Article

# Operator mixing in N=4 SYM: The Konishi anomaly revisited

Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, D-14476 Golm, Germany; Laboratoire d'Annecy-le-Vieux de Physique Théorique LAPTH, B.P. 110, F-74941 Annecy-le-Vieux, France11UMR 5108 associée à l'Université de Savoie.; Dipartimento di Fisica, Università di Roma “Tor Vergata”, INFN, Sezione di Roma “Tor Vergata”, Via della Ricerca Scientifica, I-00133 Roma, Italy

Nuclear Physics B (Impact Factor: 4.33). 01/2005; DOI: 10.1016/j.nuclphysb.2005.06.005 Source: arXiv

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**ABSTRACT:**The supersymmetry transformation relating the Konishi operator to its lowest descendant in the 10 of SU(4) is not manifest in the N=1 formulation of the theory but rather uses an equation of motion. On the classical level one finds one operator, the unintegrated chiral superpotential. In the quantum theory this term receives an admixture by a second operator, the Yang–Mills part of the Lagrangian. It has long been debated whether this “anomalous” contribution is affected by higher loop corrections. We present a first principles calculation at the second non-trivial order in perturbation theory using supersymmetric dimensional reduction as a regulator and renormalisation by Z-factors. Singular higher loop corrections to the renormalisation factor of the Yang–Mills term are required if the conformal properties of two-point functions are to be met. These singularities take the form determined in preceding work on rather general grounds. Moreover, we also find non-vanishing finite terms.The core part of the problem is the evaluation of a four-loop two-point correlator which is accomplished by the Laporta algorithm. Apart from several examples of the T1 topology with two lines of non-integer dimension we need the first few orders in the ϵ expansion of three master integrals. The approach is self-contained in that all the necessary information can be derived from the power counting finiteness of some integrals.Nuclear Physics B 02/2011; · 4.33 Impact Factor -
##### Article: Exact spectrum of planar N=4 supersymmetric Yang-Mills theory: Konishi dimension at any coupling.

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**ABSTRACT:**We compute the full dimension of the Konishi operator in planar N=4 super Yang-Mills theory for a wide range of couplings, from weak to strong coupling regime, and predict the subleading terms in its strong coupling asymptotics. For this purpose we solve numerically the integral form of the AdS/CFT Y-system equations for the exact energies of excited states proposed by us and A. Kozak.Physical Review Letters 05/2010; 104(21):211601. · 7.73 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We present results for the universal anomalous dimension \gamma_{uni}(j) of Wilson twist-2 operators in the N=4 Supersymmetric Yang-Mills theory in the first four orders of perturbation theory. Comment: 21 pages; to be published in "Subtleties in Quantum Field Theories (Lev Lipatov Festschrift)", D. Diakonov, ed., Gatchina, 201005/2010;

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