The complete one-loop dilatation operator of planar real β-deformed N$$ \mathcal{N} $$ = 4 SYM theory

A bstractWe determine the missing finite-size corrections to the asymptotic one-loop dilatation operator of the real β-deformed N$$ \mathcal{N} $$ = 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 Δ0 ≤ 4.5.