One-Point Functions of Non-protected Operators in the SO(5) symmetric D3-D7 dCFT

We study tree level one-point functions of non-protected scalar operators in the defect CFT, based on 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.Comment: 15 pages, 1 figure. Minor corrections & update

AdS/dCFT one-point functions of the SU(3) sector

We propose a closed formula for the tree-level one-point functions of non-protected operators belonging to an SU(3) sub-sector of the defect CFT dual to the D3-D5 probe brane system with background gauge field flux, k, valid for k=2. The formula passes a number of non-trivial analytical and numerical tests. Our proposal is based on expressing the one-point functions as an overlap between a Bethe eigenstate of the SU(3) spin chain and a certain matrix product state, deriving various factorization properties of the Gaudin norm and performing explicit computations for shorter spin chains. As its SU(2) counterpart, the one-point function formula for the SU(3) sub-sector is of determinant type. We discuss the the differences with the SU(2) case and the challenges in extending the present formula beyond k=2.Comment: 6 page

Deformed one-loop amplitudes in N = 4 super-Yang-Mills theory

We investigate Yangian-invariant deformations of one-loop amplitudes in N = 4 super-Yang-Mills theory employing an algebraic representation of amplitudes. In this language, we reproduce the deformed massless box integral describing the deformed four-point one-loop amplitude and compare different realizations of said amplitude.Comment: 19 page

Fusion for the one-dimensional Hubbard model

We discuss a formulation of the fusion procedure for integrable models which is suitable for application to non-standard R-matrices. It allows for construction of bound state R-matrices for AdS/CFT worldsheet scattering or equivalently for the one-dimensional Hubbard model. We also discuss some peculiar cases that arise in these models.Comment: 17 page

One-point Functions in Defect CFT and Integrability

We calculate planar tree level one-point functions of non-protected operators in the defect conformal field theory dual to the D3-D5 brane system with k units of the world volume flux. Working in the operator basis of Bethe eigenstates of the Heisenberg XXX_{1/2} spin chain we express the one-point functions as overlaps of these eigenstates with a matrix product state. For k=2 we obtain a closed expression of determinant form for any number of excitations, and in the case of half-filling we find a relation with the N\'eel state. In addition, we present a number of results for the limiting case of infinite k.Comment: 31 pages, 3 figures; v2: references adde

The S-matrix of the AdS5 x S5 superstring

In this article we review the world-sheet scattering theory of strings on AdS 5 x S5. The asymptotic spectrum of this world-sheet theory contains both fundamental particles and bound states of the latter. We explicitly derive the S-matrix that describes scattering of arbitrary bound states. The key feature that enables this derivation is the so-called Yangian symmetry which is related to the centrally extended su(2|2) superalgebra. Subsequently, we study the universal algebraic properties of the found S-matrix. As in many integrable models, the S-matrix plays a key role in the determination of the energy spectrum. In this context, we employ the Bethe ansatz approach to compute the large volume energy spectrum of string bound states.Comment: Based on PhD thesis, 177 page

A dictionary between R-operators, on-shell graphs and Yangian algebras

We translate between different formulations of Yangian invariants relevant for the computation of tree-level scattering amplitudes in N=4 super-Yang--Mills theory. While the R-operator formulation allows to relate scattering amplitudes to structures well known from integrability, it can equally well be connected to the permutations encoded by on-shell graphs.Comment: 44 pages; replaced with published versio