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Surprising One-Loop Finiteness of 6D Half-Maximal Supergravities.

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Higher-dimensional supergravities unexpectedly achieve one-loop finiteness, resolving ultraviolet divergences. This surprising result for gravity coupled to matter challenges established theories and suggests connections to string theory compactifications.

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Area of Science:

  • Theoretical Physics
  • Quantum Gravity
  • String Theory

Background:

  • Gravity coupled to matter typically shows ultraviolet divergences at one loop in four dimensions, regardless of supersymmetry.
  • Previous studies in the 1970s confirmed divergences in four-matter one-loop amplitudes of half-maximal supergravity theories.

Purpose of the Study:

  • To investigate the ultraviolet behavior of supergravities uplifted to higher dimensions.
  • To determine if half-maximal supergravity theories can exhibit one-loop finiteness in six dimensions.
  • To explore the implications of any observed finiteness for fundamental physics.

Main Methods:

  • Analysis of ultraviolet properties of specific amplitudes in six-dimensional supergravities.
  • Calculation of four-matter and two-matter two-graviton one-loop amplitudes.
  • Examination of theories with N=(2,0) and N=(1,1) supersymmetry coupled to tensor and vector multiplets.

Main Results:

  • One-loop amplitudes in six-dimensional N=(2,0) and N=(1,1) supergravities were found to be finite for specific numbers of multiplets.
  • Finiteness was observed for n_{T}=21 tensor multiplets and n_{V}=20 vector multiplets.
  • These finite results were obtained despite the existence of symmetry-preserving counterterms.

Conclusions:

  • Half-maximal supergravity theories can become one-loop finite when extended to higher dimensions.
  • The observed finiteness suggests a deeper connection to string theory, specifically type II string theories compactified on K3.
  • The results challenge conventional expectations regarding ultraviolet divergences in quantum gravity.