We construct an efficient Monte Carlo algorithm that overcomes the severe signal-to-noise ratio problems and helps us to accurately compute the conformal dimensions of large-$Q$ fields at the Wilson-Fisher fixed point in the $O(2)$ universality class. Using it we verify a recent proposal that conformal dimensions of strongly coupled conformal field theories with a global $U(1)$ charge can be obtained via a series expansion in the inverse charge $1/Q$. We find that the conformal dimensions of the lowest operator with a fixed charge $Q$ are almost entirely determined by the first few terms in the series.

We study some examples of Yang-Baxter deformations of the $AdS_5 \times S^5$ superstring with non-Abelian classical $r$-matrices which satisfy the homogeneous classical Yang-Baxter equation (CYBE). All of the resulting backgrounds satisfy the generalized type IIB supergravity equations. For some of them, we derive “T-dualized” backgrounds and show that these satisfy the usual type IIB supergravity equations. Remarkably, some of them are locally identical to undeformed $AdS_5 \times S^5$.

We calculate the anomalous dimensions of operators with large global charge $J$ in certain strongly coupled conformal field theories in three dimensions, such as the $O(2)$ model and the supersymmetric fixed point with a single chiral superfield and a $W = \Phi^3$ superpotential. Working in a $1/J$ expansion, we find that the large-$J$ sector of both examples is controlled by a conformally invariant effective Lagrangian for a Goldstone boson of the global symmetry. For both these theories, we find that the lowest state with charge $J$ is always a scalar operator whose dimension is $ \Delta(J) = a J^{3 / 2} + b J^{1 / 2} - 0.093$, up to corrections that vanish at large $J$.