Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2014-07

Jan Fokken, Christoph Sieg, Matthias Wilhelm


A piece of cake: the ground-state energies in \gamma_i-deformed N=4 SYM theory at leading wrapping order.



Abstract: In the non-supersymmetric γi-deformed N = 4 SYM theory, the scaling dimensions of the operators tr[ZL] 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 L¨uscher 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 β-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.


Keywords. PACS: 11.15.-q; 11.30.Pb; 11.25.Tq
Keywords: Super-Yang-Mills; Anomalous dimensions; Integrability;


Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), P-2014-07


21 pp.