arXiv 1509.014322015-09-04hep-thgr-qc

正则张量模型的$OSp$推广

An $OSp$ extension of Canonical Tensor Model

Gaurav Narain, Naoki Sasakura

备注：: 27pages, 27 figures
DOI：: 10.1093/ptep/ptv169

摘要：

张量模型是矩阵模型的推广，并且作为任意维度的量子引力的离散模型被研究。其中，正则张量模型（canonical tensor model，简称CTM）是一个三阶张量模型，它被表述为一个具有多个第一类约束的完全约束系统，这些第一类约束具有与广义相对论的ADM形式的约束相似的代数结构。在本文中，我们制定了一个超级扩展CTM作为一种尝试，将费米子自由度。将运动学对称群从$O(N)$推广到$OSp(N,\tilde N)$，构造约束，使它们构成第一类约束超Poisson代数.这是一个简单的超扩展，除了与费米子指数和动力学变量的阶数相关的附加符号之外，约束和它们的代数结构在形式上与纯玻色子情况没有变化。然而，CTM的这种扩展导致了量子化情况下负范数态的存在，并且需要一些未来的改进，如量子引力与费米子。另一方面，由于这是一个简单的超延拓，所以迄今为止在纯玻色子情况下获得的各种结果预计在超延拓情况下也有相似之处，例如精确的物理波函数和与对偶统计系统的连接，即随机连接的张量网络。

英文摘要：

Tensor models are generalizations of matrix models, and are studied as discrete models of quantum gravity for arbitrary dimensions. Among them, the canonical tensor model (CTM for short) is a rank-three tensor model formulated as a totally constrained system with a number of first-class constraints, which have a similar algebraic structure as the constraints of the ADM formalism of general relativity. In this paper, we formulate a super-extension of CTM as an attempt to incorporate fermionic degrees of freedom. The kinematical symmetry group is extended from $O(N)$ to $OSp(N,\tilde N)$, and the constraints are constructed so that they form a first-class constraint super-Poisson algebra. This is a straightforward super-extension, and the constraints and their algebraic structure are formally unchanged from the purely bosonic case, except for the additional signs associated to the order of the fermionic indices and dynamical variables. However, this extension of CTM leads to the existence of negative norm states in the quantized case, and requires some future improvements as quantum gravity with fermions. On the other hand, since this is a straightforward super-extension, various results obtained so far for the purely bosonic case are expected to have parallels also in the super-extended case, such as the exact physical wave functions and the connection to the dual statistical systems, i.e. randomly connected tensor networks.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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英文摘要：

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