Amplitudes, Form Factors and the Dilatation Operator in N=4 SYM Theory

TY - JOUR

T1 - Amplitudes, Form Factors and the Dilatation Operator in N=4 SYM Theory

AU - Wilhelm, Matthias

PY - 2015/2

Y1 - 2015/2

N2 - Abstract: We study the form factor of a generic gauge-invariant local composite operator in (Formula presented.) 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 (Formula presented.) 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 - Abstract: We study the form factor of a generic gauge-invariant local composite operator in (Formula presented.) 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 (Formula presented.) 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

SN - 1126-6708

VL - 2014

JO - Journal of High Energy Physics (Online)

JF - Journal of High Energy Physics (Online)

IS - 02

M1 - 149

ER -