• Corpus ID: 237346913

Large $N$ phenomena and quantization of the Loday-Quillen-Tsygan theorem

@inproceedings{Ginot2021LargeP,
  title={Large \$N\$ phenomena and quantization of the Loday-Quillen-Tsygan theorem},
  author={Gr{\'e}gory Ginot and Owen Gwilliam and Alastair Hamilton and Mahmoud Zeinalian},
  year={2021}
}

• G. Ginot, Owen Gwilliam, +1 author M. Zeinalian
• Published 27 August 2021
• Mathematics

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.