New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level.

Area of Science:

• Theoretical Physics
• High Energy Physics
• Quantum Field Theory

Background:

• The Kawai-Lewellen-Tye (KLT) and Bern-Carrasco-Johansson (BCJ) relations establish connections between scattering amplitudes in gauge theory and gravity at tree-level.
• Extending these relations to loop integrands is crucial for a deeper understanding of quantum gravity and gauge theories.

Purpose of the Study:

• To generalize the tree-level KLT and BCJ amplitude relations to the realm of loop integrands in gauge theory and gravity.
• To develop a manifestly gauge- and diffeomorphism-invariant formulation of double-copy relations for loop integrands.

Main Methods:

• Rearrangement of propagators within gauge and gravity loop integrands.
• Development of a novel formulation for double-copy relations applicable to loop integrands.
• Identification of gauge-invariant building blocks, termed 'partial integrands', for gravity loop amplitudes.

Main Results:

• The first manifestly gauge- and diffeomorphism-invariant double-copy relations for loop integrands are proposed.
• A one-loop KLT formula is derived, expressing gravity integrands via partial integrands derived from gauge theory amplitudes.
• These partial integrands satisfy a one-loop analogue of the BCJ relations, demonstrating universality across dimensions and particle types.
• One-loop integrands of Einstein-Yang-Mills theory are shown to be related to partial integrands of pure gauge theories.

Conclusions:

• The study successfully extends KLT and BCJ relations to loop integrands, providing a unified framework for gauge theory and gravity.
• The proposed double-copy formulation offers a powerful tool for investigating quantum gravity and gauge theories at loop level.
• The universality of the derived relations highlights fundamental connections between different areas of theoretical physics.