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  • Open Access

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

Yu-tin Huang1,2,3,*, Henrik Johansson4,†, Michele Santagata1,4,‡, and Congkao Wen5,§

  • *Contact author: yutin@phys.ntu.edu.tw
  • †Contact author: henrik.johansson@physics.uu.se
  • ‡Contact author: michele.santagata@physics.uu.se
  • §Contact author: c.wen@qmul.ac.uk
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Phys. Rev. Lett. 136, 111601 – Published 19 March, 2026

DOI: https://doi.org/10.1103/p9mw-gx9w

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 nT tensor and nV vector multiplets, respectively. We find that the one-loop amplitudes are finite for nT=21 and nV=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.

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References (41)

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Phys. Rev. Lett. 136, 111601– Published 19 March, 2026
  • Received 18 November 2025
  • Revised 23 December 2025
  • Accepted 4 February 2026
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