23,491 research outputs found
Quantum parameter space in super Yang-Mills, II
In [1] (hep-th/0211069), the author has discussed the quantum parameter space
of the N=1 super Yang-Mills theory with one adjoint Higgs field Phi, tree-level
superpotential W_tree = m (Phi^2)/2 + g (Phi^3)/3$, and gauge group U(Nc). In
particular, full details were worked out for U(2) and U(3). By discussing
higher rank gauge groups like U(4), for which the classical parameter space has
a large number of disconnected components, we show that the phenomena discussed
in [1] are generic. It turns out that the quantum space is connected. The
classical components are related in the quantum theory either through standard
singularities with massless monopoles or by branch cuts without going through
any singularity. The branching points associated with the branch cuts
correspond to new strong coupling singularities, which are not associated with
vanishing cycles in the geometry, and at which glueballs can become massless.
The transitions discussed recently by Cachazo, Seiberg and Witten are special
instances of those phenomena.Comment: 12 pages including 2 large figure
A Conditional Random Field for Multiple-Instance Learning
We present MI-CRF, a conditional random field (CRF) model for multiple instance learning (MIL). MI-CRF models bags as nodes in a CRF with instances as their states. It combines discriminative unary instance classifiers and pairwise dissimilarity measures. We show that both forces improve the classification performance. Unlike other approaches, MI-CRF considers all bags jointly during training as well as during testing. This makes it possible to classify test bags in an imputation setup. The parameters of MI-CRF are learned using constraint generation. Furthermore, we show that MI-CRF can incorporate previous MIL algorithms to improve on their results. MI-CRF obtains competitive results on five standard MIL datasets. 1
Operator Formalism for Bosonic Beta-Gamma Fields on General Algebraic Curves
An operator formalism for bosonic systems on arbitrary
algebraic curves is introduced. The classical degrees of freedom are identified
and their commutation relations are postulated. The explicit realization of the
algebra formed by the fields is given in a Hilbert space equipped with a
bilinear form. The construction is based on the "gaussian" representation for
systems on the complex sphere [Alvarez-Gaum\' e et al, Nucl.
Phys. B 311 (1988) 333]. Detailed computations are provided for the two and
four points correlation functions.Comment: 26 pages, plain TeX + harvma
An algebraic approach to modeling distributed multiphysics problems: The case of a DRI reactor
© 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.This paper deals with the problem of modelling a chemical reactor for the Direct Reduction of Iron ore (DRI). Such a process is being increasingly promoted as a more viable alternative to the classic Blast Furnace for the production of iron from raw minerals. Due to the inherent complexity of the process and the reactor itself, its effective monitoring and control requires advanced mathematical models containing distributed-parameter components. While classical approaches such as Finite Element or Finite Differences are still reasonable options, for accuracy and computational efficiency reasons, an algebraic approach is proposed. A full multi-physical, albeit one-dimensional model is addressed and its accuracy is analysed
A Symmetric Approach to the Massive Nonlinear Sigma Model
In the present paper we extend to the massive case the procedure of
divergences subtraction, previously introduced for the massless nonlinear sigma
model (D=4). Perturbative expansion in the number of loops is successfully
constructed. The resulting theory depends on the Spontaneous Symmetry Breaking
parameter v, on the mass m and on the radiative correction parameter \Lambda.
Fermions are not considered in the present work. SU(2) X SU(2) is the group
used.Comment: 20 page
On the asymmetric zero-range in the rarefaction fan
We consider the one-dimensional asymmetric zero-range process starting from a
step decreasing profile. In the hydrodynamic limit this initial condition leads
to the rarefaction fan of the associated hydrodynamic equation. Under this
initial condition and for totally asymmetric jumps, we show that the weighted
sum of joint probabilities for second class particles sharing the same site is
convergent and we compute its limit. For partially asymmetric jumps we derive
the Law of Large Numbers for the position of a second class particle under the
initial configuration in which all the positive sites are empty, all the
negative sites are occupied with infinitely many first class particles and with
a single second class particle at the origin. Moreover, we prove that among the
infinite characteristics emanating from the position of the second class
particle, this particle chooses randomly one of them. The randomness is given
in terms of the weak solution of the hydrodynamic equation through some sort of
renormalization function. By coupling the zero-range with the exclusion process
we derive some limiting laws for more general initial conditions.Comment: 22 pages, to appear in Journal of Statistical Physic
Matrix Models, Argyres-Douglas singularities and double scaling limits
We construct an N=1 theory with gauge group U(nN) and degree n+1 tree level
superpotential whose matrix model spectral curve develops an A_{n+1}
Argyres-Douglas singularity. We evaluate the coupling constants of the
low-energy U(1)^n theory and show that the large N expansion is singular at the
Argyres-Douglas points. Nevertheless, it is possible to define appropriate
double scaling limits which are conjectured to yield four dimensional
non-critical string theories as proposed by Ferrari. In the Argyres-Douglas
limit the n-cut spectral curve degenerates into a solution with n/2 cuts for
even n and (n+1)/2 cuts for odd n.Comment: 31 pages, 1 figure; the expression of the superpotential has been
corrected and the calculation of the coupling constants of the low-energy
theory has been adde
Anisotropic KPZ growth in 2+1 dimensions: fluctuations and covariance structure
In [arXiv:0804.3035] we studied an interacting particle system which can be
also interpreted as a stochastic growth model. This model belongs to the
anisotropic KPZ class in 2+1 dimensions. In this paper we present the results
that are relevant from the perspective of stochastic growth models, in
particular: (a) the surface fluctuations are asymptotically Gaussian on a
sqrt(ln(t)) scale and (b) the correlation structure of the surface is
asymptotically given by the massless field.Comment: 13 pages, 4 figure
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