14 research outputs found
Disturbance in weak measurements and the difference between quantum and classical weak values
The role of measurement induced disturbance in weak measurements is of
central importance for the interpretation of the weak value. Uncontrolled
disturbance can interfere with the postselection process and make the weak
value dependent on the details of the measurement process. Here we develop the
concept of a generalized weak measurement for classical and quantum mechanics.
The two cases appear remarkably similar, but we point out some important
differences. A priori it is not clear what the correct notion of disturbance
should be in the context of weak measurements. We consider three different
notions and get three different results: (1) For a `strong' definition of
disturbance, we find that weak measurements are disturbing. (2) For a weaker
definition we find that a general class of weak measurements are
non-disturbing, but that one gets weak values which depend on the measurement
process. (3) Finally, with respect to an operational definition of the `degree
of disturbance', we find that the AAV weak measurements are the least
disturbing, but that the disturbance is always non-zero.Comment: v2: Many minor changes. Additional references. One additional
appendix and another appendix rewritte
The One-Loop Spectral Problem of Strongly Twisted =4 Super Yang-Mills Theory
We investigate the one-loop spectral problem of -twisted, planar
=4 Super Yang-Mills theory in the double-scaling limit of
infinite, imaginary twist angle and vanishing Yang-Mills coupling constant.
This non-unitary model has recently been argued to be a simpler version of
full-fledged planar =4 SYM, while preserving the latter model's
conformality and integrability. We are able to derive for a number of sectors
one-loop Bethe equations that allow finding anomalous dimensions for various
subsets of diagonalizable operators. However, the non-unitarity of these
deformed models results in a large number of non-diagonalizable operators,
whose mixing is described by a very complicated structure of non-diagonalizable
Jordan blocks of arbitrarily large size and with a priori unknown generalized
eigenvalues. The description of these blocks by methods of integrability
remains unknown.Comment: 33 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
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
One-loop Wilson loops and the particle-interface potential in AdS/dCFT
We initiate the calculation of quantum corrections to Wilson loops in a class of four-dimensional defect conformal field theories with vacuum expectation values based on N=4 super Yang–Mills theory. Concretely, we consider an infinite straight Wilson line, obtaining explicit results for the one-loop correction to its expectation value in the large-N limit. This allows us to extract the particle-interface potential of the theory. In a further double-scaling limit, we compare our results to those of a previous calculation in the dual string-theory set-up consisting of a D5-D3 probe-brane system with flux, and we find perfect agreement
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