Spectral Constraints on Theories of Colored Particles and Gravity

Area of Science:

• Theoretical Physics
• High Energy Physics
• Quantum Field Theory

Background:

• Effective field theories (EFTs) describe physics at a given energy scale.
• Continuous groups and their representations are fundamental in particle physics.
• Gravity's role in EFTs, especially concerning ultraviolet (UV) completions, is a key area of research.

Purpose of the Study:

• To investigate constraints on EFTs for light fields under continuous groups in the presence of gravity.
• To explore how crossing symmetry and sum rules impact the allowed representations of UV degrees of freedom.
• To establish the role of the graviton pole in spectrum consistency.

Main Methods:

• Utilizing effective field theories for light fields.
• Applying crossing symmetry and twice-subtracted sum rules.
• Analyzing the implications of gravity on the theory's structure.
• Examining the low-energy projection of the spectrum.

Main Results:

• Demonstrated that crossing symmetry and sum rules impose constraints on irreducible representations for UV degrees of freedom.
• Showed that a spectrum is permissible only if its low-energy projection includes the graviton pole.
• Identified the graviton pole as a crucial element for theoretical consistency, not a hindrance.

Conclusions:

• The study provides constraints on the structure of theories with light fields and gravity.
• The presence of the graviton pole is a necessary condition for a consistent spectrum in these EFTs.
• This work offers insights into UV completions of theories involving gravity and continuous symmetries.