TY - JOUR

T1 - A piece of cake

T2 - the ground-state energies in gamma_i-deformed N=4 SYM theory

AU - Fokken, Jan

AU - Sieg, Christoph

AU - Wilhelm, Matthias

PY - 2014/5/26

Y1 - 2014/5/26

N2 - In the non-supersymmetric gamma_i-deformed N=4 SYM theory, the scaling dimensions of the operators tr[Z^L] composed of L scalar fields Z receive finite-size wrapping and prewrapping corrections in the 't Hooft limit. In this paper, we calculate these scaling dimensions to leading wrapping order directly from Feynman diagrams. For L>=3, the result is proportional to the maximally transcendental `cake' integral. It matches with an earlier result obtained from the integrability-based Luescher corrections, TBA and Y-system equations. At L=2, where the integrability-based equations yield infinity, we find a finite rational result. This result is renormalization-scheme dependent due to the non-vanishing beta-function of an induced quartic scalar double-trace coupling, on which we have reported earlier. This explicitly shows that conformal invariance is broken - even in the 't Hooft limit.

AB - In the non-supersymmetric gamma_i-deformed N=4 SYM theory, the scaling dimensions of the operators tr[Z^L] composed of L scalar fields Z receive finite-size wrapping and prewrapping corrections in the 't Hooft limit. In this paper, we calculate these scaling dimensions to leading wrapping order directly from Feynman diagrams. For L>=3, the result is proportional to the maximally transcendental `cake' integral. It matches with an earlier result obtained from the integrability-based Luescher corrections, TBA and Y-system equations. At L=2, where the integrability-based equations yield infinity, we find a finite rational result. This result is renormalization-scheme dependent due to the non-vanishing beta-function of an induced quartic scalar double-trace coupling, on which we have reported earlier. This explicitly shows that conformal invariance is broken - even in the 't Hooft limit.

KW - hep-th

U2 - 10.1007/JHEP09(2014)078

DO - 10.1007/JHEP09(2014)078

M3 - Journal article

VL - 2014

JO - Journal of High Energy Physics (Online)

JF - Journal of High Energy Physics (Online)

SN - 1126-6708

IS - 09

M1 - 078

ER -