117 research outputs found
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
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