Light-Front Higher-Spin Theories in Flat Space (1609.04655v3)

Abstract: We revisit the problem of interactions of higher-spin fields in flat space. We argue that all no-go theorems can be avoided by the light-cone approach, which results in more interaction vertices as compared to the usual covariant approaches. It is stressed that there exist two-derivative gravitational couplings of higher-spin fields. We show that some reincarnation of the equivalence principle still holds for higher-spin fields - the strength of gravitational interaction does not depend on spin. Moreover, it follows from the results by Metsaev that there exists a complete chiral higher-spin theory in four dimensions. We give a simple derivation of this theory and show that the four-point scattering amplitude vanishes. Also, we reconstruct the quartic vertex of the scalar field in the unitary higher-spin theory, which turns out to be perturbatively local.

Light-Front Higher-Spin Theories in Flat Space

This paper by Dmitry Ponomarev and Evgeny Skvortsov addresses the longstanding challenge of constructing interacting higher-spin (HS) theories within the framework of flat space quantum field theory. The authors propose using the light-cone approach, arguing it circumvents several no-go theorems traditionally associated with HS interactions. They reveal more interaction vertices than those obtained through conventional covariant methods, notably highlighting two-derivative gravitational couplings of HS fields, indicative of a universal interaction strength, independent of the spin.

Main Contributions

1. Avoiding No-Go Theorems: The paper methodically reviews historical no-go results including Weinberg's low energy theorem, the Coleman-Mandula theorem, and the Aragone-Deser argument. It demonstrates that light-cone techniques skirt these constraints by focusing on physical degrees of freedom, thus bypassing the typical obstructions seen in local field theory approaches.
2. Light-Cones and Interaction Vertices: Using the light-cone method, the authors find non-trivial cubic interactions between HS fields, presenting local field theories with vertices not observed in covariant descriptions. The analysis reveals a mismatch with covariant approaches, showcasing the existence of vertices such as those with two-derivative gravitational interactions, offering new insights into the interaction dynamics of HS fields.
3. Chiral Higher-Spin Theory: A pivotal result is the establishment of a complete chiral HS theory in four dimensions. Remarkably, the theory’s scattering amplitude vanishes at the four-point level, indicating potential consistency throughout higher-order interactions. However, it breaks parity and is non-unitary, standing as a conceptual counterpoint to established beliefs about HS field theories in Minkowski spacetime.
4. Towards Unitary Theories: The paper reconstructs the quartic vertex of the scalar field within a unitary HS theory context, finding it is perturbatively local. This suggests a pathway from chiral configurations to practical, parity-preserving theories, albeit requiring further development to address multiple HS interactions cohesively.
5. Higher-Spin Equivalence Principle: Extending the renowned equivalence principle, the authors propose that gravitational and Yang-Mills interactions with HS fields exhibit universality. This indicates HS fields interact with gravity at a consistent strength across different spins, presenting a novel viewpoint on the dynamics and symmetry principles governing HS fields.

Implications and Future Directions

The findings have significant implications for both theoretical advancements and practical applications. The existence of gravitational vertices at lower derivatives suggests that HS fields could be integrated into broader gravitational theories, potentially impacting cosmological models and theories of quantum gravity.

The paper encourages future exploration into the parallel development of HS theories in AdS spaces, hinting at possible connections via smooth flat limits. Furthermore, the authors suggest that a deeper understanding of HS field interactions might illuminate aspects of quantum consistency and renormalizability within non-Lorentz covariant frameworks.

Overall, Ponomarev and Skvortsov's work brings a nuanced perspective to the discourse on HS field theories, offering a substantial leap towards reconciling higher-spin interactions within conventional quantum field theory constructs. As they outline, further research is needed to explore the conditions under which unitary HS theories in flat space can exist, potentially unlocking new principles governing the structure of particle and field interactions at the quantum level.