Cutting through form factors and cross sections of non-protected operators in N=4 SYM

TY - JOUR

T1 - Cutting through form factors and cross sections of non-protected operators in N=4 SYM

AU - Nandan, Dhritiman

AU - Sieg, Christoph

AU - Wilhelm, Matthias

AU - Yang, Gang

PY - 2015/6/2

Y1 - 2015/6/2

N2 - Abstract: We study the form factors of the Konishi operator, the prime example of non-protected operators in N=4$$ \mathcal{N}=4 $$ SYM theory, via the on-shell unitarity method. Since the Konishi operator is not protected by supersymmetry, its form factors share many features with amplitudes in QCD, such as the occurrence of rational terms and of UV divergences that require renormalization. A subtle point is that this operator depends on the spacetime dimension. This requires a modification when calculating its form factors via the on-shell unitarity method. We derive a rigorous prescription that implements this modification to all loop orders and obtain the two-point form factor up to two-loop order and the three-point form factor to one-loop order. From these form factors, we construct an IR-finite cross-section-type quantity, namely the inclusive decay rate of the (off-shell) Konishi operator to any final (on-shell) state. Via the optical theorem, it is connected to the imaginary part of the two-point correlation function. We extract the Konishi anomalous dimension up to two-loop order from it.

AB - Abstract: We study the form factors of the Konishi operator, the prime example of non-protected operators in N=4$$ \mathcal{N}=4 $$ SYM theory, via the on-shell unitarity method. Since the Konishi operator is not protected by supersymmetry, its form factors share many features with amplitudes in QCD, such as the occurrence of rational terms and of UV divergences that require renormalization. A subtle point is that this operator depends on the spacetime dimension. This requires a modification when calculating its form factors via the on-shell unitarity method. We derive a rigorous prescription that implements this modification to all loop orders and obtain the two-point form factor up to two-loop order and the three-point form factor to one-loop order. From these form factors, we construct an IR-finite cross-section-type quantity, namely the inclusive decay rate of the (off-shell) Konishi operator to any final (on-shell) state. Via the optical theorem, it is connected to the imaginary part of the two-point correlation function. We extract the Konishi anomalous dimension up to two-loop order from it.

KW - hep-th

KW - hep-ph

U2 - 10.1007/JHEP06(2015)156

DO - 10.1007/JHEP06(2015)156

M3 - Journal article

SN - 1126-6708

VL - 2015

JO - Journal of High Energy Physics (Online)

JF - Journal of High Energy Physics (Online)

IS - 06

M1 - 156

ER -