We investigate the solution space of the beta-deformed Quantum Spectral Curve by studying a sample of solutions corresponding to single-trace operators that in the undeformed theory belong to the Konishi multiplet. We discuss how to set the precise boundary conditions for the leading Q-system for a given state, how to solve it, and how to build perturbative corrections to the P mu-system. We confirm and add several loop orders to known results in the literature.

We clarify the relationship between probe analysis of the supergravity dual and the large-N solution of the localization matrix model for the planar N=2 super-Yang-Mills theory. A formalism inspired by supergravity allows us to systematically solve the matrix model at strong coupling. Quite surprisingly, we find that quantum phase transitions, known to occur in the N=2 theory, start to be visible at the third order of the strong-coupling expansion and thus constitute a perturbative phenomenon on the string worldsheet.

We generalize earlier results on one-point functions in N = 4 SYM with a codimension one defect, dual to the D3-D5-brane setup in type IIB string theory on AdS(5)xS(5), to a similar setup in the beta-deformed version of the theory. The treelevel vacuum expectation values of single-trace operators in the two-scalar-subsector are expressed as overlaps between a matrix product state (MPS) and Bethe states in the corresponding twisted spin-chain picture. We comment on the properties of this MPS and present the simplest analytical overlaps and their behavior in a certain limit (of large k). Importantly, we note that the deformation alters earlier interpretations of the MPS as an integrable boundary state, seemingly obstructing simpli fi cations of the overlaps analogous to the compact determinant formula found in the non-deformed theory. The results are supplemented with some supporting numerical results for operators of length eight with four excitations.

We consider a particular set of two-point functions in the setting of N=4SYM with a defect, dual to the fuzzy-funnel solution for the probe D5-D3-brane system. The two-point functions in focus involve a single trace operator in the SU(2)-subsector of arbitrary length and a length-two operator built out of any scalars. By interpreting the contractions as a spin-chain operator, simple expressions were found for the leading contribution to the two-point functions, mapping them to earlier known formulas for the one-point functions in this setting.