Amplitudes, Form Factors and the Dilatation Operator in N=4 SYM Theory
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Amplitudes, Form Factors and the Dilatation Operator in N=4 SYM Theory. / Wilhelm, Matthias.
In: Journal of High Energy Physics (Online), Vol. 2014, No. 02, 149, 2015.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Amplitudes, Form Factors and the Dilatation Operator in N=4 SYM Theory
AU - Wilhelm, Matthias
PY - 2015
Y1 - 2015
N2 - We study the form factor of a generic gauge-invariant local composite operator in $\mathcal{N}=4$ SYM theory. At tree level and for a minimal number of external on-shell super fields, we find that the form factor precisely yields the spin-chain picture of integrability in the language of scattering amplitudes. Moreover, we compute the cut-constructible part of the one-loop correction to this minimal form factor via generalised unitarity. From its UV divergence, we obtain the complete one-loop dilatation operator of $\mathcal{N}=4$ SYM theory. Thus, we provide a field-theoretic derivation of a relation between the one-loop dilatation operator and the four-point tree-level amplitude which was observed earlier. We also comment on the implications of our findings in the context of integrability.
AB - We study the form factor of a generic gauge-invariant local composite operator in $\mathcal{N}=4$ SYM theory. At tree level and for a minimal number of external on-shell super fields, we find that the form factor precisely yields the spin-chain picture of integrability in the language of scattering amplitudes. Moreover, we compute the cut-constructible part of the one-loop correction to this minimal form factor via generalised unitarity. From its UV divergence, we obtain the complete one-loop dilatation operator of $\mathcal{N}=4$ SYM theory. Thus, we provide a field-theoretic derivation of a relation between the one-loop dilatation operator and the four-point tree-level amplitude which was observed earlier. We also comment on the implications of our findings in the context of integrability.
KW - hep-th
KW - hep-ph
U2 - 10.1007/JHEP02(2015)149
DO - 10.1007/JHEP02(2015)149
M3 - Journal article
VL - 2014
JO - Journal of High Energy Physics (Online)
JF - Journal of High Energy Physics (Online)
SN - 1126-6708
IS - 02
M1 - 149
ER -
ID: 227489048