Conformal anomaly of generalized form factors and finite loop integrals

  • Dmitry Chicherin
  • Emery Sokatchev
Open Access
Regular Article - Theoretical Physics


We reveal a new mechanism of conformal symmetry breaking at Born level. It occurs in generalized form factors with several local operators and an on-shell state of massless particles. The effect is due to hidden singularities on collinear configurations of the momenta. This conformal anomaly is different from the holomorphic anomaly of amplitudes. We present a number of examples in four and six dimensions. We find an application of the new conformal anomaly to finite loop momentum integrals with one or more massless legs. The collinear region around a massless leg creates a contact anomaly, made visible by the loop integration. The anomalous conformal Ward identity for an ℓ−loop integral is a 2nd-order differential equation whose right-hand side is an (ℓ − 1)−loop integral. It could serve as a new useful tool to find/test analytic expressions for conformal integrals. We illustrate this point with several examples of known integrals. We propose a new differential equation for the four-dimensional scalar double box.


Anomalies in Field and String Theories Conformal and W Symmetry Conformal Field Theory Scattering Amplitudes 


Open Access

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.PRISMA Cluster of ExcellenceJohannes Gutenberg UniversityMainzGermany
  2. 2.LAPTh, Université Savoie Mont Blanc, CNRS, B.P. 110Annecy-le-VieuxFrance
  3. 3.Theoretical Physics DepartmentCERNGeneva 23Switzerland

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