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On-Shell Methods for the Two-Loop Dilatation Operator and Finite Remainders

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arxiv 1504.06323 v2 pith:GGCU6SNV submitted 2015-04-23 hep-th hep-phmath-phmath.MP

classification hep-thhep-phmath-phmath.MP
keywords functionsremaindertwo-loopcorrespondingdilatationfactorsfiniteform
verification ladder T0 review T1 audit T2 compute T3 formal
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We compute the two-loop minimal form factors of all operators in the SU(2) sector of planar N=4 SYM theory via on-shell unitarity methods. From the UV divergence of this result, we obtain the two-loop dilatation operator in this sector. Furthermore, we calculate the corresponding finite remainder functions. Since the operators break the supersymmetry, the remainder functions do not have the property of uniform transcendentality. However, the leading transcendentality part turns out to be universal and is identical to the corresponding BPS expressions. The remainder functions are shown to satisfy linear relations which can be explained by Ward identities of form factors following from R-symmetry.

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