Quantum Effective Action Framework Constructs Double-Copy Theories, Elevating Scattering Amplitudes to Defining Data

The fundamental nature of space-time and gravity remains a central question in physics, and new approaches to understanding these concepts are continually sought. John Joseph M. Carrasco and Suna Zekioglu, both from Northwestern University, present a novel framework that redefines how field theory actions, including those describing gravity, are constructed, elevating scattering amplitudes to the central defining data. Their work systematically connects seemingly disparate theories, demonstrating how gravitational interactions emerge from simpler gauge-theoretic structures at the level of the action itself. By extending a principle known as color-kinematics duality, the researchers achieve a natural realisation of the ‘double copy’ relationship between gravity and gauge theory, not just in calculations of particle interactions, but in the very foundations of how these theories are built, offering a physically grounded alternative to conventional approaches to effective field theory construction and revealing deep structural connections between fundamental interactions and their descriptions.

Theories frequently emphasize compactness and off-shell symmetry, often obscuring the structure of on-shell physical observables. This work presents a constructive framework that elevates gauge-invariant scattering amplitudes to the defining data for quantum field theory actions, including effective field theories. Focusing on theories where relationships exist between different force interactions, the researchers promote components of these amplitudes to quantum operators, enabling the systematic identification of novel local operator content at each interaction multiplicity and the construction of actions compatible with the double-copy relationship, a mathematical connection between seemingly disparate theories. By applying this framework to the well-established link between Einstein’s gravity and Yang-Mills theory, the team achieves a deeper understanding of gravitational interactions and their connection to gauge theories.

Gravity From Gauge Theory Via Double Copy

Scattering amplitudes, which calculate the probabilities of particle interactions, and the double copy, a remarkable relationship between gauge theories and gravity, form the core of this research. The double copy suggests that calculations in gravity can be obtained from gauge theories through a simple mathematical transformation, hinting at a fundamental connection between these areas of physics. Color-kinematics duality, the mathematical foundation of the double copy, decomposes amplitudes into color and kinematic factors, allowing for the treatment of kinematic factors as gravitational amplitudes. Unitarity, a fundamental principle ensuring probabilities sum to one, and its extension, generalized unitarity, are used to construct complex loop amplitudes, crucial for precise predictions in particle physics.

This work builds upon these concepts, extending the double copy to higher loops and developing global bases for loop integrands, simplifying complex calculations. The research also highlights connections to string theory, a framework unifying fundamental forces, particularly through calculations involving disk integrals and α’-corrections. Applying these methods to heterotic and bosonic string theory, the team develops new techniques for constructing amplitudes, ultimately aiming to improve calculations of gravitational amplitudes and gain a better understanding of quantum gravity.

Constructing Gravity from Scattering Amplitudes

Scientists have achieved a systematic method for constructing effective field theories directly from scattering amplitudes, elevating these amplitudes to the foundational data defining the theory. This work demonstrates a pathway to identify novel local operator content at each interaction multiplicity and construct actions compatible with the double-copy relationship. By applying this framework to the well-established link between Einstein’s theory of gravity and Yang-Mills theory, researchers systematically constructed the operator expansion of gravity from components of the gauge theory, clarifying how gravitational interactions emerge from simpler gauge-theoretic structures at the action level, naturally realizing the double copy at the level of actions and asymptotic states. The formalism extends color-kinematics duality from amplitude data to operator constructions.

Investigations with Yang-Mills theory and gravity, including extensions inspired by Z-theory and open superstring amplitudes, demonstrate the power of this approach for generating higher-derivative operators. Specifically, the research establishes a basis of graph numerators, including all-orders higher-derivative corrections, to express tree-level scattering amplitudes in a wide range of theories. To illustrate the method, scientists examined a simple scalar theory and a gauge-invariant theory of a real adjoint scalar coupled to Yang-Mills, defining it through both amplitudes-based and traditional operator approaches. Analysis of three-point and four-point amplitudes revealed constraints on operator forms, ensuring gauge invariance and consistent factorization at higher multiplicities. The team determined that the four-scalar amplitude requires no four-scalar contact term to satisfy color-kinematics duality at four points. These findings provide a concrete bridge between structured amplitudes and effective actions, offering a physically grounded alternative to traditional effective field theory basis building.

Gravity and Gauge Theories from Amplitudes

This work presents a new framework that systematically connects scattering amplitudes to the local operators appearing in effective field theories. Researchers elevated gauge-invariant scattering amplitudes to the defining data for constructing field theory actions, focusing on theories where relationships exist between different force interactions. By promoting components of these amplitudes to operators, the team identified novel local operator content and built actions compatible with the double-copy relationship, a mathematical connection between gravity and gauge theories. Applying this method to the well-established link between Einstein’s theory of gravity and Yang-Mills theory, the team demonstrated a pathway to systematically construct the operator expansion of gravity from components of the gauge theory, clarifying how gravitational interactions can emerge from simpler gauge-theoretic structures at the action level, naturally realizing the double copy at the level of actions and asymptotic states.

The formalism extends color-kinematics duality from amplitude data to operator constructions. The authors acknowledge that spurious non-locality can arise in their calculations, requiring careful consideration when applying the method. Future research directions include exploring the implications of this framework for quantum gravity and further investigating the state-level descriptions of interactions. This work provides a physically grounded alternative to traditional methods of building effective field theories, revealing deep structural connections between gauge theory and gravity, from fundamental interactions to their higher-derivative extensions.