16,995 research outputs found
Correlation Functions in 2-Dimensional Integrable Quantum Field Theories
In this talk I discuss the form factor approach used to compute correlation
functions of integrable models in two dimensions. The Sinh-Gordon model is our
basic example. Using Watson's and the recursive equations satisfied by matrix
elements of local operators, I present the computation of the form factors of
the elementary field and the stress-energy tensor of
the theory.Comment: 19pp, LATEX version, (talk at Como Conference on ``Integrable Quantum
Field Theories''
Categorification of skew-symmetrizable cluster algebras
We propose a new framework for categorifying skew-symmetrizable cluster
algebras. Starting from an exact stably 2-Calabi-Yau category C endowed with
the action of a finite group G, we construct a G-equivariant mutation on the
set of maximal rigid G-invariant objects of C. Using an appropriate cluster
character, we can then attach to these data an explicit skew-symmetrizable
cluster algebra. As an application we prove the linear independence of the
cluster monomials in this setting. Finally, we illustrate our construction with
examples associated with partial flag varieties and unipotent subgroups of
Kac-Moody groups, generalizing to the non simply-laced case several results of
Gei\ss-Leclerc-Schr\"oer.Comment: 64 page
Use of lung ultrasonography in the detection of pneumothorax among medical students and emergency physician
TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT
The ground-state energy of integrably-twisted theories is analyzed in finite
volume. We derive the leading and next-to-leading order (NLO) L\"uscher-type
corrections for large volumes of the vacuum energy for integrable theories with
twisted boundary conditions and twisted S-matrix. We then derive the twisted
thermodynamic Bethe ansatz (TBA) equations to describe exactly the ground
state, from which we obtain an untwisted Y-system. The two approaches are
compared by expanding the TBA equations to NLO, and exact agreement is found.
We give explicit results for the O(4) model and for the three-parameter family
of -deformed (non-supersymmetric) planar AdS/CFT model, where the
ground-state energy can be nontrivial and can acquire finite-size corrections.
The NLO corrections, which correspond to double-wrapping diagrams, are
explicitly evaluated for the latter model at six loops.Comment: 42 pages, 2 figures, v2: references added, v3: minor correction
The low-energy limit of AdS(3)/CFT2 and its TBA
We investigate low-energy string excitations in AdS3 × S3 × T4. When the worldsheet is decompactified, the theory has gapless modes whose spectrum at low energies is determined by massless relativistic integrable S matrices of the type introduced by Al. B. Zamolodchikov. The S matrices are non-trivial only for excitations with identical worldsheet chirality, indicating that the low-energy theory is a CFT2. We construct a Thermodynamic Bethe Ansatz (TBA) for these excitations and show how the massless modes’ wrapping effects may be incorporated into the AdS3 spectral problem. Using the TBA and its associated Y-system, we determine the central charge of the low-energy CFT2 to be c = 6 from calculating the vacuum energy for antiperiodic fermions — with the vacuum energy being zero for periodic fermions in agreement with a supersymmetric theory — and find the energies of some excited states
Quantum integrability of the Alday-Arutyunov-Frolov model
We investigate the quantum integrability of the Alday-Arutyunov-Frolov (AAF)
model by calculating the three-particle scattering amplitude at the first
non-trivial order and showing that the S-matrix is factorizable at this order.
We consider a more general fermionic model and find a necessary constraint to
ensure its integrability at quantum level. We then show that the quantum
integrability of the AAF model follows from this constraint. In the process, we
also correct some missed points in earlier works.Comment: 40 pages; Replaced with published version. Appendix and comments
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A computational study on altered theta-gamma coupling during learning and phase coding
There is considerable interest in the role of coupling between theta and gamma oscillations in the brain in the context of learning and memory. Here we have used a neural network model which is capable of producing coupling of theta phase to gamma amplitude firstly to explore its ability to reproduce reported learning changes and secondly to memory-span and phase coding effects. The spiking neural network incorporates two kinetically different GABAA receptor-mediated currents to generate both theta and gamma rhythms and we have found that by selective alteration of both NMDA receptors and GABAA,slow receptors it can reproduce learning-related changes in the strength of coupling between theta and gamma either with or without coincident changes in theta amplitude. When the model was used to explore the relationship between theta and gamma oscillations, working memory capacity and phase coding it showed that the potential storage capacity of short term memories, in terms of nested gamma-subcycles, coincides with the maximal theta power. Increasing theta power is also related to the precision of theta phase which functions as a potential timing clock for neuronal firing in the cortex or hippocampus
Characterization of cumulus cloud fields using trajectories in the center of gravity versus water mass phase space: 1. Cloud tracking and phase space description
We study the evolution of warm convective cloud fields using large eddy simulations of continental and trade cumulus. Individual clouds are tracked a posteriori from formation to dissipation using a 3‐D cloud‐tracking algorithm, and results are presented in the phase space of center of gravity altitude versus cloud liquid water mass (CvM space). The CvM space is shown to contain rich information on cloud field characteristics, cloud morphology, and common cloud development pathways, together facilitating a comprehensive understanding of the cloud field. In this part we show how the meteorological (thermodynamic) conditions that determine the cloud properties are projected on the CvM phase space and how changes in the initial conditions affect the clouds\u27 trajectories in this space. This part sets the stage for a detailed microphysical analysis that will be shown in part II
Spherical perspective
We survey the present state of spherical perspective, regarding both mathematical structure and drawing practice, with a view to applications in the visual arts. We define a spherical perspective as the entailment of a conical anamorphosis with a compact flattening of the visual sphere. We examine a general framework for solving spherical perspectives, exemplified with the azimuthal equidistant (“fisheye”) and equirectangular cases. We consider the relation between spherical and curvilinear perspectives. We briefly discuss computer renderings but focus on methods adapted to freehand sketching or technical drawing with simple instruments such as ruler and compass. We discuss how handmade spherical perspective drawings can generate immersive anamorphoses, which can be rendered as virtual reality panoramas, leading to hybrid visual creations that bridge the gap between traditional drawing and digital environments.info:eu-repo/semantics/publishedVersio
Parent formulation at the Lagrangian level
The recently proposed first-order parent formalism at the level of equations
of motion is specialized to the case of Lagrangian systems. It is shown that
for diffeomorphism-invariant theories the parent formulation takes the form of
an AKSZ-type sigma model. The proposed formulation can be also seen as a
Lagrangian version of the BV-BRST extension of the Vasiliev unfolded approach.
We also discuss its possible interpretation as a multidimensional
generalization of the Hamiltonian BFV--BRST formalism. The general construction
is illustrated by examples of (parametrized) mechanics, relativistic particle,
Yang--Mills theory, and gravity.Comment: 26 pages, discussion of the truncation extended, typos corrected,
references adde
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