Abstract
In this paper, we discuss lumps (sigma model instantons) in flag manifold sigma models. In particular, we focus on the moduli space of BPS lumps in general Kähler flag manifold sigma models. Such a Kähler flag manifold, which takes the form \( \frac{\textrm{U}\left({n}_1+\cdots +{n}_{L+1}\right)}{\textrm{U}\left({n}_1\right)\times \cdots \times \textrm{U}\left({n}_{L+1}\right)} \), can be realized as a vacuum moduli space of a U(N1) × ··· × U(NL) quiver gauged linear sigma model. When the gauge coupling constants are finite, the gauged linear sigma model admits BPS vortex configurations, which reduce to BPS lumps in the low energy effective sigma model in the large gauge coupling limit. We derive an ADHM-like quotient construction of the moduli space of BPS vortices and lumps by generalizing the quotient construction in U(N) gauge theories by Hanany and Tong. As an application, we check the dualities of the 2d models by computing the vortex partition functions using the quotient construction.
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Acknowledgments
This work is supported by the Ministry of Education, Culture, Sports, Science, and Technology(MEXT)-Supported Program for the Strategic Research Foundation at Private Universities “Topological Science” (Grant No. S1511006) and by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (KAKENHI) Grant Number (18H01217). This work is also supported in part by JSPS KAKENHI Grant Numbers JP21K03558 (T. F.) and JP22H01221 (M. N.).
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This paper is dedicated to Prof. Norisuke Sakai, who passed away in June 2022. He contributed to the development of the moduli matrix formalism, which forms the basis of this paper, and built it together with us.
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Fujimori, T., Nitta, M. & Ohashi, K. Moduli spaces of instantons in flag manifold sigma models. Vortices in quiver gauge theories. J. High Energ. Phys. 2024, 230 (2024). https://doi.org/10.1007/JHEP02(2024)230
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DOI: https://doi.org/10.1007/JHEP02(2024)230