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arXiv 2106.09353hep-thmath-phmath.MPmath.RT
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Jackiw-Teitelboim超引力的超群结构

Supergroup Structure of Jackiw-Teitelboim Supergravity

Yale Fan, Thomas G. Mertens

备注：
55 pages + extensive appendices, v3: fixed typos and added references, matches published version
发表信息：
JHEP 2208 (2022) 002
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摘要：

我们在$\text{OSp}(1|2, \mathbb{R})$超群的基础上发展了$\mathcal{N}=1$ Jackiw-Teitelboim超引力的规范理论公式，重点讨论了边界动力学和引力振幅的精确结构。我们证明了BF描述在全息边界上简化为超Schwarzian量子力学，其中边界锚定的Wilson线映射为超Schwarzian理论中的双定域算符。根据$\text{OSp}(1|2, \mathbb{R})$的单值性对缺陷进行分类，并根据批量中的字符插入进行解释。从数学的角度来看，我们构建的主要系列表示的$\text{OSp}(1|2, \mathbb{R})$和相应的Plancherel措施，而不匹配的状态密度的$\mathcal{N}=1$ JT超引力，一个限制的积极的子半群$\text{OSp}^+(1|2, \mathbb{R})$产生正确的状态密度，反映了玻色子JT引力的类似结果。我们说明了这些结果与几个引力的应用，特别是计算在JT超引力后期的复杂性增长。

英文摘要：

We develop the gauge theory formulation of $\mathcal{N}=1$ Jackiw-Teitelboim supergravity in terms of the underlying $\text{OSp}(1|2, \mathbb{R})$ supergroup, focusing on boundary dynamics and the exact structure of gravitational amplitudes. We prove that the BF description reduces to a super-Schwarzian quantum mechanics on the holographic boundary, where boundary-anchored Wilson lines map to bilocal operators in the super-Schwarzian theory. A classification of defects in terms of monodromies of $\text{OSp}(1|2, \mathbb{R})$ is carried out and interpreted in terms of character insertions in the bulk. From a mathematical perspective, we construct the principal series representations of $\text{OSp}(1|2, \mathbb{R})$ and show that whereas the corresponding Plancherel measure does not match the density of states of $\mathcal{N}=1$ JT supergravity, a restriction to the positive subsemigroup $\text{OSp}^+(1|2, \mathbb{R})$ yields the correct density of states, mirroring the analogous results for bosonic JT gravity. We illustrate these results with several gravitational applications, in particular computing the late-time complexity growth in JT supergravity.

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