215 research outputs found
The effective theory of the Calogero- Sutherland model and Luttinger systems.
We construct the effective field theory of the Calogero-Sutherland model in
the thermodynamic limit of large number of particles . It is given by a
\winf conformal field theory (with central charge ) that describes {\it
exactly} the spatial density fluctuations arising from the low-energy
excitations about the Fermi surface. Our approach does not rely on the
integrable character of the model, and indicates how to extend previous results
to any order in powers of . Moreover, the same effective theory can also
be used to describe an entire universality class of -dimensional
fermionic systems beyond the Calogero-Sutherland model, that we identify with
the class of {\it chiral Luttinger systems}. We also explain how a systematic
bosonization procedure can be performed using the \winf generators, and
propose this algebraic approach to {\it classify} low-dimensional
non-relativistic fermionic systems, given that all representations of \winf
are known. This approach has the appeal of being mathematically complete and
physically intuitive, encoding the picture suggested by Luttinger's theorem.Comment: 13 pages, plain LaTeX, no figures
The extended conformal theory of Luttinger systems
We describe the recently introduced method of algebraic bosonization of the
-dimensional Luttinger systems by discussing in detail the specific case
of the Calogero-Sutherland model, and mentioning the hard-core Bose gas. We
also compare our findings with the exact Bethe Ansatz results.Comment: 9 pages, plain Latex file, ,based on a talk given by S. Sciuto at the
II International Sakharov Conference on Physics, Moscow, Russia, 20-24 May 9
Algebraic bosonization: the study of the Heisenberg and Calogero-Sutherland models
We propose an approach to treat (1+1)--dimensional fermionic systems based on
the idea of algebraic bosonization. This amounts to decompose the elementary
low-lying excitations around the Fermi surface in terms of basic building
blocks which carry a representation of the W_{1+\infty} \times {\overline
W_{1+\infty}} algebra, which is the dynamical symmetry of the Fermi quantum
incompressible fluid. This symmetry simply expresses the local particle-number
current conservation at the Fermi surface. The general approach is illustrated
in detail in two examples: the Heisenberg and Calogero-Sutherland models, which
allow for a comparison with the exact Bethe Ansatz solution.Comment: 51 pages, plain LaTe
The extended conformal theory of the Calogero-Sutherland model
We describe the recently introduced method of Algebraic Bosonization of
(1+1)-dimensional fermionic systems by discussing the specific case of the
Calogero-Sutherland model. A comparison with the Bethe Ansatz results is also
presented.Comment: 12 pages, plain LaTeX, no figures; To appear in the proceedings of
the IV Meeting "Common Trends in Condensed Matter and High Energy Physics",
Chia Laguna, Cagliari, Italy, 3-10 Sep. 199
Gauge theory renormalizations from the open bosonic string
We present a unified point of view on the different methods available in the
literature to extract gauge theory renormalization constants from the
low-energy limit of string theory. The Bern-Kosower method, based on an
off-shell continuation of string theory amplitudes, and the construction of
low-energy string theory effective actions for gauge particles, can both be
understood in terms of strings interacting with background gauge fields, and
thus reproduce, in the low-energy limit, the field theory results of the
background field method. We present in particular a consistent off-shell
continuation of the one-loop gluon amplitudes in the open bosonic string that
reproduces exactly the results of the background field method in the Feynman
gauge.Comment: 14 pages, latex, no figure
Modular and duality properties of surface operators in N=2* gauge theories
We calculate the instanton partition function of the four-dimensional N=2*
SU(N) gauge theory in the presence of a generic surface operator, using
equivariant localization. By analyzing the constraints that arise from
S-duality, we show that the effective twisted superpotential, which governs the
infrared dynamics of the two-dimensional theory on the surface operator,
satisfies a modular anomaly equation. Exploiting the localization results, we
solve this equation in terms of elliptic and quasi-modular forms which resum
all non-perturbative corrections. We also show that our results, derived for
monodromy defects in the four-dimensional theory, match the effective twisted
superpotential describing the infrared properties of certain two-dimensional
sigma models coupled either to pure N=2 or to N=2* gauge theories.Comment: 51 pages, v3: references added, typos fixed, footnote added, some
small changes in the text, appendix B streamlined. Matches the published
versio
Non-perturbative studies of N=2 conformal quiver gauge theories
We study N=2 super-conformal field theories in four dimensions that
correspond to mass-deformed linear quivers with n gauge groups and
(bi-)fundamental matter. We describe them using Seiberg-Witten curves obtained
from an M-theory construction and via the AGT correspondence. We take
particular care in obtaining the detailed relation between the parameters
appearing in these descriptions and the physical quantities of the quiver gauge
theories. This precise map allows us to efficiently reconstruct the
non-perturbative prepotential that encodes the effective IR properties of these
theories. We give explicit expressions in the cases n=1,2, also in the presence
of an Omega-background in the Nekrasov-Shatashvili limit. All our results are
successfully checked against those of the direct microscopic evaluation of the
prepotential a la Nekrasov using localization methods.Comment: 56 pages, 7 figures, PdfLaTeX. v2: a few references added, version to
appear on Fortschritte der Physi
Surface operators in 5d gauge theories and duality relations
We study half-BPS surface operators in 5d N=1 gauge theories compactified on
a circle. Using localization methods and the twisted chiral ring relations of
coupled 3d/5d quiver gauge theories, we calculate the twisted chiral
superpotential that governs the infrared properties of these surface operators.
We make a detailed analysis of the localization integrand, and by comparing
with the results from the twisted chiral ring equations obtain constraints on
the 3d and 5d Chern-Simons levels so that the instanton partition function does
not depend on the choice of integration contour. For these values of the
Chern-Simons couplings, we comment on how the distinct quiver theories that
realize the same surface operator are related to each other by Aharony-Seiberg
dualities.Comment: 39 pages. v2: A few sentences rephrased, references added, and typos
corrected. Matches version published in JHE
Trace checking of Metric Temporal Logic with Aggregating Modalities using MapReduce
Modern complex software systems produce a large amount of execution data,
often stored in logs. These logs can be analyzed using trace checking
techniques to check whether the system complies with its requirements
specifications. Often these specifications express quantitative properties of
the system, which include timing constraints as well as higher-level
constraints on the occurrences of significant events, expressed using aggregate
operators. In this paper we present an algorithm that exploits the MapReduce
programming model to check specifications expressed in a metric temporal logic
with aggregating modalities, over large execution traces. The algorithm
exploits the structure of the formula to parallelize the evaluation, with a
significant gain in time. We report on the assessment of the implementation -
based on the Hadoop framework - of the proposed algorithm and comment on its
scalability.Comment: 16 pages, 6 figures, Extended version of the SEFM 2014 pape
The Lorentz force between D0 and D6 branes in string and M(atrix) theory
We use different techniques to analyze the system formed by a D0 brane and a
D6 brane (with background gauge fields) in relative motion. In particular,
using the closed string formalism of boosted boundary states, we show the
presence of a term linear in the velocity, corresponding to the Lorentz force
experienced by the D0 brane moving in the magnetic background produced by the
D6 brane. This term, that was missed in previous analyses of this system, comes
entirely from the R-R odd spin structure and is also reproduced by a M(atrix)
theory calculation.Comment: 13 pages, plain LaTeX; some clarifying comments and a reference adde
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