A note on quiver quantum toroidal algebra
Abstract Recently, Li and Yamazaki proposed a new class of infinite-dimensional algebras, quiver Yangian, which generalizes the affine Yangian gl $$ \mathfrak{gl} $$ 1. The characteristic feature of the algebra is the action on BPS states for non-compact toric Calabi-Yau threefolds, which are in one...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-05-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP05(2022)011 |
| _version_ | 1818007225236455424 |
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| author | Go Noshita Akimi Watanabe |
| author_facet | Go Noshita Akimi Watanabe |
| author_sort | Go Noshita |
| collection | DOAJ |
| description | Abstract Recently, Li and Yamazaki proposed a new class of infinite-dimensional algebras, quiver Yangian, which generalizes the affine Yangian gl $$ \mathfrak{gl} $$ 1. The characteristic feature of the algebra is the action on BPS states for non-compact toric Calabi-Yau threefolds, which are in one-to-one correspondence with the crystal melting models. These algebras can be bootstrapped from the action on the crystals and have various truncations. In this paper, we propose a q-deformed version of the quiver Yangian, referred to as the quiver quantum toroidal algebra (QQTA). We examine some of the consistency conditions of the algebra. In particular, we show that QQTA is a Hopf superalgebra with a formal super coproduct, like known quantum toroidal algebras. QQTA contains an extra central charge C. When it is trivial (C = 1), QQTA has a representation acting on the three-dimensional crystals, like Li-Yamazaki’s quiver Yangian. While we focus on the toric Calabi-Yau threefolds without compact 4-cycles, our analysis can likely be generalized to all toric Calabi-Yau threefolds. |
| first_indexed | 2024-04-14T05:12:58Z |
| format | Article |
| id | doaj.art-ca861001c2584348b1064ef1a7adcf9f |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-14T05:12:58Z |
| publishDate | 2022-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-ca861001c2584348b1064ef1a7adcf9f2022-12-22T02:10:30ZengSpringerOpenJournal of High Energy Physics1029-84792022-05-012022514310.1007/JHEP05(2022)011A note on quiver quantum toroidal algebraGo Noshita0Akimi Watanabe1Department of Physics, The University of TokyoDepartment of Physics, The University of TokyoAbstract Recently, Li and Yamazaki proposed a new class of infinite-dimensional algebras, quiver Yangian, which generalizes the affine Yangian gl $$ \mathfrak{gl} $$ 1. The characteristic feature of the algebra is the action on BPS states for non-compact toric Calabi-Yau threefolds, which are in one-to-one correspondence with the crystal melting models. These algebras can be bootstrapped from the action on the crystals and have various truncations. In this paper, we propose a q-deformed version of the quiver Yangian, referred to as the quiver quantum toroidal algebra (QQTA). We examine some of the consistency conditions of the algebra. In particular, we show that QQTA is a Hopf superalgebra with a formal super coproduct, like known quantum toroidal algebras. QQTA contains an extra central charge C. When it is trivial (C = 1), QQTA has a representation acting on the three-dimensional crystals, like Li-Yamazaki’s quiver Yangian. While we focus on the toric Calabi-Yau threefolds without compact 4-cycles, our analysis can likely be generalized to all toric Calabi-Yau threefolds.https://doi.org/10.1007/JHEP05(2022)011Conformal and W SymmetryConformal Field TheoryHigher Spin SymmetryQuantum Groups |
| spellingShingle | Go Noshita Akimi Watanabe A note on quiver quantum toroidal algebra Journal of High Energy Physics Conformal and W Symmetry Conformal Field Theory Higher Spin Symmetry Quantum Groups |
| title | A note on quiver quantum toroidal algebra |
| title_full | A note on quiver quantum toroidal algebra |
| title_fullStr | A note on quiver quantum toroidal algebra |
| title_full_unstemmed | A note on quiver quantum toroidal algebra |
| title_short | A note on quiver quantum toroidal algebra |
| title_sort | note on quiver quantum toroidal algebra |
| topic | Conformal and W Symmetry Conformal Field Theory Higher Spin Symmetry Quantum Groups |
| url | https://doi.org/10.1007/JHEP05(2022)011 |
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