Abstract
We conjecture a set of differential equations that characterizes the Liouville irregular states of half-integer ranks, which extends the generalized AGT correspondence to all the (A1, Aeven) and (A1, Dodd) types Argyres-Douglas theories. For lower half-integer ranks, our conjecture is verified by deriving it as a suitable limit of a similar set of differential equations for integer ranks. This limit is interpreted as the 2D counterpart of a 4D RG-flow from (A1, D2n) to (A1, D2n−1). For rank 3/2, we solve the conjectured differential equations and find a power series expression for the irregular state |I(3/2)〉. For rank 5/2, our conjecture is consistent with the differential equations recently discovered by H. Poghosyan and R. Poghossian.
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Acknowledgments
We are grateful to Yasuyuki Hatsuda, Katsushi Ito, Kazunobu Maruyoshi, and Sanefumi Moriyama for helpful discussions. T. Nishinaka also thanks Takuya Kimura for helpful discussions in a separate but related collaboration. The authors’ research is partially supported by JSPS KAKENHI Grant Number JP21H04993. In addition, T. Nakanishi’s research is partially supported by JST Program “The Establishment of University Fellowships Towards the Creation of Science Technology Innovation” Grant Number JPMJFS2138, and T. Nishinaka’s research is partially supported by JSPS KAKENHI Grant Numbers JP18K13547, 23K03394 and 23K03393.
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Hamachika, R., Nakanishi, T., Nishinaka, T. et al. Liouville irregular states of half-integer ranks. J. High Energ. Phys. 2024, 112 (2024). https://doi.org/10.1007/JHEP06(2024)112
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DOI: https://doi.org/10.1007/JHEP06(2024)112