10,859 research outputs found
Ramification points of Seiberg-Witten curves
When the Seiberg-Witten curve of a four-dimensional N = 2 supersymmetric gauge theory wraps a Riemann surface as a multi-sheeted cover, a topological constraint requires that in general the curve should develop ramification points. We show that, while some of the branch points of the covering map can be identified with the punctures that appear in the work of Gaiotto, the ramification points give us additional branch points whose locations on the Riemann surface can have dependence not only on gauge coupling parameters but on Coulomb branch parameters and mass parameters of the theory. We describe how these branch points can help us to understand interesting physics in various limits of the parameters, including Argyres-Seiberg duality and Argyres-Douglas fixed points
ADE Spectral Networks
We introduce a new perspective and a generalization of spectral networks for
4d theories of class associated to Lie algebras
, , , and
. Spectral networks directly compute the BPS spectra of 2d
theories on surface defects coupled to the 4d theories. A Lie algebraic
interpretation of these spectra emerges naturally from our construction,
leading to a new description of 2d-4d wall-crossing phenomena. Our construction
also provides an efficient framework for the study of BPS spectra of the 4d
theories. In addition, we consider novel types of surface defects associated
with minuscule representations of .Comment: 68 pages plus appendices; visit
http://het-math2.physics.rutgers.edu/loom/ to use 'loom,' a program that
generates spectral networks; v2: version published in JHEP plus minor
correction
BPS Graphs: From Spectral Networks to BPS Quivers
We define "BPS graphs" on punctured Riemann surfaces associated with
theories of class . BPS graphs provide a bridge between
two powerful frameworks for studying the spectrum of BPS states: spectral
networks and BPS quivers. They arise from degenerate spectral networks at
maximal intersections of walls of marginal stability on the Coulomb branch.
While the BPS spectrum is ill-defined at such intersections, a BPS graph
captures a useful basis of elementary BPS states. The topology of a BPS graph
encodes a BPS quiver, even for higher-rank theories and for theories with
certain partial punctures. BPS graphs lead to a geometric realization of the
combinatorics of Fock-Goncharov -triangulations and generalize them in
several ways.Comment: 48 pages, 44 figure
Axion as a cold dark matter candidate: low-mass case
Axion as a coherently oscillating scalar field is known to behave as a cold
dark matter in all cosmologically relevant scales. For conventional axion mass
with 10^{-5} eV, the axion reveals a characteristic damping behavior in the
evolution of density perturbations on scales smaller than the solar system
size. The damping scale is inversely proportional to the square-root of the
axion mass. We show that the axion mass smaller than 10^{-24} eV induces a
significant damping in the baryonic density power spectrum in cosmologically
relevant scales, thus deviating from the cold dark matter in the scale smaller
than the axion Jeans scale. With such a small mass, however, our basic
assumption about the coherently oscillating scalar field is broken in the early
universe. This problem is shared by other dark matter models based on the
Bose-Einstein condensate and the ultra-light scalar field. We introduce a
simple model to avoid this problem by introducing evolving axion mass in the
early universe, and present observational effects of present-day low-mass axion
on the baryon density power spectrum, the cosmic microwave background radiation
(CMB) temperature power spectrum, and the growth rate of baryon density
perturbation. In our low-mass axion model we have a characteristic small-scale
cutoff in the baryon density power spectrum below the axion Jeans scale. The
small-scale deviations from the cold dark matter model in both matter and CMB
power spectra clearly differ from the ones expected in the cold dark matter
model mixed with the massive neutrinos as a hot dark matter component.Comment: 9 pages, 8 figure
Universality class of the restricted solid-on-solid model with hopping
We study the restricted solid-on-solid (RSOS) model with finite hopping
distance , using both analytical and numerical methods. Analytically, we
use the hard-core bosonic field theory developed by the authors [Phys. Rev. E
{\bf 62}, 7642 (2000)] and derive the Villain-Lai-Das Sarma (VLD) equation for
the case which corresponds to the conserved RSOS (CRSOS) model
and the Kardar-Parisi-Zhang (KPZ) equation for all finite values of .
Consequently, we find that the CRSOS model belongs to the VLD universality
class and the RSOS models with any finite hopping distance belong to the KPZ
universality class. There is no phase transition at a certain finite hopping
distance contrary to the previous result. We confirm the analytic results using
the Monte Carlo simulations for several values of the finite hopping distance.Comment: 13 pages, 3 figure
Derivation of continuum stochastic equations for discrete growth models
We present a formalism to derive the stochastic differential equations (SDEs)
for several solid-on-solid growth models. Our formalism begins with a mapping
of the microscopic dynamics of growth models onto the particle systems with
reactions and diffusion. We then write the master equations for these
corresponding particle systems and find the SDEs for the particle densities.
Finally, by connecting the particle densities with the growth heights, we
derive the SDEs for the height variables. Applying this formalism to discrete
growth models, we find the Edwards-Wilkinson equation for the symmetric
body-centered solid-on-solid (BCSOS) model, the Kardar-Parisi-Zhang equation
for the asymmetric BCSOS model and the generalized restricted solid-on-solid
(RSOS) model, and the Villain--Lai--Das Sarma equation for the conserved RSOS
model. In addition to the consistent forms of equations for growth models, we
also obtain the coefficients associated with the SDEs.Comment: 5 pages, no figur
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