355 research outputs found
AQFT from n-functorial QFT
There are essentially two different approaches to the axiomatization of
quantum field theory (QFT): algebraic QFT, going back to Haag and Kastler, and
functorial QFT, going back to Atiyah and Segal. More recently, based on ideas
by Baez and Dolan, the latter is being refined to "extended" functorial QFT by
Freed, Hopkins, Lurie and others. The first approach uses local nets of
operator algebras which assign to each patch an algebra "of observables", the
latter uses n-functors which assign to each patch a "propagator of states".
In this note we present an observation about how these two axiom systems are
naturally related: we demonstrate under mild assumptions that every
2-dimensional extended Minkowskian QFT 2-functor ("parallel surface transport")
naturally yields a local net. This is obtained by postcomposing the propagation
2-functor with an operation that mimics the passage from the Schroedinger
picture to the Heisenberg picture in quantum mechanics.
The argument has a straightforward generalization to general
pseudo-Riemannian structure and higher dimensions.Comment: 39 pages; further examples added: Hopf spin chains and asymptotic
inclusion of subfactors; references adde
From boundary to bulk in logarithmic CFT
The analogue of the charge-conjugation modular invariant for rational
logarithmic conformal field theories is constructed. This is done by
reconstructing the bulk spectrum from a simple boundary condition (the analogue
of the Cardy `identity brane'). We apply the general method to the c_1,p
triplet models and reproduce the previously known bulk theory for p=2 at c=-2.
For general p we verify that the resulting partition functions are modular
invariant. We also construct the complete set of 2p boundary states, and
confirm that the identity brane from which we started indeed exists. As a
by-product we obtain a logarithmic version of the Verlinde formula for the
c_1,p triplet models.Comment: 35 pages, 2 figures; v2: minor corrections, version to appear in
J.Phys.
Bulk flows in Virasoro minimal models with boundaries
The behaviour of boundary conditions under relevant bulk perturbations is
studied for the Virasoro minimal models. In particular, we consider the bulk
deformation by the least relevant bulk field which interpolates between the mth
and (m-1)st unitary minimal model. In the presence of a boundary this bulk flow
induces an RG flow on the boundary, which ensures that the resulting boundary
condition is conformal in the (m-1)st model. By combining perturbative RG
techniques with insights from defects and results about non-perturbative
boundary flows, we determine the endpoint of the flow, i.e. the boundary
condition to which an arbitrary boundary condition of the mth theory flows to.Comment: 34 pages, 6 figures. v4: Typo in fig. 2 correcte
Constructing Gauge Theory Geometries from Matrix Models
We use the matrix model -- gauge theory correspondence of Dijkgraaf and Vafa
in order to construct the geometry encoding the exact gaugino condensate
superpotential for the N=1 U(N) gauge theory with adjoint and symmetric or
anti-symmetric matter, broken by a tree level superpotential to a product
subgroup involving U(N_i) and SO(N_i) or Sp(N_i/2) factors. The relevant
geometry is encoded by a non-hyperelliptic Riemann surface, which we extract
from the exact loop equations. We also show that O(1/N) corrections can be
extracted from a logarithmic deformation of this surface. The loop equations
contain explicitly subleading terms of order 1/N, which encode information of
string theory on an orientifolded local quiver geometry.Comment: 52 page
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Overview of recent KDP damage experiments and implications for NIF tripler performance
Considerable attention has been paid over the years to the problem of growing high purity KDP and KD*P to meet damage threshold requirements of ICF lasers at LLNL. The maximum fluence requirement for KD*P triplers on the National Ignition Facility (NIF) is 14.3 J/cm2 at 351 nm in a 3 ns pulse. Currently KD*P (conventional or rapid grown) cannot meet this requirement without laser (pre)conditioning. In this overview, recent experiments to understand laser conditioning and damage phenomena in KDP and KD*P will be discussed. These experiments have lead to a fundamental revision of damage test methods and test result interpretation. In particular, the concept of a damage threshold has given way to measuring performance by damage distributions using millimeter sixed beams. Automated R/l (conditioned) damage tests have shown that the best rapidly grown KDP crystals exhibit the same damage distributions at the best conventionally grown KD*P. Continuous filtration of the growth solution and post growth thermal sealing are shown to increase the damage performance as well. In addition, centimeter size beams from multijoule lasers have been used to study stepwise laser conditioning in KDP. These tests have shown that an increase in the damage threshold of ~1.5X is attainable with 8-12 shots of increasing fluence. The experiments show that the damage density (pinpoints/mm3) evolves exponentially and once formed, the micron sized bulk pinpoints remain stable against increases in local fluence. The information obtained from damage distributions and conditioning studies has been used with model NIF spatial profiles to determine the probability of damage and the local pinpoint density generated in a tripler. Calculations based on test data have shown that .for well conditioned, high quality rapid growth KDP or conventional growth KD*P the damage probability is less than 3%. Furthermore, the fluence profiles expected on NIF lead to only small numbers of generated pinpoints which are not expected to adversely affect NIF operations. To check the validity of the results, the 37 cm KD*P tripler from the Beamlet laser was mapped for damage. The inspection revealed pinpoint densities of the order of predicted by the damage evolution calculation
W-Extended Fusion Algebra of Critical Percolation
Two-dimensional critical percolation is the member LM(2,3) of the infinite
series of Yang-Baxter integrable logarithmic minimal models LM(p,p'). We
consider the continuum scaling limit of this lattice model as a `rational'
logarithmic conformal field theory with extended W=W_{2,3} symmetry and use a
lattice approach on a strip to study the fundamental fusion rules in this
extended picture. We find that the representation content of the ensuing closed
fusion algebra contains 26 W-indecomposable representations with 8 rank-1
representations, 14 rank-2 representations and 4 rank-3 representations. We
identify these representations with suitable limits of Yang-Baxter integrable
boundary conditions on the lattice and obtain their associated W-extended
characters. The latter decompose as finite non-negative sums of W-irreducible
characters of which 13 are required. Implementation of fusion on the lattice
allows us to read off the fusion rules governing the fusion algebra of the 26
representations and to construct an explicit Cayley table. The closure of these
representations among themselves under fusion is remarkable confirmation of the
proposed extended symmetry.Comment: 30 page
The logarithmic triplet theory with boundary
The boundary theory for the c=-2 triplet model is investigated in detail. In
particular, we show that there are four different boundary conditions that
preserve the triplet algebra, and check the consistency of the corresponding
boundary operators by constructing their OPE coefficients explicitly. We also
compute the correlation functions of two bulk fields in the presence of a
boundary, and verify that they are consistent with factorisation.Comment: 43 pages, LaTeX; v2: references added, typos corrected, footnote 4
adde
An Introduction to Conformal Field Theory
A comprehensive introduction to two-dimensional conformal field theory is
given.Comment: 69 pages, LaTeX; references adde
One-point functions in massive integrable QFT with boundaries
We consider the expectation value of a local operator on a strip with
non-trivial boundaries in 1+1 dimensional massive integrable QFT. Using finite
volume regularisation in the crossed channel and extending the boundary state
formalism to the finite volume case we give a series expansion for the
one-point function in terms of the exact form factors of the theory. The
truncated series is compared with the numerical results of the truncated
conformal space approach in the scaling Lee-Yang model. We discuss the
relevance of our results to quantum quench problems.Comment: 43 pages, 20 figures, v2: typos correcte
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