最簡帶質量散射矩陣: 從最小耦合到黑洞

The simplest Massive S-matrix: from minimal coupling to Black Holes

鍾明志(Ming-Zhi Chung)

指導教授 ： 黃宇廷

國立臺灣大學/理學院/物理學研究所/碩士(2019年)

https://doi.org/10.6342/NTU201901616

摘要

在本篇文章裡, 我們從在殼觀點探索帶質量高自旋態與電磁場與重力場的耦合, 從三點散射振幅開始, 我們關注在最簡單的振幅, 並將其在紫外領域中與最小耦合對應, 在紅外領域中, 這樣的振幅對於任意自旋皆可推得g = 2; 我們接著計算廣義自旋的重力子康普頓振幅, 我們發現對重力最小耦合外的領導項耦合做變形會造成不自洽的分解所以這樣的變形必須被禁止, 在規範理論中, 相對應的耦合變形帶有異常磁矩的資訊, 這造成符合規範理論平方 = 重力的系統中, 例如微擾弦論, 所有帶電態必須符合g = 2, 我們很自然地問, 對於廣義的自旋而言, 什麼樣的理論可以推得最小耦合? 透過和單體有效作用量, 我們發現對於極大的自旋, 最小耦合對應克爾黑洞, 因此最小耦合即為在殼觀點中黑洞無毛定理的敘述, 最後我們利用這樣的對應以及新的重力子康普頓振幅計算2PM 自旋四次方的黑洞古典位能

關鍵字

最小耦合 ； 自旋 ； 重力子康普頓振幅 ； 單體有效位能 ； 克爾黑洞

並列摘要

In this paper, we explore the physics of electromagnetically and gravitationally coupled massive higher spin states from the on-shell point of view. Starting with the three-point amplitude, we focus on the simplest amplitude characterized by matching to minimal coupling in the UV. In the IR, for charged states this leads to g = 2 for arbitrary spin, and the leading deformation corresponds to the anomalous magnetic dipole moment. We proceed to construct the (gravitational) Compton amplitude for generic spins via consistent factorization. We find that in gravitation couplings, the leading deformation leads to inconsistent factorization. This implies that for systems with Gauge^2 = Gravity relations, such as perturbative string theory, all charged states must have g = 2. It is then natural to ask for generic spin, what is the theory that yields such minimal coupling. By matching to the one body effective action, we verify that for large spins the answer is Kerr black holes. This identification is then an on-shell avatar of the no- hair theorem. Finally using this identification as well as the newly constructed Compton amplitudes, we proceed to compute the spin-dependent pieces for the classical potential at 2PM order up to degree four in spin operator of either black holes.

並列關鍵字

Minimal coupling ； spin ； graviton Compton amplitude ； one body effective action ； Kerr black hole

參考文獻

[1] F. Cachazo and A. Guevara, Leading Singularities and Classical Gravitational Scattering, 1705.10262.

[2] N. Arkani-Hamed, T.-C. Huang and Y.-t. Huang, Scattering Amplitudes For All Masses and Spins, 1709.04891.

[3] A. Guevara, Holomorphic Classical Limit for Spin Effects in Gravitational and Electromagnetic Scattering, 1706.02314.

[4] S. Ferrara, M. Porrati and V. L. Telegdi, g = 2 as the natural value of the tree level gyromagnetic ratio of elementary particles, Phys. Rev. D46 (1992) 3529–3537.

[5] S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516–B524.