Elliptic blowup equations for 6d SCFTs. Part IV. Matters

Abstract Given the recent geometrical classification of 6d (1, 0) SCFTs, a major question is how to compute for this large class their elliptic genera. The latter encode the refined BPS spectrum of the SCFTs, which determines geometric invariants of the associated elliptic non-compact Calabi-Yau thr...

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Autores principales:	Jie Gu, Babak Haghighat, Albrecht Klemm, Kaiwen Sun, Xin Wang
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Solitons Monopoles and Instantons Supersymmetric Gauge Theory Topological Strings Conformal Field Theory Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/5a6e52ba4e8f4a7c81617c7728b6fefe
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spelling	oai:doaj.org-article:5a6e52ba4e8f4a7c81617c7728b6fefe2021-11-21T12:40:45ZElliptic blowup equations for 6d SCFTs. Part IV. Matters10.1007/JHEP11(2021)0901029-8479https://doaj.org/article/5a6e52ba4e8f4a7c81617c7728b6fefe2021-11-01T00:00:00Zhttps://doi.org/10.1007/JHEP11(2021)090https://doaj.org/toc/1029-8479Abstract Given the recent geometrical classification of 6d (1, 0) SCFTs, a major question is how to compute for this large class their elliptic genera. The latter encode the refined BPS spectrum of the SCFTs, which determines geometric invariants of the associated elliptic non-compact Calabi-Yau threefolds. In this paper we establish for all 6d (1, 0) SCFTs in the atomic classification blowup equations that fix these elliptic genera to large extent. The latter fall into two types: the unity and the vanishing blowup equations. For almost all rank one theories, we find unity blowup equations which determine the elliptic genera completely. We develop several techniques to compute elliptic genera and BPS invariants from the blowup equations, including a recursion formula with respect to the number of strings, a Weyl orbit expansion, a refined BPS expansion and an ϵ 1 , ϵ 2 expansion. For higher-rank theories, we propose a gluing rule to obtain all their blowup equations based on those of rank one theories. For example, we explicitly give the elliptic blowup equations for the three higher-rank non-Higgsable clusters, ADE chain of −2 curves and conformal matter theories. We also give the toric construction for many elliptic non-compact Calabi- Yau threefolds which engineer 6d (1, 0) SCFTs with various matter representations.Jie GuBabak HaghighatAlbrecht KlemmKaiwen SunXin WangSpringerOpenarticleSolitons Monopoles and InstantonsSupersymmetric Gauge TheoryTopological StringsConformal Field TheoryNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENJournal of High Energy Physics, Vol 2021, Iss 11, Pp 1-170 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Solitons Monopoles and Instantons Supersymmetric Gauge Theory Topological Strings Conformal Field Theory Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Solitons Monopoles and Instantons Supersymmetric Gauge Theory Topological Strings Conformal Field Theory Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Jie Gu Babak Haghighat Albrecht Klemm Kaiwen Sun Xin Wang Elliptic blowup equations for 6d SCFTs. Part IV. Matters
description	Abstract Given the recent geometrical classification of 6d (1, 0) SCFTs, a major question is how to compute for this large class their elliptic genera. The latter encode the refined BPS spectrum of the SCFTs, which determines geometric invariants of the associated elliptic non-compact Calabi-Yau threefolds. In this paper we establish for all 6d (1, 0) SCFTs in the atomic classification blowup equations that fix these elliptic genera to large extent. The latter fall into two types: the unity and the vanishing blowup equations. For almost all rank one theories, we find unity blowup equations which determine the elliptic genera completely. We develop several techniques to compute elliptic genera and BPS invariants from the blowup equations, including a recursion formula with respect to the number of strings, a Weyl orbit expansion, a refined BPS expansion and an ϵ 1 , ϵ 2 expansion. For higher-rank theories, we propose a gluing rule to obtain all their blowup equations based on those of rank one theories. For example, we explicitly give the elliptic blowup equations for the three higher-rank non-Higgsable clusters, ADE chain of −2 curves and conformal matter theories. We also give the toric construction for many elliptic non-compact Calabi- Yau threefolds which engineer 6d (1, 0) SCFTs with various matter representations.
format	article
author	Jie Gu Babak Haghighat Albrecht Klemm Kaiwen Sun Xin Wang
author_facet	Jie Gu Babak Haghighat Albrecht Klemm Kaiwen Sun Xin Wang
author_sort	Jie Gu
title	Elliptic blowup equations for 6d SCFTs. Part IV. Matters
title_short	Elliptic blowup equations for 6d SCFTs. Part IV. Matters
title_full	Elliptic blowup equations for 6d SCFTs. Part IV. Matters
title_fullStr	Elliptic blowup equations for 6d SCFTs. Part IV. Matters
title_full_unstemmed	Elliptic blowup equations for 6d SCFTs. Part IV. Matters
title_sort	elliptic blowup equations for 6d scfts. part iv. matters
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/5a6e52ba4e8f4a7c81617c7728b6fefe
work_keys_str_mv	AT jiegu ellipticblowupequationsfor6dscftspartivmatters AT babakhaghighat ellipticblowupequationsfor6dscftspartivmatters AT albrechtklemm ellipticblowupequationsfor6dscftspartivmatters AT kaiwensun ellipticblowupequationsfor6dscftspartivmatters AT xinwang ellipticblowupequationsfor6dscftspartivmatters
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Elliptic blowup equations for 6d SCFTs. Part IV. Matters

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