Classifying large N limits of multiscalar theories by algebra
| Autor: | Flodgren, Nadia, Sundborg, Bo |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 23 pages, 5 figures, Added qualitative discussion of: two loops for couplings with vanishing one-loop beta function, early uses of the algebra, origin of the non-associativity, and algebra for the simple O(N) model |
| Databáze: | arXiv |
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