Analytic result for the two-loop six-point NMHV amplitude in $ \mathcal{N} = {4} $ super Yang-Mills theory
Analytic result for the two-loop six-point NMHV amplitude in $ \mathcal{N} = {4} $ super Yang-Mills theory
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$ mathcal{N} = {4} $ super Yang-Mills 理论中二环六点 NMHV 振幅的解析结果
DOI：
10.1007/jhep01(2012)024
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发表时间：
2011
影响因子：
5.4
通讯作者：
J. Henn
中科院分区：
文献类型：
--
作者：
L. Dixon;J. Drummond;J. Henn
A bstractWe provide a simple analytic formula for the two-loop six-point ratio function of planar $ \mathcal{N} = {4} $ super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behaviour, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral Ω(2), also plays a key role in a new representa- tion of the remainder function $ {\text{R}}_6^{{(2)}} $ in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) × (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) × (parity even) part. The second non-polylogarithmic function, the loop integral $ \widetilde{\Omega } $(2), characterizes this sector. Both Ω(2) and $ \widetilde{\Omega } $(2) can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.
A bstractWe provide a simple analytic formula for the two-loop six-point ratio function of planar $ \mathcal{N} = {4} $ super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behaviour, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral Ω(2), also plays a key role in a new representa- tion of the remainder function $ {\text{R}}_6^{{(2)}} $ in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) × (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) × (parity even) part. The second non-polylogarithmic function, the loop integral $ \widetilde{\Omega } $(2), characterizes this sector. Both Ω(2) and $ \widetilde{\Omega } $(2) can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.
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影响因子：
5.4
作者：
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通讯作者：
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影响因子：
5.4
作者：
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通讯作者：
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影响因子：
5.4
作者：
L. Mason;David Skinner
通讯作者：
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影响因子：
5.4
作者：
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通讯作者：
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