# Duality and integrability of a supermatrix model with an external source

@article{Kimura2014DualityAI, title={Duality and integrability of a supermatrix model with an external source}, author={Taro Kimura}, journal={Progress of Theoretical and Experimental Physics}, year={2014}, volume={2014} }

We study the Hermitian supermatrix model involving an external source. We derive the determinantal formula for the supermatrix partition function, and also for the expectation value of the characteristic polynomial ratio, which yields the duality between the characteristic polynomial and the external source with an arbitrary matrix potential function. We also show that the supermatrix integral satisfies the one and two dimensional Toda lattice equations as well as the ordinary matrix model.

## 4 Citations

### The Schur Expansion of Characteristic Polynomials and Random Matrices

- Mathematics
- 2021

We develop a new framework to compute the exact correlators of characteristic polynomials, and their inverses, in random matrix theory. Our results hold for general potentials and incorporate the…

### Characteristic Polynomials in Coupled Matrix Models

- Mathematics
- 2022

We study correlation functions of the characteristic polynomials in coupled matrix models based on the Schur polynomial expansion, which manifests their determinantal structure.

### Toward U ( N | M ) knot invariant from ABJM theory

- Mathematics
- 2017

We study U ( N | M ) character expectation value with the supermatrix Chern– Simons theory, known as the ABJM matrix model, with emphasis on its connection to the knot invariant. This average just…

### Toward $$\mathrm {U}(N|M)$$U(N|M) knot invariant from ABJM theory

- Mathematics
- 2014

We study $$\mathrm {U}(N|M)$$U(N|M) character expectation value with the supermatrix Chern–Simons theory, known as the ABJM matrix model, with emphasis on its connection to the knot invariant. This…

## References

SHOWING 1-10 OF 35 REFERENCES

### Supermatrix models, loop equations, and duality

- Mathematics
- 2010

We study integrals over Hermitian supermatrices of arbitrary size p + q, which are parametrized by an external field X and a source Y of respective sizes m + n and p + q. We show that these integrals…

### Integrability and matrix models

- Engineering
- 1993

The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Discrete 1-matrix, 2-matrix, 'conformal' (multicomponent) and Kontsevich models are…

### A supermatrix model for N = 6 super Chern-Simons-matter theory

- Physics
- 2010

We construct the Wilson loop operator of N = 6 super Chern-Simons-matter which is invariant under half of the supercharges of the theory and is dual to the simplest macroscopic open string in AdS4…

### An exact formula for general spectral correlation function of random Hermitian matrices

- Mathematics
- 2003

We have found an exact formula expressing a general correlation function containing both products and ratios of characteristic polynomials of random Hermitian matrices. The answer is given in the…

### Derivation of determinantal structures for random matrix ensembles in a new way

- Mathematics
- 2010

There are several methods to treat ensembles of random matrices in symmetric spaces, circular matrices, chiral matrices and others. Orthogonal polynomials and the supersymmetry method are particular…

### A supermatrix model for $$ \mathcal{N} $$ = 6 super Chern-Simons-matter theory

- Physics
- 2009

We construct the Wilson loop operator of $$ \mathcal{N} $$ = 6 super Chern-Simons-matter which is invariant under half of the supercharges of the theory and is dual to the simplest macroscopic open…

### Gelfand-Tzetlin coordinates for the unitary supergroup

- Mathematics
- 1996

The Gelfand-Tzetlin method provides explicit coordinates on the parameter space of the unitary groupU(k) which make direct evaluations of group integrals possible. It is closely related to the…

### New correlation functions for random matrices and integrals over supergroups

- Mathematics
- 2002

The averages of ratios of characteristic polynomials det(lambda - X) of N x N random matrices X, are investigated in the large N limit for the GUE, GOE and GSE ensemble. The density of states and the…

### Exact results for Wilson loops in superconformal Chern-Simons theories with matter

- Physics
- 2010

We use localization techniques to compute the expectation values of supersymmetric Wilson loops in Chern-Simons theories with matter. We find the path-integral reduces to a non-Gaussian matrix model.…

### Dyson’s correlation functions and graded symmetry

- Physics, Mathematics
- 1991

A new derivation of Dyson’s k‐level correlation functions of the Gaussian unitary ensemble (GUE) is given. The method uses matrices with graded symmetry. The number of integrations needed for the…