Multi-matrix models and Noncommutative Frobenius algebras obtained from symmetric groups and Brauer algebras

Abstract

It has been understood that correlation functions of multi-trace operators in $\mathcal{N}=4$ SYM can be neatly computed using the group algebra of symmetric groups or walled Brauer algebras. On the other hand such algebras have been known to construct 2D topological field theories (TFTs). After reviewing the construction of 2D TFTs based on symmetric groups, we construct 2D TFTs based on walled Brauer algebras. In the construction, the introduction of a dual basis manifests a similarity between the two theories. We next construct a class of 2D field theories whose physical operators have the same symmetry as multi-trace operators constructed from some matrices. Such field theories correspond to non-commutative Frobenius algebras. A matrix structure arises as a consequence of the noncommutativity. Correlation functions of the Gaussian complex multi-matrix models can be translated into correlation functions of the two-dimensional field theories.

40 pages, 7 figures

References in corpus (7)

• Diagonal multi-matrix correlators and BPS operators in N=4 SYM
• Nonplanar Integrability
• Giant Gravitons - with Strings Attached (III)
• Giant Gravitons - with Strings Attached (II)
• Enhanced symmetries of gauge theory and resolving the spectrum of local operators
• From counting to construction of BPS states in N=4 SYM
• Restricted Schur Polynomials and Finite N Counting

Cited by in corpus (1)

• BPS states, conserved charges and centres of symmetric group algebras