Conformal anomaly of generalized form factors and finite loop integrals

Abstract

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 $\ell -$loop integral is a 2nd-order differential equation whose right-hand side is an $(\ell -1)-$loop integral. We show several examples, in particular the four-dimensional scalar double box.

36 pages, 9 figures; reference added, typos corrected

References in corpus (6)

• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Amplitudes and Spinor-Helicity in Six Dimensions
• The Elliptic Double-Box Integral: Massless Amplitudes Beyond Polylogarithms
• Exacting N=4 Superconformal Symmetry
• New differential equations for on-shell loop integrals
• Correlation functions of local composite operators from generalized unitarity

Cited by in corpus (20)

• The Elliptic Double-Box Integral: Massless Amplitudes Beyond Polylogarithms
• Analytic form of the full two-loop five-gluon all-plus helicity amplitude
• Yangian Bootstrap for Conformal Feynman Integrals
• The elliptic double box and symbology beyond polylogarithms
• Implications of nonplanar dual conformal symmetry
• The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
• Amplitudes from superconformal Ward identities
• Yangian Bootstrap for Massive Feynman Integrals
• Conformal Invariance of the One-Loop All-Plus Helicity Scattering Amplitudes
• Bootstrapping elliptic Feynman integrals using Schubert analysis
• Cutting the traintracks: Cauchy, Schubert and Calabi-Yau
• The Two-Loop Remainder Function for Eight and Nine Particles
• One-loop hexagon integral to higher orders in the dimensional regulator
• Exact scattering amplitudes in conformal fishnet theory
• Integrability for Feynman Integrals
• Twistor fishnets
• Amplitudes from anomalous superconformal symmetry
• Amplitudes in fishnet theories in diverse dimensions and Box ladder diagrams
• Properties of the Conformal Yangian in Scalar and Gauge Field Theories
• Anomalous Ward identities for on-shell amplitudes at the conformal fixed point