期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 6, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP06(2011)100
关键词
Supersymmetric gauge theory; Conformal and W Symmetry; Field Theories in Higher Dimensions
资金
- US Department of Energy [DE-AC02-76SF00515]
We provide an analytic formula for the (rescaled) one-loop six-dimensional scalar hexagon integral (Phi) over tilde (6) with all external legs massless, in terms of classical polylogarithms. We show that this integral is closely connected to two integrals appearing in one- and two-loop amplitudes in planar N = 4 super-Yang-Mills theory, Omega((1)) and Omega((2)). The derivative of Omega((2)) with respect to one of the conformal invariants yields (Phi) over tilde (6), while another first-order differential operator applied to (Phi) over tilde (6) yields Omega((1)). We also introduce some kinematic variables that rationalize the arguments of the polylogarithms, making it easy to verify the latter differential equation. We also give a further example of a six-dimensional integral relevant for amplitudes in N = 4 super-Yang-Mills theory.
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