Off-shell Partition Functions in 3d Gravity
Off-shell Partition Functions in 3d Gravity
复制标题
3d 重力中的壳外配分函数
DOI：
10.1007/s00220-024-04963-2
复制
发表时间：
2022
影响因子：
2.4
通讯作者：
Lorenz Eberhardt
中科院分区：
文献类型：
--
作者：
Lorenz Eberhardt
We explore three-dimensional gravity with negative cosmological constant via canonical quantization. We focus on chiral gravity which is related to a single copy of $\mathrm{PSL}(2,\mathbb{R})$ Chern-Simons theory and is simpler to treat in canonical quantization. Its phase space for an initial value surface $\Sigma$ is given by the appropriate moduli space of Riemann surfaces. We use geometric quantization to compute partition functions of chiral gravity on three-manifolds of the form $\Sigma \times \mathrm{S}^1$, where $\Sigma$ can have asymptotic boundaries. Most of these topologies do not admit a classical solution and are thus not amenable to a direct semiclassical path integral computation. We use an index theorem that expresses the partition function as an integral of characteristic classes over phase space. In the presence of $n$ asymptotic boundaries, we use techniques from equivariant cohomology to localize the integral to a finite-dimensional integral over $\overline{\mathcal{M}}_{g,n}$, which we evaluate in low genus cases. Higher genus partition functions quickly become complicated since they depend in an oscillatory way on Newton's constant. There is a precise sense in which one can isolate the non-oscillatory part which we call the fake partition function. We establish that there is a topological recursion that computes the fake partition functions for arbitrary Riemann surfaces $\Sigma$. There is a scaling limit in which the model reduces to JT gravity and our methods give a novel way to compute JT partition functions via equivariant localization.
We explore three-dimensional gravity with negative cosmological constant via canonical quantization. We focus on chiral gravity which is related to a single copy of $\mathrm{PSL}(2,\mathbb{R})$ Chern-Simons theory and is simpler to treat in canonical quantization. Its phase space for an initial value surface $\Sigma$ is given by the appropriate moduli space of Riemann surfaces. We use geometric quantization to compute partition functions of chiral gravity on three-manifolds of the form $\Sigma \times \mathrm{S}^1$, where $\Sigma$ can have asymptotic boundaries. Most of these topologies do not admit a classical solution and are thus not amenable to a direct semiclassical path integral computation. We use an index theorem that expresses the partition function as an integral of characteristic classes over phase space. In the presence of $n$ asymptotic boundaries, we use techniques from equivariant cohomology to localize the integral to a finite-dimensional integral over $\overline{\mathcal{M}}_{g,n}$, which we evaluate in low genus cases. Higher genus partition functions quickly become complicated since they depend in an oscillatory way on Newton's constant. There is a precise sense in which one can isolate the non-oscillatory part which we call the fake partition function. We establish that there is a topological recursion that computes the fake partition functions for arbitrary Riemann surfaces $\Sigma$. There is a scaling limit in which the model reduces to JT gravity and our methods give a novel way to compute JT partition functions via equivariant localization.
影响因子：
5.4
作者：
Jean-Marc Schlenker;E. Witten
通讯作者：
Jean-Marc Schlenker;E. Witten
影响因子：
5.4
作者：
D. Marolf;Henry Maxfield
通讯作者：
D. Marolf;Henry Maxfield
影响因子：
5.4
作者：
Animik Ghosh;Henry Maxfield;G. Turiaci
通讯作者：
Animik Ghosh;Henry Maxfield;G. Turiaci