13,804 research outputs found
Bosonic Anomalies, Induced Fractional Quantum Numbers and Degenerate Zero Modes: the anomalous edge physics of Symmetry-Protected Topological States
The boundary of symmetry-protected topological states (SPTs) can harbor new
quantum anomaly phenomena. In this work, we characterize the bosonic anomalies
introduced by the 1+1D non-onsite-symmetric gapless edge modes of 2+1D bulk
bosonic SPTs with a generic finite Abelian group symmetry (isomorphic to
). We
demonstrate that some classes of SPTs (termed "Type II") trap fractional
quantum numbers (such as fractional charges) at the 0D kink of the
symmetry-breaking domain walls; while some classes of SPTs (termed "Type III")
have degenerate zero energy modes (carrying the projective representation
protected by the unbroken part of the symmetry), either near the 0D kink of a
symmetry-breaking domain wall, or on a symmetry-preserving 1D system
dimensionally reduced from a thin 2D tube with a monodromy defect 1D line
embedded. More generally, the energy spectrum and conformal dimensions of
gapless edge modes under an external gauge flux insertion (or twisted by a
branch cut, i.e., a monodromy defect line) through the 1D ring can distinguish
many SPT classes. We provide a manifest correspondence from the physical
phenomena, the induced fractional quantum number and the zero energy mode
degeneracy, to the mathematical concept of cocycles that appears in the group
cohomology classification of SPTs, thus achieving a concrete physical
materialization of the cocycles. The aforementioned edge properties are
formulated in terms of a long wavelength continuum field theory involving
scalar chiral bosons, as well as in terms of Matrix Product Operators and
discrete quantum lattice models. Our lattice approach yields a regularization
with anomalous non-onsite symmetry for the field theory description. We also
formulate some bosonic anomalies in terms of the Goldstone-Wilczek formula.Comment: 29 pages, 12 Figures. v3 clarification to be accessible for both HEP
and CMT. Thanks to Roman Jackiw for introducing new Ref
Trisecting non-Lagrangian theories
We propose a way to define and compute invariants of general smooth
4-manifolds based on topological twists of non-Lagrangian 4d N=2 and N=3
theories in which the problem is reduced to a fairly standard computation in
topological A-model, albeit with rather unusual targets, such as compact and
non-compact Gepner models, asymmetric orbifolds, N=(2,2) linear dilaton
theories, "self-mirror" geometries, varieties with complex multiplication, etc.Comment: 49 pages, 8 figures, 8 tables, v2: a reference adde
Non-conformal examples of AdS/CFT
Asymptotically anti-de Sitter spacetimes with Poincare invariance along the
boundary can describe, via the AdS/CFT correspondence, either relevant
deformations of a conformal field theory or non-conformal vacuum states. I
consider examples of both types constructed in the framework of
five-dimensional gauged supergravity. I explain the proof and motivation of a
gravitational ``c-theorem'' which is independent of dimension. I show how one
class of examples can be elevated to ten-dimensional geometries involving
distributions of parallel D3-branes. For these cases some peculiar properties
of two-point functions emerge, and I close with speculations on their physical
origin.Comment: 16 pages, two figures, latex. Strings '99 tal
Hoare-style Specifications as Correctness Conditions for Non-linearizable Concurrent Objects
Designing scalable concurrent objects, which can be efficiently used on
multicore processors, often requires one to abandon standard specification
techniques, such as linearizability, in favor of more relaxed consistency
requirements. However, the variety of alternative correctness conditions makes
it difficult to choose which one to employ in a particular case, and to compose
them when using objects whose behaviors are specified via different criteria.
The lack of syntactic verification methods for most of these criteria poses
challenges in their systematic adoption and application.
