From gauged linear sigma models to geometric representation of W C P (N, N) in 2D

Chao Hsiang Sheu, Mikhail Shifman

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In this paper two issues are addressed. First, we discuss renormalization properties of a class of gauged linear sigma models (GLSM), which reduce to WCP(N,Ñ) nonlinear sigma models (NLSM) in the low-energy limit. Sometimes they are referred to as the Hanany-Tong models. If supersymmetry is 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=Ñ 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 N=(0,2) GLSMs considered previously. In this case renormalization is not limited to one loop; all orders exact β functions for GLSMs are known. We discuss logarithmically divergent loops at one- and two-loop levels.

Original languageEnglish (US)
Article number025007
JournalPhysical Review D
Issue number2
StatePublished - Jan 14 2020

Bibliographical note

Funding Information:
The authors are grateful to Jin Chen, Sasha Gorsky, Sergey Ketov, Andrei Losev, David Tong, and Alexey Yung for very useful discussions and correspondence. This work is supported in part by DOE Grant No. DE-SC0011842.

Publisher Copyright:
© 2020 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "" Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP.


Dive into the research topics of 'From gauged linear sigma models to geometric representation of W C P (N, N) in 2D'. Together they form a unique fingerprint.

Cite this