The Fokker?Planck formalism for closed bosonic strings
The Fokker?Planck formalism for closed bosonic strings
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封闭玻色弦的福克·普朗克形式主义
DOI：
10.1093/ptep/ptad014
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发表时间：
2023
影响因子：
3.5
通讯作者：
Ishibashi Nobuyuki
中科院分区：
文献类型：
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作者：
Yusuke Namekawa;Akira Mizuta;Ishibashi Nobuyuki
每一个具有亏格和穿孔的黎曼曲面都有一个双曲度量，如果2g− 2 +n> 0。这样的曲面可以分解成以测地线为边界的裤子。基于这种裤子分解，我们构造了闭玻色弦的弦场论。为了做到这一点，我们推导出一个递归关系所满足的离壳振幅，使用Mirzakhani的计划计算积分的模空间的边界黎曼曲面。递归关系可以通过福克-普朗克形式化转化为弦场论。Fokker-Planck哈密顿量由动力学项和三个弦顶点组成。不幸的是，世界面BRST对称性在这样构造的理论中并不明显。我们将证明，不变性可以通过引入辅助场来表现。
Every Riemann surface with genusgandnpunctures admits a hyperbolic metric, if 2g− 2 +n> 0. Such a surface can be decomposed into pairs of pants whose boundaries are geodesics. We construct a string field theory for closed bosonic strings based on this pants decomposition. In order to do so, we derive a recursion relation satisfied by the off-shell amplitudes, using Mirzakhani’s scheme for computing integrals over the moduli space of bordered Riemann surfaces. The recursion relation can be turned into a string field theory via the Fokker–Planck formalism. The Fokker–Planck Hamiltonian consists of kinetic terms and three-string vertices. Unfortunately, the worldsheet BRST symmetry is not manifest in the theory thus constructed. We will show that the invariance can be made manifest by introducing auxiliary fields.