4,053 research outputs found
't Hooft anomalies of discrete gauge theories and non-abelian group cohomology
We study discrete symmetries of Dijkgraaf-Witten theories and their gauging
in the framework of (extended) functorial quantum field theory. Non-abelian
group cohomology is used to describe discrete symmetries and we derive concrete
conditions for such a symmetry to admit 't Hooft anomalies in terms of the
Lyndon-Hochschild-Serre spectral sequence. We give an explicit realization of a
discrete gauge theory with 't Hooft anomaly as a state on the boundary of a
higher-dimensional Dijkgraaf-Witten theory. This allows us to calculate the
2-cocycle twisting the projective representation of physical symmetries via
transgression. We present a general discussion of the bulk-boundary
correspondence at the level of partition functions and state spaces, which we
make explicit for discrete gauge theories.Comment: 46 pages, 1 figure; v2: minor corrections and clarifying comments
added, references updated; Final version to appear in Communications in
Mathematical Physic
Extended quantum field theory, index theory and the parity anomaly
We use techniques from functorial quantum field theory to provide a geometric
description of the parity anomaly in fermionic systems coupled to background
gauge and gravitational fields on odd-dimensional spacetimes. We give an
explicit construction of a geometric cobordism bicategory which incorporates
general background fields in a stack, and together with the theory of symmetric
monoidal bicategories we use it to provide the concrete forms of invertible
extended quantum field theories which capture anomalies in both the path
integral and Hamiltonian frameworks. Specialising this situation by using the
extension of the Atiyah-Patodi-Singer index theorem to manifolds with corners
due to Loya and Melrose, we obtain a new Hamiltonian perspective on the parity
anomaly. We compute explicitly the 2-cocycle of the projective representation
of the gauge symmetry on the quantum state space, which is defined in a
parity-symmetric way by suitably augmenting the standard chiral fermionic Fock
spaces with Lagrangian subspaces of zero modes of the Dirac Hamiltonian that
naturally appear in the index theorem. We describe the significance of our
constructions for the bulk-boundary correspondence in a large class of
time-reversal invariant gauge-gravity symmetry-protected topological phases of
quantum matter with gapless charged boundary fermions, including the standard
topological insulator in 3+1 dimensions.Comment: 63 pages, 3 figures; v2: clarifying comments and references added;
Final version to be published in Communications in Mathematical Physic
The distinguished invertible object as ribbon dualizing object in the Drinfeld center
We prove that the Drinfeld center of a pivotal finite tensor
category comes with the structure of a ribbon
Grothendieck-Verdier category in the sense of Boyarchenko-Drinfeld. Phrased
operadically, this makes into a cyclic algebra over the framed
-operad. The underlying object of the dualizing object is the
distinguished invertible object of appearing in the well-known
Radford isomorphism of Etingof-Nikshych-Ostrik. Up to equivalence, this is the
unique ribbon Grothendieck-Verdier structure on extending the
canonical balanced braided structure that already comes
equipped with. The duality functor of this ribbon Grothendieck-Verdier
structure coincides with the rigid duality if and only if is
spherical in the sense of Douglas-Schommer-Pries-Snyder. The main topological
consequence of our algebraic result is that gives rise to an
ansular functor, in fact even a modular functor regardless of whether
is spherical or not. In order to prove the aforementioned
uniqueness statement for the ribbon Grothendieck-Verdier structure, we derive a
seven-term exact sequence characterizing the space of ribbon
Grothendieck-Verdier structures on a balanced braided category. This sequence
features the Picard group of the balanced version of the M\"uger center of the
balanced braided category.Comment: 21 pages, diagrams partly in color; v2: minor changes, Cor. 3.1
strengthene
The Little Bundles Operad
Hurwitz spaces are homotopy quotients of the braid group action on the moduli
space of principal bundles over a punctured plane. By considering a certain
model for this homotopy quotient we build an aspherical topological operad that
we call the little bundles operad. As our main result, we describe this operad
as a groupoid-valued operad in terms of generators and relations and prove that
the categorical little bundles algebras are precisely Turaev's crossed
categories. Moreover, we prove that the evaluation on the circle of a
homotopical two-dimensional equivariant topolological field theory yields a
little bundles algebra up to coherent homotopy.Comment: 33 pages, 6 figures, lots of diagrams; small changes; final version
to appear in Algebr. Geom. Topo
Cyclic framed little disks algebras, Grothendieck-Verdier duality and handlebody group representations
We characterize cyclic algebras over the associative and the framed little
disks operad in any symmetric monoidal bicategory. The cyclicity is
appropriately treated in a homotopy coherent way. When the symmetric monoidal
bicategory is specified to be a certain symmetric monoidal bicategory of linear
categories subject to finiteness conditions, we prove that cyclic associative
and cyclic framed little disks algebras, respectively, are equivalent to
pivotal Grothendieck-Verdier categories and balanced braided
Grothendieck-Verdier categories, a type of category that was introduced by
