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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.11923 |
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| _version_ | 1866913115110637568 |
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| author | Glennon, Keith |
| author_facet | Glennon, Keith |
| contents | We examine the proposal of [29] that M-theory may admit a Sugawara-type current algebra formulation based on $E_{11} \otimes_s l_1$. Motivated by the role of generalized coordinates in E-theory, we ask whether current algebra relations of this type can be derived in a setting that includes those coordinates systematically. We show that such a construction can indeed be carried out for a rigid $E_{11}$ model in which the generalized coordinates are treated as inert under the rigid symmetry, in contrast with E-theory. We also argue that the bilinear form entering the Schwinger term requires closer scrutiny, since any natural ad-invariant extension of the $E_{11}$ Cartan-Killing form to $E_{11} \otimes_s l_1$ is degenerate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11923 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Sugawara Current Algebra Proposal for M-Theory Glennon, Keith High Energy Physics - Theory We examine the proposal of [29] that M-theory may admit a Sugawara-type current algebra formulation based on $E_{11} \otimes_s l_1$. Motivated by the role of generalized coordinates in E-theory, we ask whether current algebra relations of this type can be derived in a setting that includes those coordinates systematically. We show that such a construction can indeed be carried out for a rigid $E_{11}$ model in which the generalized coordinates are treated as inert under the rigid symmetry, in contrast with E-theory. We also argue that the bilinear form entering the Schwinger term requires closer scrutiny, since any natural ad-invariant extension of the $E_{11}$ Cartan-Killing form to $E_{11} \otimes_s l_1$ is degenerate. |
| title | On the Sugawara Current Algebra Proposal for M-Theory |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.11923 |