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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:
 [1];  [1]
  1. 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 2470-0010
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 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.},
doi = {10.1103/physrevd.101.045003},
journal = {Physical Review. D.},
number = 4,
volume = 101,
place = {United States},
year = {2020},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/physrevd.101.045003

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Cited by: 5 works
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Works referencing / citing this record:

Sigma model on a squashed sphere with a Wess-Zumino term
journal, January 2021