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Title: From gauged linear sigma models to geometric representation of W C P ( N , N ˜ ) 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.

Authors:
ORCiD logo;
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}
}

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