From gauged linear sigma models to geometric representation of in 2D
Abstract
In this paper two issues are addressed. First, we discuss renormalization properties of a class of gauged linear sigma models (GLSM), which reduce to $$\mathbb{WCP}(N,\tilde{N})$$ nonlinear sigma models (NLSM) in the low-energy limit. Sometimes they are referred to as the Hanany-Tong models. If supersymmetry is $$\mathcal{N}$$ = (2, 2) the ultraviolet-divergent logarithm in GLSM appears, in the renormalization of the Fayet-Iliopoulos parameter, and is exhausted by a single tadpole graph. This is not the case in the daughter NLSMs. As a result, the one-loop renormalizations are different in GLSMs and their daughter NLSMs. We explain this difference and identify its source. In particular, we show why at $$N =\tilde{N}$$ there is no UV logarithm in the parent GLSM, while they do appear in the corresponding NLSM. In the second part of the paper we discuss the same problem for a class of $$\mathcal{N}$$ = (0, 2) GLSMs considered previously. In this case renormalization is not limited to one loop; all orders exact $$\beta$$ functions for GLSMs are known. We discuss logarithmically divergent loops at one- and two-loop levels.
- Publication Date:
- Research Org.:
- Univ. of Minnesota, Minneapolis, MN (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1582745
- Alternate Identifier(s):
- OSTI ID: 1802274
- 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: 2; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Astronomy & Astrophysics; Physics
Citation Formats
Sheu, Chao-Hsiang, and Shifman, Mikhail. From gauged linear sigma models to geometric representation of W C P ( N , N ˜ ) in 2D. United States: N. p., 2020.
Web. doi:10.1103/PhysRevD.101.025007.
Sheu, Chao-Hsiang, & Shifman, Mikhail. From gauged linear sigma models to geometric representation of W C P ( N , N ˜ ) in 2D. United States. https://doi.org/10.1103/PhysRevD.101.025007
Sheu, Chao-Hsiang, and Shifman, Mikhail. Tue .
"From gauged linear sigma models to geometric representation of W C P ( N , N ˜ ) in 2D". United States. https://doi.org/10.1103/PhysRevD.101.025007.
@article{osti_1582745,
title = {From gauged linear sigma models to geometric representation of W C P ( N , N ˜ ) in 2D},
author = {Sheu, Chao-Hsiang and Shifman, Mikhail},
abstractNote = {In this paper two issues are addressed. First, we discuss renormalization properties of a class of gauged linear sigma models (GLSM), which reduce to $\mathbb{WCP}(N,\tilde{N})$ nonlinear sigma models (NLSM) in the low-energy limit. Sometimes they are referred to as the Hanany-Tong models. If supersymmetry is $\mathcal{N}$ = (2, 2) the ultraviolet-divergent logarithm in GLSM appears, in the renormalization of the Fayet-Iliopoulos parameter, and is exhausted by a single tadpole graph. This is not the case in the daughter NLSMs. As a result, the one-loop renormalizations are different in GLSMs and their daughter NLSMs. We explain this difference and identify its source. In particular, we show why at $N =\tilde{N}$ there is no UV logarithm in the parent GLSM, while they do appear in the corresponding NLSM. In the second part of the paper we discuss the same problem for a class of $\mathcal{N}$ = (0, 2) GLSMs considered previously. In this case renormalization is not limited to one loop; all orders exact $\beta$ functions for GLSMs are known. We discuss logarithmically divergent loops at one- and two-loop levels.},
doi = {10.1103/PhysRevD.101.025007},
journal = {Physical Review D},
number = 2,
volume = 101,
place = {United States},
year = {2020},
month = {1}
}
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/PhysRevD.101.025007
https://doi.org/10.1103/PhysRevD.101.025007
Other availability
Search WorldCat to find libraries that may hold this journal
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Phases of N = 2 theories in two dimensions
journal, August 1993
- Witten, Edward
- Nuclear Physics B, Vol. 403, Issue 1-2
Vortex Strings and Four-Dimensional Gauge Dynamics
journal, April 2004
- Hanany, Amihay; Tong, David
- Journal of High Energy Physics, Vol. 2004, Issue 04
Effective world-sheet theory for non-Abelian semilocal strings in supersymmetric QCD
journal, June 2011
- Shifman, M.; Vinci, W.; Yung, A.
- Physical Review D, Vol. 83, Issue 12
Three-loop β-function for the bosonic non-linear sigma model
journal, November 1987
- Graham, S. J.
- Physics Letters B, Vol. 197, Issue 4
Heterotic flux tubes in supersymmetric QCD with preserving deformations
journal, June 2008
- Shifman, M.; Yung, A.
- Physical Review D, Vol. 77, Issue 12
Instatons, the quark model, and the 1/N expansion
journal, March 1979
- Witten, Edward
- Nuclear Physics B, Vol. 149, Issue 2
Composite non-Abelian strings with Grassmannian models on the worldsheet
journal, September 2019
- Ireson, Edwin; Shifman, Mikhail; Yung, Alexei
- Physical Review Research, Vol. 1, Issue 2
Remarks on the Novikov-Shifman-Vainshtein-Zakahrov β functions in two-dimensional N = ( 0 , 2 ) supersymmetric models
journal, March 2019
- Chen, Jin; Shifman, Mikhail
- Physical Review D, Vol. 99, Issue 6
Exact Gell-Mann-Low function of supersymmetric Kähler sigma models
journal, December 1984
- Morozov, Alexei Y.; Perelomov, Askold M.; Shifman, Michael A.
- Nuclear Physics B, Vol. 248, Issue 2
Heterotic vortex strings
journal, May 2007
- Edalati, Mohammad; Tong, David
- Journal of High Energy Physics, Vol. 2007, Issue 05
On isometry anomalies in minimal 𝒩 = (0,1) and 𝒩 = (0,2) sigma models
journal, September 2016
- Chen, Jin; Cui, Xiaoyi; Shifman, Mikhail
- International Journal of Modern Physics A, Vol. 31, Issue 27
Quantum dynamics of low-energy theory on semilocal non-Abelian strings
journal, September 2011
- Koroteev, P.; Shifman, M.; Vinci, W.
- Physical Review D, Vol. 84, Issue 6
deformation of the model: Two-dimensional analog of Yang-Mills theory in four dimensions
journal, February 2012
- Cui, Xiaoyi; Shifman, M.
- Physical Review D, Vol. 85, Issue 4