The simplest massive S-matrix: from minimal coupling to Black Holes (1812.08752v3)

Abstract: 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 which is characterized by matching to minimal coupling in the UV. In the IR such amplitude leads to g = 2 for arbitrary charged spin states, and the best high energy behavior for a given spin. We proceed to construct the (gravitational) Compton amplitude for generic spins. We find that the leading deformation away from minimal coupling, in the gravitation sector, will lead to inconsistent factorizations and are thus forbidden. As the corresponding deformation in the gauge sector encodes the anomalous magnetic dipole moment, this leads to the prediction that for systems with gauge2 =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, remarkably 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.

Insights into Massive Spin-S States and Their Role in Black Hole Dynamics

The paper "The simplest massive S-matrix: from minimal coupling to Black Holes" rigorously explores the properties and interactions of massive spin-S states in the realms of electromagnetism and gravity, specifically through the lens of S-matrix theory and their implications in black hole physics. The authors explore these complex systems, guided by both theoretical abstractions and empirical consistencies, shedding light on minimal coupling and its association with macroscopic astronomical phenomena such as Kerr black holes.

Overview of Key Findings

1. Minimal Coupling and High Energy Behavior: The discussion on minimal coupling centers around its identification in the UV limit, where it matches with minimal massless amplitude involving the fewest possible derivatives. This framework is essential for constructing the simplest S-matrix for massive higher spin states and is characterized by minimal non-triviality in both electromagnetic and gravitational contexts.
2. Photon Coupling and Magnetic Dipole Moments: A significant result of the paper is the observation that minimal coupling in electromagnetism leads to a classical magnetic dipole moment value of $g=2$ for arbitrary spins. This aligns with the conventional understanding of the gyromagnetic ratio and offers a remarkable simplification in analyzing charged particles, asserting that $g=2$ is consistently demanded for systems where gauge interactions are linked with gravity.
3. Gravitational Interactions and Spin: The complications addressed in gravitational coupling reveal the uniqueness of minimal coupling at work—a choice that naturally aligns with general covariance, thereby forbidding certain $\lambda_3^2$ deformations and stabilizing spin interactions. This approach indicates a universality in the gravito-magnetic dipole moment across different configurations, hinting at black holes' intrinsic simplicity.
4. Identification of Kerr Black Holes: The formal articulation that Kerr black holes represent an on-shell counterpart to minimal coupling underscores an elegant alignment with quantum gravity frameworks. This identification demonstrates the relevance of minimal coupling in translating fundamental physical principles to macroscopic singularities in spacetime described by the no-hair theorem.
5. Compton Amplitudes for General Spins: The paper presents methodologies for constructing gravitational Compton amplitudes across various spin states, enforced by consistent factorization protocols. These contributions are vital for understanding potential ambiguities at higher spins, where minimal coupling can still offer a fertile ground for theoretical exploration.

Implications and Future Directions

The implications of this research are multifaceted, affecting both the theoretical understanding of particle interactions and the practical frameworks used in gravitational wave astronomy and black hole physics. Minimal coupling serves as a defining feature in distinguishing between different theoretical models and lays the foundation for future explorations into the quantum attributes of black holes.

Moreover, the paper opens avenues for further inquiry into the correspondences between string theory and classical gravitational phenomena. Investigating how string resonances match simplified representation through minimal coupling remains a promising avenue of exploration.

Finally, the next phase in this line of research could be focused on extending these findings to other fundamental forces and interactions across different dimensions and energy scales. This exploration may reveal deeper symmetries and conservation laws intrinsic to the universe's very fabric.

In summary, "The simplest massive S-matrix: from minimal coupling to Black Holes" provides an intellectually stimulating resource for bridging abstract quantum field theories with classical representations in astrophysics. Its content serves as both a thorough academic paper and a catalyst for further groundbreaking advancements in the field.