744 research outputs found
The modular S-matrix as order parameter for topological phase transitions
We study topological phase transitions in discrete gauge theories in two
spatial dimensions induced by the formation of a Bose condensate. We analyse a
general class of euclidean lattice actions for these theories which contain one
coupling constant for each conjugacy class of the gauge group. To probe the
phase structure we use a complete set of open and closed anyonic string
operators. The open strings allow one to determine the particle content of the
condensate, whereas the closed strings enable us to determine the matrix
elements of the modular -matrix, also in the broken phase. From the measured
broken -matrix we may read off the sectors that split or get identified in
the broken phase, as well as the sectors that are confined. In this sense the
modular -matrix can be employed as a matrix valued non-local order parameter
from which the low-energy effective theories that occur in different regions of
parameter space can be fully determined.
To verify our predictions we studied a non-abelian anyon model based on the
quaternion group of order eight by Monte Carlo simulation. We
probe part of the phase diagram for the pure gauge theory and find a variety of
phases with magnetic condensates leading to various forms of (partial)
confinement in complete agreement with the algebraic breaking analysis. Also
the order of various transitions is established.Comment: 37 page
Fourier transform and the Verlinde formula for the quantum double of a finite group
A Fourier transform S is defined for the quantum double D(G) of a finite
group G. Acting on characters of D(G), S and the central ribbon element of D(G)
generate a unitary matrix representation of the group SL(2,Z). The characters
form a ring over the integers under both the algebra multiplication and its
dual, with the latter encoding the fusion rules of D(G). The Fourier transform
relates the two ring structures. We use this to give a particularly short proof
of the Verlinde formula for the fusion coefficients.Comment: 15 pages, small errors corrected and references added, version to
appear in Journal of Physics
Vortices on Higher Genus Surfaces
We consider the topological interactions of vortices on general surfaces. If
the genus of the surface is greater than zero, the handles can carry magnetic
flux. The classical state of the vortices and the handles can be described by a
mapping from the fundamental group to the unbroken gauge group. The allowed
configurations must satisfy a relation induced by the fundamental group. Upon
quantization, the handles can carry ``Cheshire charge.'' The motion of the
vortices can be described by the braid group of the surface. How the motion of
the vortices affects the state is analyzed in detail.Comment: 28 pages with 10 figures; uses phyzzx and psfig; Caltech preprint
CALT-68-187
The Primary Spin-4 Casimir Operators in the Holographic SO(N) Coset Minimal Models
Starting from SO(N) current algebra, we construct two lowest primary higher
spin-4 Casimir operators which are quartic in spin-1 fields. For N is odd, one
of them corresponds to the current in the WB_{\frac{N-1}{2}} minimal model. For
N is even, the other corresponds to the current in the WD_{\frac{N}{2}} minimal
model. These primary higher spin currents, the generators of wedge subalgebra,
are obtained from the operator product expansion of fermionic (or bosonic)
primary spin-N/2 field with itself in each minimal model respectively. We
obtain, indirectly, the three-point functions with two real scalars, in the
large N 't Hooft limit, for all values of the 't Hooft coupling which should be
dual to the three-point functions in the higher spin AdS_3 gravity with matter.Comment: 65 pages; present the main results only and to appear in JHEP where
one can see the Appendi
Hourly resolved cloud modification factors in the ultraviolet
Cloud impacts on the transfer of ultraviolet (UV) radiation through the atmosphere can be assessed by using a cloud modification factor (CMF). CMF, which is based on total global solar irradiation (SOL<sub>CMF</sub>), has proved to be a solid basis to derive CMFs for the UV radiation (UV<sub>CMF</sub>). This is an advantage, because total global irradiance, the basis for SOL<sub>CMF</sub>, is frequently measured and forecasted by numerical weather prediction systems and includes all relevant effects for radiation transmission, such as cloud optical depth, different cloud layers, multiple reflection, as well as the distinct difference as to whether the solar disc is obscured by clouds or not. In the UV range clouds decrease the irradiance to a lesser extent than in the visible and infrared spectral range. Thus the relationship between CMFs for solar radiation and for UV-radiation is not straight forward, but will depend on whether, for example, the solar zenith angle (SZA) and wavelength band or action spectrum in the UV have been taken into consideration. Den Outer et al. provide a UV<sub>CMF</sub> algorithm on a daily basis, which accounts for these influences. It requires as input a daily SOL<sub>CMF</sub> and the SZA at noon. The calculation of