On-shell methods for the two-loop dilatation operator and finite remainders

Florian Loebbert; Dhritiman Nandan; Christoph Sieg; Matthias Wilhelm; Gang Yang

doi:10.1007/JHEP10(2015)012

On-shell methods for the two-loop dilatation operator and finite remainders

Florian Loebbert, Dhritiman Nandan^*, Christoph Sieg, Matthias Wilhelm, Gang Yang

^*Corresponding author for this work

35 Citations (Scopus)

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Abstract

Abstract: We compute the two-loop minimal form factors of all operators in the SU(2) sector of planar N=4$$ \mathcal{N}=4 $$ SYM theory via on-shell unitarity methods. From the UV diver-gence 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 transcen-dentality. However, the leading transcendentality part turns out to be universal and is identical to the corresponding BPS expression. The remainder functions are shown to satisfy linear relations which can be explained by Ward identities of form factors following from R-symmetry.

Original language	English
Article number	12
Journal	Journal of High Energy Physics
Volume	2015
Issue number	10
Number of pages	24
ISSN	1126-6708
DOIs	https://doi.org/10.1007/JHEP10(2015)012
Publication status	Published - 1 Oct 2015
Externally published	Yes

Keywords

Integrable Field Theories
Scattering Amplitudes

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abstract = "Abstract: We compute the two-loop minimal form factors of all operators in the SU(2) sector of planar N=4$$ \mathcal{N}=4 $$ SYM theory via on-shell unitarity methods. From the UV diver-gence 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 transcen-dentality. However, the leading transcendentality part turns out to be universal and is identical to the corresponding BPS expression. 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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T1 - On-shell methods for the two-loop dilatation operator and finite remainders

AU - Loebbert, Florian

AU - Nandan, Dhritiman

AU - Sieg, Christoph

AU - Wilhelm, Matthias

AU - Yang, Gang

PY - 2015/10/1

Y1 - 2015/10/1

N2 - Abstract: We compute the two-loop minimal form factors of all operators in the SU(2) sector of planar N=4$$ \mathcal{N}=4 $$ SYM theory via on-shell unitarity methods. From the UV diver-gence 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 transcen-dentality. However, the leading transcendentality part turns out to be universal and is identical to the corresponding BPS expression. The remainder functions are shown to satisfy linear relations which can be explained by Ward identities of form factors following from R-symmetry.

AB - Abstract: We compute the two-loop minimal form factors of all operators in the SU(2) sector of planar N=4$$ \mathcal{N}=4 $$ SYM theory via on-shell unitarity methods. From the UV diver-gence 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 transcen-dentality. However, the leading transcendentality part turns out to be universal and is identical to the corresponding BPS expression. The remainder functions are shown to satisfy linear relations which can be explained by Ward identities of form factors following from R-symmetry.

KW - Integrable Field Theories

KW - Scattering Amplitudes

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DO - 10.1007/JHEP10(2015)012

M3 - Journal article

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VL - 2015

JO - Journal of High Energy Physics (Online)

JF - Journal of High Energy Physics (Online)

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ER -

On-shell methods for the two-loop dilatation operator and finite remainders

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