Recently, it has been found that Jackiw-Teitelboim (JT) gravity, which is a two-dimensional theory with bulk action −1/2∫d2xgϕ(R+2), is dual to a matrix model, that is, a random ensemble of quantum systems rather than a specific quantum mechanical system. In this article, we argue that a deformation of JT gravity with bulk action −1/2∫d2xg(ϕR+W(ϕ)) is likewise dual to a matrix model. With a specific procedure for defining the path integral of the theory, we determine the density of eigenvalues of the dual matrix model. There is a simple answer if W(0) = 0, and otherwise a rather complicated answer.

中文翻译：

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JT重力的矩阵模型和变形


最近，人们发现 Jackiw-Teitelboim (JT) 引力是一种具有体积作用 −1/2∫d2xgphi(R+2) 的二维理论，它与矩阵模型（即随机系综）是对偶的量子系统而不是特定的量子力学系统。在本文中，我们认为具有体积作用的 JT 重力变形 −1/2∫d2xg(ψR+W(ψ)) 同样与矩阵模型对偶。通过定义理论路径积分的特定过程，我们确定了对偶矩阵模型的特征值密度。如果 W(0) = 0，则答案很简单，否则答案相当复杂。