti_1598081,
title = {Sigma models on fiber bundles with a Grassmannian base space},
author = {Schubring, Daniel and Shifman, Mikhail},
abstractNote = {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 leftsymmetric 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 twopoint function in the UV limit, which has a power law dependence with an exponent dependent on the RG trajectory.},
doi = {10.1103/physrevd.101.045003},
journal = {Physical Review. D.},
number = 4,
volume = 101,
place = {United States},
year = {2020},
month = {2}
}
https://doi.org/10.1103/physrevd.101.045003
Web of Science
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Works referencing / citing this record:
Sigma model on a squashed sphere with a WessZumino term
journal, January 2021
 Schubring, Daniel; Shifman, Mikhail
 Physical Review D, Vol. 103, Issue 2