[en] In this review we discuss recent advances in the computation of one-point functions in defect conformal field theories with holographic duals. We briefly review the appearance of integrable spin chains in super Yang–Mills theory and reformulate the problem of computing one-point functions to determining overlaps between Bethe states and a matrix product State. We will then demonstrate how these overlaps can be computed by determinant formulas. This work is based on lectures given at the Young Researchers Integrability School and Workshop 2018. (topical review)

[en] In this paper we work out the RTT realization for the Yangian algebra of the Hubbard model and anti-de Sitter/conformal field theory correspondence. We find that this Yangian algebra is of a non-standard type in which the levels of the Yangian mix. The crucial feature that allows this is a braiding factor that deforms the coproduct and generates the central extensions of the underlying sl(2|2) Lie algebra. In our RTT realization we have also been able to incorporate the so-called secret symmetry and we were able to extend it to higher Yangian levels. Finally, we discuss the center of the Yangian and the automorphisms related to crossing symmetry. (paper)

[en] We classify all fundamental integrable spin chains with two-dimensional (2D) local Hilbert space which have regular R-matrices of difference form. This means that the R-matrix underlying the integrable structures is of the form and reduces to the permutation operator at some particular point. We find a total of 14 independent solutions, eight of which correspond to well-known eight or lower vertex models. The remaining six models appear to be new and some have peculiar properties such as not being diagonalizable or being nilpotent. Furthermore, for even R-matrices, we find a bijection between solutions of the Yang–Baxter equation (YBE) and the graded YBE which extends our results to the graded 2D case. (paper)

[en] In this paper we find new integrable one-dimensional lattice models of electrons. We describe all such nearest-neighbour integrable models with $\mathfrak{s}\mathfrak{u}\left(2\right)\times <!--\; ??\; -->\mathfrak{s}\mathfrak{u}\left(2\right)$ symmetry by classifying solutions of the Yang–Baxter equation following the procedure first introduced in [1]. We find 12 R-matrices of difference form, some of which can be related to known models such as the XXX spin chain and the free Hubbard model, and some are new models. In addition, integrable generalizations of the Hubbard model are found by keeping the kinetic term of the Hamiltonian and adding all terms which preserve fermion number. We find that most of the new models cannot be diagonalized using the standard nested Bethe Ansatz. (paper)

[en] We study tree level one-point functions of non-protected scalar operators in the defect CFT, based on $\mathcal{N}=4$ SYM, which is dual to the SO(5) symmetric D3–D7 probe brane system with non-vanishing instanton number. Whereas symmetries prevent operators from the SU(2) and SU(3) sub-sectors from having non-vanishing one-point functions, more general scalar conformal operators, which in particular constitute Bethe eigenstates of the integrable SO(6) spin chain, are allowed to have non-trivial one-point functions. For a series of operators with a small number of excitations we find closed expressions in terms of Bethe roots for these one-point functions, valid for any value of the instanton number. In addition, we present some numerical results for operators with more excitations. (paper)

[en] Starting with a discussion of the general applicability of the simplified mirror thermodynamic Bethe ansatz (TBA) equations to simple deformations of the AdS₅ x S⁵ superstring, we proceed to study a specific type of orbifold to which the undeformed simplified TBA equations directly apply. We then use this set of equations, as well as Luescher's approach, to determine the next-to-leading-order wrapping correction to the energy of what we call the orbifolded Konishi state and show that they perfectly agree. In addition we discuss wrapping corrections to the ground-state energy of the orbifolded model under consideration.

[en] We consider integrable deformations of the XXZ spin chain for periodic and open boundary conditions. In particular, we classify all long-range deformations and study their impact on the spectrum. As compared to the XXX case, we have the z-spin at our disposal, which induces two additional deformations: the short-range magnetic twist and a new long-range momentum-dependent twist. (paper)

[en] We find a new quantum affine symmetry of the S-matrix of the one-dimensional Hubbard chain. We show that this symmetry originates from the quantum affine superalgebra U_q(gl-hat(2|2)), and in the rational limit exactly reproduces the secret symmetry of the AdS/CFT worldsheet S-matrix. (paper)

[en] We consider boundary scattering for a semi-infinite one-dimensional deformed Hubbard chain with boundary conditions of the same type as for the Y = 0 giant graviton in the AdS/CFT correspondence. We show that the recently constructed quantum affine algebra of the deformed Hubbard chain has a co-ideal subalgebra which is consistent with the reflection (boundary Yang–Baxter) equation. We derive the corresponding reflection matrix and furthermore show that the aforementioned algebra in the rational limit specializes to the (generalized) twisted Yangian of the Y = 0 giant graviton. (paper)