The Hamiltonian Structure of Soliton Equations and Deformed W-Algebras

The Poisson bracket algebra corresponding to the second Hamiltonian structure of a large class of generalized KdV and mKdV integrable hierarchies is carefully analysed. These algebras are known to have conformal properties, and their relation to $\cal W$-algebras has been previously investigated in some particular cases. The class of equations that is considered includes practically all the generalizations of the Drinfel'd-Sokolov hierarchies constructed in the literature. In particular, it has been recently shown that it includes matrix generalizations of the Gelfand-Dickey and the constrained KP hierarchies. Therefore, our results provide a unified description of the relation between the Hamiltonian structure of soliton equations and $\cal W$-algebras, and it comprises almost all the results formerly obtained by other authors. The main result of this paper is an explicit general equation showing that the second Poisson bracket algebra is a deformation of the Dirac bracket algebra corresponding to the $\cal W$-algebras obtained through Hamiltonian reduction.Comment: 41 pages, plain TeX, no figures. New introduction and references added. Version to be published in Annals of Physics (N.Y.

Semi-classical spectrum of the Homogeneous sine-Gordon theories

The semi-classical spectrum of the Homogeneous sine-Gordon theories associated with an arbitrary compact simple Lie group G is obtained and shown to be entirely given by solitons. These theories describe quantum integrable massive perturbations of Gepner's G-parafermions whose classical equations-of-motion are non-abelian affine Toda equations. One-soliton solutions are constructed by embeddings of the SU(2) complex sine-Gordon soliton in the regular SU(2) subgroups of G. The resulting spectrum exhibits both stable and unstable particles, which is a peculiar feature shared with the spectrum of monopoles and dyons in N=2 and N=4 supersymmetric gauge theories.Comment: 28 pages, plain TeX, no figure

Tau-Functions generating the Conservation Laws for Generalized Integrable Hierarchies of KdV and Affine-Toda type

For a class of generalized integrable hierarchies associated with affine (twisted or untwisted) Kac-Moody algebras, an explicit representation of their local conserved densities by means of a single scalar tau-function is deduced. This tau-function acts as a partition function for the conserved densities, which fits its potential interpretation as the effective action of some quantum system. The class consists of multi-component generalizations of the Drinfel'd-Sokolov and the two-dimensional affine Toda lattice hierarchies. The relationship between the former and the approach of Feigin, Frenkel and Enriquez to soliton equations of KdV and mKdV type is also discussed. These results considerably simplify the calculation of the conserved charges carried by the soliton solutions to the equations of the hierarchy, which is important to establish their interpretation as particles. By way of illustration, we calculate the charges carried by a set of constrained KP solitons recently constructed.Comment: 47 pages, plain TeX with AMS fonts, no figure

Solitonic Integrable Perturbations of Parafermionic Theories

The quantum integrability of a class of massive perturbations of the parafermionic conformal field theories associated to compact Lie groups is established by showing that they have quantum conserved densities of scale dimension 2 and 3. These theories are integrable for any value of a continuous vector coupling constant, and they generalize the perturbation of the minimal parafermionic models by their first thermal operator. The classical equations-of-motion of these perturbed theories are the non-abelian affine Toda equations which admit (charged) soliton solutions whose semi-classical quantization is expected to permit the identification of the exact S-matrix of the theory.Comment: 18 pages, plain TeX, no figure

PMCTrack: Delivering performance monitoring counter support to the OS scheduler

Hardware performance monitoring counters (PMCs) have proven effective in characterizing application performance. Because PMCs can only be accessed directly at the OS privilege level, kernellevel tools must be developed to enable the end-user and userspace programs to access PMCs. A large body of work has demonstrated that the OS can perform effective runtime optimizations in multicore systems by leveraging performance-counter data. Special attention has been paid to optimizations in the OS scheduler. While existing performance monitoring tools greatly simplify the collection of PMC application data from userspace, they do not provide an architecture-agnostic kernel-level mechanism that is capable of exposing high-level PMC metrics to OS components, such as the scheduler. As a result, the implementation of PMC-based OS scheduling schemes is typically tied to specific processor models. To address this shortcoming we present PMCTrack, a novel tool for the Linux kernel that provides a simple architecture-independent mechanism that makes it possible for the OS scheduler to access per-thread PMC data. Despite being an OSoriented tool, PMCTrack still allows the gathering of monitoring data from userspace, enabling kernel developers to carry out the necessary offline analysis and debugging to assist them during the scheduler design process. In addition, the tool provides both the OS and the user-space PMCTrack components with other insightful metrics available in modern processors and which are not directly exposed as PMCs, such as cache occupancy or energy consumption. This information is also of great value when it comes to analyzing the potential benefits of novel scheduling policies on real systems. In this paper, we analyze different case studies that demonstrate the flexibility, simplicity and powerful features of PMCTrack.Facultad de InformáticaInstituto de Investigación en Informátic

PMCTrack: Delivering performance monitoring counter support to the OS scheduler

Hardware performance monitoring counters (PMCs) have proven effective in characterizing application performance. Because PMCs can only be accessed directly at the OS privilege level, kernellevel tools must be developed to enable the end-user and userspace programs to access PMCs. A large body of work has demonstrated that the OS can perform effective runtime optimizations in multicore systems by leveraging performance-counter data. Special attention has been paid to optimizations in the OS scheduler. While existing performance monitoring tools greatly simplify the collection of PMC application data from userspace, they do not provide an architecture-agnostic kernel-level mechanism that is capable of exposing high-level PMC metrics to OS components, such as the scheduler. As a result, the implementation of PMC-based OS scheduling schemes is typically tied to specific processor models. To address this shortcoming we present PMCTrack, a novel tool for the Linux kernel that provides a simple architecture-independent mechanism that makes it possible for the OS scheduler to access per-thread PMC data. Despite being an OSoriented tool, PMCTrack still allows the gathering of monitoring data from userspace, enabling kernel developers to carry out the necessary offline analysis and debugging to assist them during the scheduler design process. In addition, the tool provides both the OS and the user-space PMCTrack components with other insightful metrics available in modern processors and which are not directly exposed as PMCs, such as cache occupancy or energy consumption. This information is also of great value when it comes to analyzing the potential benefits of novel scheduling policies on real systems. In this paper, we analyze different case studies that demonstrate the flexibility, simplicity and powerful features of PMCTrack.Facultad de InformáticaInstituto de Investigación en Informátic

T-duality in Massive Integrable Field Theories: The Homogeneous and Complex sine-Gordon Models

The T-duality symmetries of a family of two-dimensional massive integrable field theories defined in terms of asymmetric gauged Wess-Zumino-Novikov-Witten actions modified by a potential are investigated. These theories are examples of massive non-linear sigma models and, in general, T-duality relates two different dual sigma models perturbed by the same potential. When the unperturbed theory is self-dual, the duality transformation relates two perturbations of the same sigma model involving different potentials. Examples of this type are provided by the Homogeneous sine-Gordon theories, associated with cosets of the form G/U(1)^r where G is a compact simple Lie group of rank r. They exhibit a duality transformation for each element of the Weyl group of G that relates two different phases of the model. On-shell, T-duality provides a map between the solutions to the equations of motion of the dual models that changes Noether soliton charges into topological ones. This map is carefully studied in the complex sine-Gordon model, where it motivates the construction of Bogomol'nyi-like bounds for the energy that provide a novel characterisation of the already known one-solitons solutions where their classical stability becomes explicit.Comment: 29 pages, LaTe