86,444 research outputs found
Line operators from M-branes on compact Riemann surfaces
In this paper, we determine the charge lattice of mutually local Wilson and
't Hooft line operators for class S theories living on M5-branes wrapped on
compact Riemann surfaces. The main ingredients of our analysis are the
fundamental group of the N-cover of the Riemann surface, and a quantum
constraint on the six-dimensional theory. This latter plays a central role in
excluding some of the possible lattices and imposing consistency conditions on
the charges. This construction gives a geometric explanation for the mutual
locality among the lines, fixing their charge lattice and the structure of the
four-dimensional gauge group.Comment: 17 pages, 8 figure
Exploring the S-Matrix of Massless Particles
We use the recently proposed generalised on-shell representation for
scattering amplitudes and a consistency test to explore the space of tree-level
consistent couplings in four-dimensional Minkowski spacetime. The extension of
the constructible notion implied by the generalised on-shell representation,
i.e. the possibility to reconstruct at tree level all the scattering amplitudes
from the three-particle ones, together with the imposition of the consistency
conditions at four-particle level, allow to rediscover all the known theories
and their algebra structure, if any. Interestingly, this analysis seems to
leave room for high-spin couplings, provided that at least the requirement of
locality is weakened. We do not claim to have found tree-level consistent
high-spin theories, but rather that our methods show signatures of them and
very likely, with a suitable modification, they can be a good framework to
perform a systematic search.Comment: 44 pages, 1 figur
The relation between degrees of belief and binary beliefs: A general impossibility theorem
Agents are often assumed to have degrees of belief (“credences”) and also binary beliefs (“beliefs simpliciter”). How are these related to each other? A much-discussed answer asserts that it is rational to believe a proposition if and only if one has a high enough degree of belief in it. But this answer runs into the “lottery paradox”: the set of believed propositions may violate the key rationality conditions of consistency and deductive closure. In earlier work, we showed that this problem generalizes: there exists no local function from degrees of belief to binary beliefs that satisfies some minimal conditions of rationality and non-triviality. “Locality” means that the binary belief in each proposition depends only on the degree of belief in that proposition, not on the degrees of belief in others. One might think that the impossibility can be avoided by dropping the assumption that binary beliefs are a function of degrees of belief. We prove that, even if we drop the “functionality” restriction, there still exists no local relation between degrees of belief and binary beliefs that satisfies some minimal conditions. Thus functionality is not the source of the impossibility; its source is the condition of locality. If there is any non-trivial relation between degrees of belief and binary beliefs at all, it must be a “holistic” one. We explore several concrete forms this “holistic” relation could take
General fixed points of quasi-local frustration-free quantum semigroups: from invariance to stabilization
We investigate under which conditions a mixed state on a finite-dimensional
multipartite quantum system may be the unique, globally stable fixed point of
frustration-free semigroup dynamics subject to specified quasi-locality
constraints. Our central result is a linear-algebraic necessary and sufficient
condition for a generic (full-rank) target state to be frustration-free
quasi-locally stabilizable, along with an explicit procedure for constructing
Markovian dynamics that achieve stabilization. If the target state is not
full-rank, we establish sufficiency under an additional condition, which is
naturally motivated by consistency with pure-state stabilization results yet
provably not necessary in general. Several applications are discussed, of
relevance to both dissipative quantum engineering and information processing,
and non-equilibrium quantum statistical mechanics. In particular, we show that
a large class of graph product states (including arbitrary thermal graph
states) as well as Gibbs states of commuting Hamiltonians are frustration-free
stabilizable relative to natural quasi-locality constraints. Likewise, we
provide explicit examples of non-commuting Gibbs states and non-trivially
entangled mixed states that are stabilizable despite the lack of an underlying
commuting structure, albeit scalability to arbitrary system size remains in
this case an open question.Comment: 44 pages, main results are improved, several proofs are more
streamlined, application section is refine
Holography from Conformal Field Theory
The locality of bulk physics at distances below the AdS length is one of the
remarkable aspects of AdS/CFT duality, and one of the least tested. It requires
that the AdS radius be large compared to the Planck length and the string
length. In the CFT this implies a large-N expansion and a gap in the spectum of
anomalous dimensions. We conjecture that the implication also runs in the other
direction, so that any CFT with a planar expansion and a large gap has a local
bulk dual. For an abstract CFT we formulate the consistency conditions, most
notably crossing symmetry, and show that the conjecture is true in a broad
range of CFT's, to first nontrivial order in 1/N^2: any CFT with a gap and a
planar expansion is generated via the AdS/CFT dictionary from a local bulk
interaction. We establish this result by a counting argument on each side, and
also investigate various properties of some explicit solutions.Comment: 49 pages. Minor corrections. Figure and references adde
Logical Bell Inequalities
Bell inequalities play a central role in the study of quantum non-locality
and entanglement, with many applications in quantum information. Despite the
huge literature on Bell inequalities, it is not easy to find a clear conceptual
answer to what a Bell inequality is, or a clear guiding principle as to how
they may be derived. In this paper, we introduce a notion of logical Bell
inequality which can be used to systematically derive testable inequalities for
a very wide variety of situations. There is a single clear conceptual
principle, based on purely logical consistency conditions, which underlies our
notion of logical Bell inequalities. We show that in a precise sense, all Bell
inequalities can be taken to be of this form. Our approach is very general. It
applies directly to any family of sets of commuting observables. Thus it covers
not only the n-partite scenarios to which Bell inequalities are standardly
applied, but also Kochen-Specker configurations, and many other examples. There
is much current work on experimental tests for contextuality. Our approach
directly yields, in a systematic fashion, testable inequalities for a very
general notion of contextuality.
There has been much work on obtaining proofs of Bell's theorem `without
inequalities' or `without probabilities'. These proofs are seen as being in a
sense more definitive and logically robust than the inequality-based proofs. On
the hand, they lack the fault-tolerant aspect of inequalities. Our approach
reconciles these aspects, and in fact shows how the logical robustness can be
converted into systematic, general derivations of inequalities with provable
violations. Moreover, the kind of strong non-locality or contextuality
exhibited by the GHZ argument or by Kochen-Specker configurations can be shown
to lead to maximal violations of the corresponding logical Bell inequalities.Comment: 12 page
Cluster expansion for ground states of local Hamiltonians
A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench
Power-counting theorem for non-local matrix models and renormalisation
Solving the exact renormalisation group equation a la Wilson-Polchinski
perturbatively, we derive a power-counting theorem for general matrix models
with arbitrarily non-local propagators. The power-counting degree is determined
by two scaling dimensions of the cut-off propagator and various topological
data of ribbon graphs. As a necessary condition for the renormalisability of a
model, the two scaling dimensions have to be large enough relative to the
dimension of the underlying space. In order to have a renormalisable model one
needs additional locality properties--typically arising from orthogonal
polynomials--which relate the relevant and marginal interaction coefficients to
a finite number of base couplings. The main application of our power-counting
theorem is the renormalisation of field theories on noncommutative R^D in
matrix formulation.Comment: 35 pages, 70 figures, LaTeX with svjour macros. v2: proof simplified
because a discussion originally designed for \phi^4 on noncommutative R^2 was
actually not necessary, see hep-th/0307017. v3: consistency conditions
removed because models of interest relate automatically the relevant/marginal
interactions to a finite number of base couplings, see hep-th/0401128. v4:
integration procedure improved so that the initial cut-off can be directly
removed; to appear in Commun. Math. Phy
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