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

Gu, Jie
•
Haghighat, Babak
•
Klemm, Albrecht
altro
Wang, Xin
2021
  • journal article

Periodico
JOURNAL OF HIGH ENERGY PHYSICS
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 epsilon(1), epsilon(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.
DOI
10.1007/jhep11(2021)090
WOS
WOS:000718261600001
Archivio
https://hdl.handle.net/20.500.11767/142413
info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-85119341174
https://arxiv.org/abs/2006.03030
https://ricerca.unityfvg.it/handle/20.500.11767/142413
Diritti
open access
Soggetti
  • Solitons Monopoles an...

  • Supersymmetric Gauge ...

  • Topological Strings

  • Conformal Field Theor...

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