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

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Abstract
In four dimensions, it has long been established that gravity coupled to matter exhibits ultraviolet divergences at one loop, irrespective of supersymmetry. Notably, the four-matter one-loop amplitudes of half-maximal supergravity coupled to Maxwell multiplets were shown in the 1970s to be divergent. Surprisingly, we demonstrate in this Letter that half-maximal theories can nevertheless become one-loop finite when uplifted to higher dimensions, contrary to naive expectations. Specifically, we study the ultraviolet properties of the four-matter and two-matter two-graviton amplitudes in six-dimensional N = ( 2 , 0 ) and N = ( 1 , 1 ) supergravities, coupled to n T tensor and n V vector multiplets, respectively. We find that the one-loop amplitudes are finite for n T = 21 and n V = 20 . This finiteness is unexpected, as symmetry-preserving counterterms do exist. Interestingly, both values exactly correspond to low-energy limits of type II string theories compactified on K3, which hints at possible origins to the surprising cancellations.
Funding Information
  • National Science and Technology Council (112-2628-M-002-003-MY3)
  • National Science and Technology Council (114-2923-M-002-011-MY5)
  • Knut och Alice Wallenbergs Stiftelse (KAW 2018.0116)
  • Knut och Alice Wallenbergs Stiftelse (KAW 2018.0162)
  • European Commission
  • European Research Council (101167287)
  • Royal Society (URF\R\221015)
  • Science and Technology Facilities Council (ST\T000686\1)

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