We study the ratio of pairs of adjacent correlators of Coulomb-branch operators in SU(2) N=2 SQCD with four flavors within the framework of the Large Quantum Number Expansion. Capitalizing on the order-by-order S-duality invariance of the large-R-charge expansion we compute ab initio the dependence of the leading large-J behavior on the marginal coupling τ and we find excellent agreement with numerical estimates from localization.

We study the $O(4)$ Wilson–Fisher fixed point in $2+1$ dimensions in fixed large-charge sectors identified by products of two spin-$j$ representations $(j_L,j_R)$. Using effective field theory we derive a formula for the conformal dimensions $D(j_L, j_R)$ of the leading operator in terms of two constants, $c_{ 3 / 2}$ and $c_{ 1 / 2}$, when the sum $j_L + j_R$ is much larger than the difference $|j_L-j_R|$. We compute $D(j_L,j_R)$ when $j_L= j_R$ with Monte Carlo calculations in a discrete formulation of the $O(4)$ lattice field theory, and show excellent agreement with the predicted formula and estimate $c_{ 3 / 2}=1.068(4)$ and $c_{ 1 / 2}=0.083(3)$.

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 $J$.