The complete one-loop dilatation operator of planar real beta-deformed N=4 SYM theory

Abstract

We determine the missing finite-size corrections to the asymptotic one-loop dilatation operator of the real $\beta$-deformed $\mathcal{N}=4$ SYM theory for the gauge groups $U(N)$ and $SU(N)$ in the 't Hooft limit. In the $SU(N)$ case, the absence of the $U(1)$ field components leads to a new kind of finite-size effect, which we call prewrapping. We classify which states are potentially affected by prewrapping at generic loop orders and comment on the necessity to include it into the integrability-based description. As a further result, we identify classes of $n$-point correlation functions which at all loop orders in the planar theory are given by the values of their undeformed counterparts. Finally, we determine the superconformal multiplet structure and one-loop anomalous dimensions of all single-trace states with classical scaling dimension ${\Delta }_0\le 4.5$.

Latex, feynmp, pstricks, 37 pages, 6 tables, v2: formulations improved, references added, typos corrected, v3: typos corrected, matches published version

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