SOL<sub>CMF</sub> uses the clear-sky algorithm of the European Solar Radiation Atlas to account for varying turbidity impacts. The algorithm's capability to derive hourly UV<sub>CMFs</sub> based on the SZA at the corresponding hour and its worldwide applicability is validated for erythemal UV using observational data retrieved from the databases of the COST-Action 726 on "Long-term changes and climatology of UV radiation over Europe" and the USDA UV-B Monitoring Program. The clear-sky part of the models has proved to be of good quality. Accumulated to daily doses it forms a tight cluster of points to the highest measured daily sums. All sky model performances for hourly resolution are shown to be comparable in accuracy with the well performing daily models of the COST-726 model intercomparison
The Operator Product Expansion of the Lowest Higher Spin Current at Finite N
For the N=2 Kazama-Suzuki(KS) model on CP^3, the lowest higher spin current
with spins (2, 5/2, 5/2,3) is obtained from the generalized GKO coset
construction. By computing the operator product expansion of this current and
itself, the next higher spin current with spins (3, 7/2, 7/2, 4) is also
derived. This is a realization of the N=2 W_{N+1} algebra with N=3 in the
supersymmetric WZW model. By incorporating the self-coupling constant of lowest
higher spin current which is known for the general (N,k), we present the
complete nonlinear operator product expansion of the lowest higher spin current
with spins (2, 5/2, 5/2, 3) in the N=2 KS model on CP^N space. This should
coincide with the asymptotic symmetry of the higher spin AdS_3 supergravity at
the quantum level. The large (N,k) 't Hooft limit and the corresponding
classical nonlinear algebra are also discussed.Comment: 62 pages; the footnotes added, some redundant appendices removed, the
presentations in the whole paper improved and to appear in JHE
The Coset Spin-4 Casimir Operator and Its Three-Point Functions with Scalars
We find the GKO coset construction of the dimension 4 Casimir operator that
contains the quartic WZW currents contracted with completely symmetric SU(N)
invariant tensors of ranks 4, 3, and 2. The requirements, that the operator
product expansion with the diagonal current is regular and it should be primary
under the coset Virasoro generator of dimension 2, fix all the coefficients in
spin-4 current, up to two unknown coefficients. The operator product expansion
of coset primary spin-3 field with itself fixes them completely. We compute the
three-point functions with scalars for all values of the 't Hooft coupling in
the large N limit. At fixed 't Hooft coupling, these three-point functions are
dual to that found by Chang and Yin recently in the undeformed AdS_3 bulk
theory (higher spin gravity with matter).Comment: 65 pages; the ambiguity for the two coefficient functions is
clarified and the abstract, the introduction, the subsection 3.4 and the
conclusion are improved and to appear in JHE
Strings from Gauged Wess-Zumino-Witten Models
We present an algebraic approach to string theory. An embedding of
in a super Lie algebra together with a grading on the Lie algebra determines a
nilpotent subalgebra of the super Lie algebra. Chirally gauging this subalgebra
in the corresponding Wess-Zumino-Witten model, breaks the affine symmetry of
the Wess-Zumino-Witten model to some extension of the superconformal
algebra. The extension is completely determined by the embedding. The
realization of the superconformal algebra is determined by the grading. For a
particular choice of grading, one obtains in this way, after twisting, the BRST
structure of a string theory. We classify all embeddings of into Lie
super algebras and give a detailed account of the branching of the adjoint
representation. This provides an exhaustive classification and characterization
of both all extended superconformal algebras and all string theories
which can be obtained in this way.Comment: 50 pages, LaTe
The Large N 't Hooft Limit of Kazama-Suzuki Model
We consider N=2 Kazama-Suzuki model on CP^N=SU(N+1)/SU(N)xU(1). It is known
that the N=2 current algebra for the supersymmetric WZW model, at level k, is a
nonlinear algebra. The N=2 W_3 algebra corresponding to N=2 was recovered from
the generalized GKO coset construction previously. For N=4, we construct one of
the higher spin currents, in N=2 W_5 algebra, with spins (2, 5/2, 5/2, 3). The
self-coupling constant in the operator product expansion of this current and
itself depends on N as well as k explicitly. We also observe a new higher spin
primary current of spins (3, 7/2, 7/2, 4). From the behaviors of N=2, 4 cases,
we expect the operator product expansion of the lowest higher spin current and
itself in N=2 W_{N+1} algebra. By taking the large (N, k) limit on the various
operator product expansions in components, we reproduce, at the linear order,
the corresponding operator product expansions in N=2 classical
W_{\infty}^{cl}[\lambda] algebra which is the asymptotic symmetry of the higher
spin AdS_3 supergravity found recently.Comment: 44 pages; the two typos in the first paragraph of page 23 corrected
and to appear in JHE
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