Large $N$ phenomena and quantization of the Loday-Quillen-Tsygan theorem
| Autor: | Ginot, Grégory, Gwilliam, Owen, Hamilton, Alastair, Zeinalian, Mahmoud |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We offer a new approach to large $N$ limits using the Batalin-Vilkovisky formalism, both commutative and noncommutative, and we exhibit how the Loday-Quillen-Tsygan Theorem admits BV quantizations in that setting. Matrix integrals offer a key example: we demonstrate how this formalism leads to a recurrence relation that in principle allows us to compute all multi-point correlation functions. We also explain how the Harer-Zagier relations may be expressed in terms of this noncommutative geometry derived from the BV formalism. As another application, we consider the problem of quantization in the large $N$ limit and demonstrate how the Loday-Quillen-Tsygan Theorem leads us to a solution in terms of noncommutative geometry. These constructions are relevant to open topological field theories and string field theory, providing a mechanism that relates moduli of categories of branes to moduli of brane gauge theories. Comment: 45 pages |
| Databáze: | arXiv |
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