In this paper, we argue for using Hoare-style program logics as an
alternative and uniform approach for specification and compositional formal
verification of safety properties for concurrent objects and their client
programs. Through a series of case studies, we demonstrate how an existing
program logic for concurrency can be employed off-the-shelf to capture
important state and history invariants, allowing one to explicitly quantify
over interference of environment threads and provide intuitive and expressive
Hoare-style specifications for several non-linearizable concurrent objects that
were previously specified only via dedicated correctness criteria. We
illustrate the adequacy of our specifications by verifying a number of
concurrent client scenarios, that make use of the previously specified
concurrent objects, capturing the essence of such correctness conditions as
concurrency-aware linearizability, quiescent, and quantitative quiescent
consistency. All examples described in this paper are verified mechanically in
Coq.Comment: 18 page
Wall-Crossing in Coupled 2d-4d Systems
We introduce a new wall-crossing formula which combines and generalizes the
Cecotti-Vafa and Kontsevich-Soibelman formulas for supersymmetric 2d and 4d
systems respectively. This 2d-4d wall-crossing formula governs the
wall-crossing of BPS states in an N=2 supersymmetric 4d gauge theory coupled to
a supersymmetric surface defect. When the theory and defect are compactified on
a circle, we get a 3d theory with a supersymmetric line operator, corresponding
to a hyperholomorphic connection on a vector bundle over a hyperkahler space.
The 2d-4d wall-crossing formula can be interpreted as a smoothness condition
for this hyperholomorphic connection. We explain how the 2d-4d BPS spectrum can
be determined for 4d theories of class S, that is, for those theories obtained
by compactifying the six-dimensional (0,2) theory with a partial topological
twist on a punctured Riemann surface C. For such theories there are canonical
surface defects. We illustrate with several examples in the case of A_1
theories of class S. Finally, we indicate how our results can be used to
produce solutions to the A_1 Hitchin equations on the Riemann surface C.Comment: 170 pages, 45 figure
Vertex algebras and 4-manifold invariants
We propose a way of computing 4-manifold invariants, old and new, as chiral
correlation functions in half-twisted 2d theories that
arise from compactification of fivebranes. Such formulation gives a new
interpretation of some known statements about Seiberg-Witten invariants, such
as the basic class condition, and gives a prediction for structural properties
of the multi-monopole invariants and their non-abelian generalizations.Comment: 67 pages, 11 figure
Quantum Vortex Strings: A Review
The quantum worldsheet dynamics of vortex strings contains information about
the 4d non-Abelian gauge theory in which the string lives. Here I tell this
story. The string worldsheet theory is typically some variant of the CP^{N-1}
sigma-model, describing the orientation of the string in a U(N) gauge group.
Qualitative parallels between 2d sigma-models and 4d non-Abelian gauge theories
have been known since the 1970s. The vortex string provides a quantitative link
between the two. In 4d theories with N=2 supersymmetry, the exact BPS spectrum
of the worldsheet coincides with the bulk spectrum in 4d. Moreover, by tuning
parameters, the CP^{N-1} sigma-model can be coaxed to flow to an interacting
conformal fixed point which is related to the 4d Argyres-Douglas fixed point.
For theories with N=1 supersymmetry, the worldsheet theory suffers dynamical
supersymmetry breaking and, more interestingly, supersymmetry restoration, in a
way which captures the physics of Seiberg's quantum deformed moduli space.Comment: Adams Prize Essay. 40 pages with 4 colourful picture
Diverse roles of Dpb2, the non-catalytic subunit of DNA polymerase Δ
Timely progression of living cells through the cell cycle is precisely regulated. This involves a series of phosphorylation events which are regulated by various cyclins, activated in coordination with the cell cycle progression. Phosphorylated proteins govern cell growth, division as well as duplication of the genetic material and transcriptional activation of genes involved in these processes. A subset of these tightly regulated genes, which depend on the MBF transcription factor and are mainly involved in DNA replication and cell division, is transiently activated at the transition from G1 to S phase. A Saccharomyces cerevisiae mutant in the Dpb2 non-catalytic subunit of DNA polymerase Δ (PolΔ) demonstrates abnormalities in transcription of MBF-dependent genes even in normal growth conditions. It is, therefore, tempting to speculate that Dpb2 which, as described previously, participates in the early stages of DNA replication initiation, has an impact on the regulation of replication-related genes expression with possible implications for genomic stability
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