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JHEP 07, 101 (2026)

How gluon leading singularities discover curves on surfaces

Sérgio Carrôlo, Carolina Figueiredo

  • Scattering Amplitudes
  • Leading Singularities
  • Surfaceology
arXiv:2512.17019 INSPIRE
Eq. (5.4) of the paper: closed curves on a non-planar fat graph. Only the curve homotopic to an internal boundary (purely left-turning) has exponent 1 − D; the others have −D.
Eq. (5.4) of the paper: closed curves on a non-planar fat graph. Only the curve homotopic to an internal boundary (purely left-turning) has exponent 1 − D; the others have −D.

We show that by gluing three-gluon amplitudes in QFT, we rediscover the combinatorial structure of curves on surfaces provided by surfaceology. Using some nice graphical arguments we can fix the expression for the exponents of closed curves.