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Spectral Constraints on Theories of Colored Particles and Gravity

Aaron Hillman, Yu-tin Huang, Laurentiu Rodina, Justinas Rumbutis

TL;DR

This work establishes general constraints on the UV spectra of theories with gauge or global symmetries in the presence of gravity, using crossing symmetry and twice-subtraction dispersion relations for 2→2 massless scattering. By building a dispersive framework with a color- and spin-resolved basis and employing SDPB numerics, it shows that the graviton pole forces the UV completion to include irreps beyond those present in the low-energy spectrum, with fundamental matter requiring at least two irreps and adjoint matter at least three (the only viable three-irrep set being singlet, adjoint, and antisymmetric). The graviton must reside in the singlet in a nontrivial numerical bootstrap, suggesting strong constraints on UV completions and supporting a form of the Completeness-like requirement for irreps. These results connect to swampland ideas and offer a concrete, calculable criterion for UV content in gravitationally coupled gauge/global theories, with potential implications for explicit UV constructions and higher-spin constraints.

Abstract

In this letter, we consider effective field theories for light fields transforming under the fundamental or adjoint representation of a continuous group. We demonstrate that in the presence of gravity, crossing symmetry combined with two subtraction sum rules, leads to stringent constraints on the spectrum of its ultraviolet (UV) completion. Such constraints come in the form of necessary conditions on the symmetry group irreps of the UV states. This is in sharp contrast with non-gravitational theories where anything goes. Beautifully, the graviton pole is the anchor of our argument, not an obstruction. Using numerical methods, we also demonstrate that the massless spin-2 must be a singlet under said symmetry group.

Spectral Constraints on Theories of Colored Particles and Gravity

TL;DR

This work establishes general constraints on the UV spectra of theories with gauge or global symmetries in the presence of gravity, using crossing symmetry and twice-subtraction dispersion relations for 2→2 massless scattering. By building a dispersive framework with a color- and spin-resolved basis and employing SDPB numerics, it shows that the graviton pole forces the UV completion to include irreps beyond those present in the low-energy spectrum, with fundamental matter requiring at least two irreps and adjoint matter at least three (the only viable three-irrep set being singlet, adjoint, and antisymmetric). The graviton must reside in the singlet in a nontrivial numerical bootstrap, suggesting strong constraints on UV completions and supporting a form of the Completeness-like requirement for irreps. These results connect to swampland ideas and offer a concrete, calculable criterion for UV content in gravitationally coupled gauge/global theories, with potential implications for explicit UV constructions and higher-spin constraints.

Abstract

In this letter, we consider effective field theories for light fields transforming under the fundamental or adjoint representation of a continuous group. We demonstrate that in the presence of gravity, crossing symmetry combined with two subtraction sum rules, leads to stringent constraints on the spectrum of its ultraviolet (UV) completion. Such constraints come in the form of necessary conditions on the symmetry group irreps of the UV states. This is in sharp contrast with non-gravitational theories where anything goes. Beautifully, the graviton pole is the anchor of our argument, not an obstruction. Using numerical methods, we also demonstrate that the massless spin-2 must be a singlet under said symmetry group.

Paper Structure

This paper contains 13 sections, 37 equations, 1 figure, 5 tables.

Table of Contents

  1. Introduction
  2. The dispersive representation for colored S-matrix
  3. Expansion basis for colored amplitudes
  4. Twice subtraction sum rules
  5. Color Projectors
  6. Implications of gravity
  7. Fundamental and Adjoint matter
  8. Graviton poles as other irreps
  9. Conclusions
  10. Adjoint representation matrices
  11. Vectors $v$ for adjoint
  12. Improved dispersion relation
  13. Choices of parameters and numerical results

Figures (1)

  • Figure 1: $G_{32}/(8 \pi G)$ vs $G_p/(8 \pi G)$ with graviton in singlet representation in $d=5$. The bounds seem to be already convergent with low spin truncation. The null constraints here refer to forward limit ($t=0$) null constraints. We find that if the graviton is in some other representation than singlet, there is no allowed region.