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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:
;
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 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

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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Works referenced in this record:

The axial vector current in beta decay
journal, May 1960


Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models
journal, August 1979


Generalized non-linear σ-models with gauge invariance
journal, April 1980


Principal Chiral Model in Correlated Electron Systems
journal, November 2018


Curvatures of left invariant metrics on lie groups
journal, September 1976


Two-dimensional sigma models: Modelling non-perturbative effects in quantum chromodynamics
journal, December 1984


Exact solution of the O(3) nonlinear σ-model
journal, March 1985


Nonlinear σ models for triangular quantum antiferromagnets
journal, April 1989


Theory of nonabelian goldstone bosons in two dimensions
journal, November 1983


Instatons, the quark model, and the 1/N expansion
journal, March 1979


The massive model for frustrated spin systems
journal, September 1995


Quantum phase transitions in frustrated quantum antiferromagnets
journal, September 1994


Exact factorized S-matrix of the chiral field in two dimensions
journal, July 1984


A renormalization-group study of helimagnets in D = 2 + ϵ dimensions
journal, November 1993


Nonuniversality in helical and canted-spin systems
journal, June 1990