Spectral Constraints on Theories of Colored Particles and Gravity
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1.
California Institute of Technology
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2.
National Taiwan University
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3.
National Center for Theoretical Sciences
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4.
Tsinghua University
Abstract
In this Letter, we consider effective field theories for light fields transforming under the fundamental or adjoint representation of a continuous group. Assuming tree-level completions, we demonstrate that, in the presence of gravity, crossing symmetry combined with twice-subtracted sum rules leads to constraints on the irreducible representations that the ultraviolet degrees of freedom must populate. A spectrum is allowed only if its low energy projection contains the graviton pole. Beautifully, the graviton pole is the anchor of our argument, not an obstruction.
Copyright and License
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Acknowledgement
We thank Simon Caron-Huot and Alexander Zhiboedov for discussions. The work of J. R. is supported by Taiwan NSTC Grant No. 112-2811-M-002 -054 -MY2, while Y-t. H. is supported by Taiwan NSTC Grant No. 112-2628-M-002 -003 -MY3. L. R. is supported by the Beijing Natural Science Foundation International Scientist Project No. IS24014, and the National Natural Science Foundation of China General Program No. 12475070. A. H. is supported by the Department of Energy (Grant No. DE-SC0011632) and by the Walter Burke Institute for Theoretical Physics.
Supplemental Material
Provides the details of SO(n) projectors, linear transforms between projectors of different channels and the vectors $v$ that yields the constraint for the main text.
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Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2411.04857 (arXiv)
- Is supplemented by
- Supplemental Material: https://journals.aps.org/prl/supplemental/10.1103/k23f-y47w/Supplemantry.pdf (URL)
Funding
- National Science and Technology Council
- 112-2811-M-002-054-MY2
- National Science and Technology Council
- 112-2628-M-002-003-MY3
- National Natural Science Foundation of China
- IS24014
- National Natural Science Foundation of China
- 12475070
- United States Department of Energy
- DE-SC0011632
- California Institute of Technology
- SCOAP3
Dates
- Accepted
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2025-07-10