Modular factorization of superconformal indices

doi:10.1007/JHEP10(2023)105

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	Modular factorization of superconformal indices
	Jejjala, Vishnu 1; Lei, Yang 2,3; van Leuven, Sam 1; Li, Wei 4
刊名	JOURNAL OF HIGH ENERGY PHYSICS
	2023
期号	10 页码:105
关键词	LENS SPACES N=1
ISSN号	1029-8479
DOI	10.1007/JHEP10(2023)105
英文摘要	Superconformal indices of four-dimensional N = 1 gauge theories factorize into holomorphic blocks. We interpret this as a modular property resulting from the combined action of an SL(3, Z) and SL(2, Z) proportional to Z2 transformation. The former corresponds to a gluing transformation and the latter to an overall large diffeomorphism, both associated with a Heegaard splitting of the underlying geometry. The extension to more general transformations leads us to argue that a given index can be factorized in terms of a family of holomorphic blocks parametrized by modular (congruence sub)groups. We find precise agreement between this proposal and new modular properties of the elliptic G function. This leads to our conjecture for the modular factorization of superconformal lens indices of general N = 1 gauge theories. We provide evidence for the conjecture in the context of the free chiral multiplet and SQED and sketch the extension of our arguments to more general gauge theories. Assuming the validity of the conjecture, we systematically prove that a normalized part of superconformal lens indices defines a non-trivial first cohomology class associated with SL(3, Z). Finally, we use this framework to propose a formula for the general lens space index.
学科主题	Physics
语种	英语
内容类型	期刊论文
源URL	[http://ir.itp.ac.cn/handle/311006/28024]
专题	理论物理研究所_理论物理所1978-2010年知识产出
作者单位	1.Univ Witwatersrand, Mandelstam Inst Theoret Phys, Sch Phys, NITheCS, ZA-2050 Johannesburg, South Africa 2.Univ Witwatersrand, DSI NRF Ctr Excellence Math & Stat Sci CoE MaSS, ZA-2050 Johannesburg, South Africa 3.Soochow Univ, Inst Adv Study, Suzhou 215006, Peoples R China 4.Soochow Univ, Sch Phys Sci & Technol, Suzhou 215006, Peoples R China 5.Chinese Acad Sci, Inst Theoret Phys, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Jejjala, Vishnu,Lei, Yang,van Leuven, Sam,et al. Modular factorization of superconformal indices[J]. JOURNAL OF HIGH ENERGY PHYSICS,2023(10):105.
APA	Jejjala, Vishnu,Lei, Yang,van Leuven, Sam,&Li, Wei.(2023).Modular factorization of superconformal indices.JOURNAL OF HIGH ENERGY PHYSICS(10),105.
MLA	Jejjala, Vishnu,et al."Modular factorization of superconformal indices".JOURNAL OF HIGH ENERGY PHYSICS .10(2023):105.