arXiv subjects

Chun-Hong Zhang

Publications and source records attributed to Chun-Hong Zhang.

5 recordsLinked to original sources

arXiv2022

CFT approach to constraint operators for ($β$-deformed) hermitian one-matrix models

Since the ($β$-deformed) hermitian one-matrix models can be represented as the integrated conformal field theory (CFT) expectation values, we construct the operators in terms of the generators of the Heisenberg algebra such that the constraints can be derived by inserting the constructed operators into the integrated expectation values. We also obtain the second order total derivative operators associating with the derived constraint operators and analyze their properties. We explore the intrinsic connection between the derived constraint operators and $W$-representations of some matrix models. For the Gaussian hermitian one-matrix model in the external field and $β$-deformed $N\times N$ complex matrix model, we investigate the superintegrability and derive the corresponding character expansions from their $W$-representations. Moreover a conjectured formula for the averages of Jack polynomials in the literature is proved.

hep-th↗

arXiv2022

Superintegrability for ($β$-deformed) partition function hierarchies with $W$-representations

We construct the ($β$-deformed) partition function hierarchies with $W$-representations. Based on the $W$-representations, we analyze the superintegrability property and derive their character expansions with respect to the Schur functions and Jack polynomials, respectively. Some well known superintegrable matrix models such as the Gaussian hermitian one-matrix model (in the external field), $N\times N$ complex matrix model, $β$-deformed Gaussian hermitian and rectangular complex matrix models are contained in the constructed hierarchies.

hep-th↗

arXiv2019

$W_{1+\infty}$ constraints for the hermitian one-matrix model

We construct the multi-variable realizations of the $W_{1+\infty}$ algebra such that they lead to the $W_{1+\infty}$ $n$-algebra. Based on our realizations of the $W_{1+\infty}$ algebra, we derive the $W_{1+\infty}$ constraints for the hermitian one-matrix model. The constraint operators yield not only the $W_{1+\infty}$ algebra but also the closed $W_{1+\infty}$ $n$-algebra.

hep-th↗

arXiv2019

On $W_{1+\infty}$ $n$-algebra

We present the nontrivial $W_{1+\infty}$ $n$-algebra and analyze its remarkable properties. We investigate the $W_{1+\infty}$ $n$-algebra in the Landau problem and discuss the realization of the classical $w_{\infty}$ 3-algebra. Furthermore, we discuss the case of the many-body system in the lowest Landau level and derive the constraints for correlation functions of the vertex operators.

hep-th↗

arXiv2017

3-Algebraic structures of the quantum Calogero-Moser model

We investigate the quantum Calogero-Moser model and reveal its hidden symmetries, i.e., the $W_{1+\infty}$ and Virasoro-Witt 3-algebras. In the large $N$ limit, we note that these two infinite dimensional 3-algebras reduce to the $w_{\infty}$ and special Virasoro-Witt 3-algebras which satisfy the fundamental identity condition, respectively.

hep-th↗