5 research outputs found
A non-integrable quench from AdS/dCFT
We study the matrix product state which appears as the boundary state of the
AdS/dCFT set-up where a probe D7 brane wraps two two-spheres stabilized by
fluxes. The matrix product state plays a dual role, on one hand acting as a
tool for computing one-point functions in a domain wall version of N=4 SYM and
on the other hand acting as the initial state in the study of quantum quenches
of the Heisenberg spin chain. We derive a number of selection rules for the
overlaps between the matrix product state and the eigenstates of the Heisenberg
spin chain and in particular demonstrate that the matrix product state does not
fulfill a recently proposed integrability criterion. Accordingly, we find that
the overlaps can not be expressed in the usual factorized determinant form.
Nevertheless, we derive some exact results for one-point functions of simple
operators and present a closed formula for one-point functions of more general
operators in the limit of large spin-chain length.Comment: 6 page
Two-point functions in AdS/dCFT and the boundary conformal bootstrap equations
We calculate the leading contributions to the connected two-point functions
of protected scalar operators in the defect version of N=4 SYM theory which is
dual to the D5-D3 probe-brane system with k units of background gauge field
flux. This involves several types of two-point functions which are vanishing in
the theory without the defect, such as two-point functions of operators of
unequal conformal dimension. We furthermore exploit the operator product
expansion (OPE) and the boundary operator expansion (BOE), which form the basis
of the boundary conformal bootstrap equations, to extract conformal data both
about the defect CFT and about N=4 SYM theory without the defect. From the
knowledge of the one- and two-point functions of the defect theory, we extract
certain structure constants of N=4 SYM theory using the (bulk) OPE and
constrain certain bulk-bulk-to-boundary couplings using the BOE. The extraction
of the former relies on a non-trivial, polynomial k dependence of the one-point
functions, which we explicitly demonstrate. In addition, it requires the
knowledge of the one-point functions of SU descendant operators, which we
likewise explicitly determine.Comment: 34 pages, 2 figure