Classifying large N limits of multiscalar theories by algebra
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2023
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| _version_ | 1866914788116791296 |
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| author | Flodgren, Nadia Sundborg, Bo |
| author_facet | Flodgren, Nadia Sundborg, Bo |
| contents | We develop a new approach to RG flows and show that one-loop flows in multiscalar theories can be described by commutative but non-associative algebras. As an example related to $D$-brane field theories and tensor models, we study the algebra of a theory with $M$ $SU(N)$ adjoint scalars and its large $N$ limits. The algebraic concepts of idempotents and Peirce numbers/Kowalevski exponents are used to characterise the RG flows. We classify and describe all large $N$ limits of algebras of multiadjoint scalar models: the standard `t Hooft matrix theory limit, a `multi-matrix' limit, each with one free parameter, and an intermediate case with extra symmetry and no free parameter of the algebra, but an emergent free parameter from a line of one-loop fixed points. The algebra identifies these limits without diagrammatic or combinatorial analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04954 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Classifying large N limits of multiscalar theories by algebra Flodgren, Nadia Sundborg, Bo High Energy Physics - Theory High Energy Physics - Phenomenology We develop a new approach to RG flows and show that one-loop flows in multiscalar theories can be described by commutative but non-associative algebras. As an example related to $D$-brane field theories and tensor models, we study the algebra of a theory with $M$ $SU(N)$ adjoint scalars and its large $N$ limits. The algebraic concepts of idempotents and Peirce numbers/Kowalevski exponents are used to characterise the RG flows. We classify and describe all large $N$ limits of algebras of multiadjoint scalar models: the standard `t Hooft matrix theory limit, a `multi-matrix' limit, each with one free parameter, and an intermediate case with extra symmetry and no free parameter of the algebra, but an emergent free parameter from a line of one-loop fixed points. The algebra identifies these limits without diagrammatic or combinatorial analysis. |
| title | Classifying large N limits of multiscalar theories by algebra |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2312.04954 |