8 research outputs found
Asymptotic one-point functions in AdS/dCFT
We take the first step in extending the integrability approach to one-point
functions in AdS/dCFT to higher loop orders. More precisely, we argue that the
formula encoding all tree-level one-point functions of SU(2) operators in the
defect version of N=4 SYM theory, dual to the D5-D3 probe-brane system with
flux, has a natural asymptotic generalization to higher loop orders. The
asymptotic formula correctly encodes the information about the one-loop
correction to the one-point functions of non-protected operators once dressed
by a simple flux-dependent factor, as we demonstrate by an explicit computation
involving a novel object denoted as an amputated matrix product state.
Furthermore, when applied to the BMN vacuum state, the asymptotic formula gives
a result for the one-point function which in a certain double-scaling limit
agrees with that obtained in the dual string theory up to wrapping order.Comment: 6 pages; v2: statement about match up to wrapping order clarified,
version accepted for publicatio
A quantum check of AdS/dCFT
We build the framework for performing loop computations in the defect version
of N=4 super Yang-Mills theory which is dual to the probe D5-D3 brane system
with background gauge-field flux. In this dCFT, a codimension-one defect
separates two regions of space-time with different ranks of the gauge group and
three of the scalar fields acquire non-vanishing and space-time-dependent
vacuum expectation values. The latter leads to a highly non-trivial mass mixing
problem between different colour and flavour components, which we solve using
fuzzy-sphere coordinates. Furthermore, the resulting space-time dependence of
the theory's Minkowski space propagators is handled by reformulating these as
propagators in an effective AdS4. Subsequently, we initiate the computation of
quantum corrections. The one-loop correction to the one-point function of any
local gauge-invariant scalar operator is shown to receive contributions from
only two Feynman diagrams. We regulate these diagrams using dimensional
reduction, finding that one of the two diagrams vanishes, and discuss the
procedure for calculating the one-point function of a generic operator from the
SU(2) subsector. Finally, we explicitly evaluate the one-loop correction to the
one-point function of the BPS vacuum state, finding perfect agreement with an
earlier string-theory prediction. This constitutes a highly non-trivial test of
the gauge-gravity duality in a situation where both supersymmetry and conformal
symmetry are partially broken.Comment: 41 pages; v2: typos corrected, one comment added, matches published
versio
One-Loop One-Point Functions in Gauge-Gravity Dualities with Defects
We initiate the calculation of loop corrections to correlation functions in
4D defect CFTs. More precisely, we consider N=4 SYM with a codimension-one
defect separating two regions of space, x_3>0 and x_3<0, where the gauge group
is SU(N) and SU(N-k), respectively. This set-up is made possible by some of the
real scalar fields acquiring a non-vanishing and x_3-dependent vacuum
expectation value for x_3>0. The holographic dual is the D3-D5 probe brane
system where the D5 brane geometry is AdS_4 x S^2 and a background gauge field
has k units of flux through the S^2. We diagonalise the mass matrix of the
defect CFT making use of fuzzy-sphere coordinates and we handle the
x_3-dependence of the mass terms in the 4D Minkowski space propagators by
reformulating these as standard massive AdS_4 propagators. Furthermore, we show
that only two Feynman diagrams contribute to the one-loop correction to the
one-point function of any single-trace operator and we explicitly calculate
this correction in the planar limit for the simplest chiral primary. The result
of this calculation is compared to an earlier string-theory computation in a
certain double-scaling limit, finding perfect agreement. Finally, we discuss
how to generalise our calculation to any single-trace operator, to finite N and
to other types of observables such as Wilson loops.Comment: 7 pages, 3 figures, 1 table; v2: shortened, regularisation changed,
match with string theory, v3: typo in table corrected, title changed to match
journal versio
One-point functions in AdS/dCFT from matrix product states
One-point functions of certain non-protected scalar operators in the defect CFT dual to the D3-D5 probe brane system with k units of world volume flux can be expressed as overlaps between Bethe eigenstates of the Heisenberg spin chain and a matrix product state. We present a closed expression of determinant form for these one-point functions, valid for any value of k. The determinant formula factorizes into the k = 2 result times a k-dependent pre-factor. Making use of the transfer matrix of the Heisenberg spin chain we recursively relate the matrix product state for higher even and odd k to the matrix product state for k = 2 and k = 3 respectively. We furthermore find evidence that the matrix product states for k = 2 and k = 3 are related via a ratio of Baxter's Q-operators. The general k formula has an interesting thermodynamical limit involving a non-trivial scaling of k, which indicates that the match between string and field theory one-point functions found for chiral primaries might be tested for non-protected operators as well. We revisit the string computation for chiral primaries and discuss how it can be extended to non-protected operators