Boyarchenko-Drinfeld based on Barr's notion of a -autonomous category. We
use these results and Costello's modular envelope construction to obtain two
applications to quantum topology: I) We extract a consistent system of
handlebody group representations from any balanced braided Grothendieck-Verdier
category inside a certain symmetric monoidal bicategory of linear categories
and show that this generalizes the handlebody part of Lyubashenko's mapping
class group representations. II) We establish a Grothendieck-Verdier duality
for the category extracted from a modular functor by evaluation on the circle
(without any assumption on semisimplicity), thereby generalizing results of
Tillmann and Bakalov-Kirillov.Comment: 60 pages, lots of figures and diagrams (some in color); v2:
presentation improved, details and examples added in several place
Spread and establishment of Aedes albopictus in southern Switzerland between 2003 and 2014 : an analysis of oviposition data and weather conditions
The Asian tiger mosquito, Aedes albopictus, is a highly invasive mosquito species of public health importance. In the wake of its arrival in neighbouring Italy the authorities of the canton of Ticino in southern Switzerland initiated a surveillance programme in 2000 that is still on-going. Here we explored the unique data set, compiled from 2003 to 2014, to analyse the local dynamic of introduction and establishment of Ae. albopictus, its relative density in relation to precipitation and temperature, and its potential distribution at the passage from southern to northern Europe.; The presence of Ae. albopictus was recorded by ovitraps placed across Ticino. In addition to presence-absence, the relationship between relative egg densities and year, month, temperature and precipitation was analysed by a generalised linear mixed model.; Since its first detection in 2003 at Ticino's border with Italy Ae. albopictus has continuously spread north across the lower valleys, mainly along the trans-European motorway, E35. Detailed local analysis showed that industrial areas were colonised by the mosquito before residential areas and that, afterwards, the mosquito was more present in residential than in industrial areas. Ae. albopictus appeared sporadically and then became more present in the same places the following years, suggesting gradual establishment of locally reproducing populations that manage to overwinter. This trend continues as witnessed by both a growing area being infested and increasing egg counts in the ovitraps. There was a clear South-North gradient with more traps being repeatedly positive in the South and fewer eggs laid during periods of intensive precipitation. In the North, the mosquito appeared repeatedly through the years, but never managed to establish, probably because of unfavourable weather conditions and low road traffic.; Given the present results we assume that additional areas may still become infested. While the current study provides good estimates of relative egg densities and shows the local and regional dynamics of Ae. albopictus invasion, additional parameters ought to be measured to make an objective risk assessment for epidemic disease transmission. The likelihood of Ae. albopictus to further spread and increase in densities calls for continued surveillance
Probing the Constituent Structure of Black Holes
Based on recent ideas, we propose a framework for the description of black
holes in terms of constituent graviton degrees of freedom. Within this
formalism a large black hole can be understood as a bound state of N
longitudinal gravitons. In this context black holes are similar to baryonic
bound states in quantum chromodynamics which are described by fundamental quark
degrees of freedom. As a quantitative tool we employ a quantum bound state
description originally developed in QCD that allows to consider black holes in
a relativistic Hartree like framework. As an application of our framework we
calculate the cross section for scattering processes between graviton emitters
outside of a Schwarzschild black hole and absorbers in its interior, that is
gravitons. We show that these scatterings allow to directly extract structural
observables such as the momentum distribution of black hole constituents.Comment: Extended version, accepted for publication in JHE
Hard-switched switched capacitor converter design
Switched capacitor (SC) converters are becoming quite popular for use in DC-DC power conversion. The concept of equivalent resistance in SC converters is frequently used to determine the conduction losses due to the load current. A variety of methodologies have been presented in the literature to predict the equivalent resistance in hard-switched SC converters. However, a majority of the methods described are difficult to apply to general SC converter topologies. Additionally, previous works have not considered all nonidealities in their analysis, such as switching losses or stray inductances. This work presents a generalized and easy to use model to determine the equivalent resistance of any high-order SC converter. The presented concepts are combined to derive a complete loss model for SC converters.
The challenges of implementing output voltage regulation are addressed as well. A current-fed SC topology is presented in this work that overcomes the problems associated with voltage regulation. The new topology opens up a variety of additional operating modes, such as power sharing. These additional operating modes are explored as well.
The presented concepts are verified using digital simulation tools and prototype converters. --Abstract, page iii
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