1,588 research outputs found
WDVV equations for 6d Seiberg-Witten theory and bi-elliptic curves
We present a generic derivation of the WDVV equations for 6d Seiberg-Witten
theory, and extend it to the families of bi-elliptic spectral curves. We find
that the elliptization of the naive perturbative and nonperturbative 6d systems
roughly "doubles" the number of moduli describing the system.Comment: 24 page
On Charge-3 Cyclic Monopoles
We determine the spectral curve of charge 3 BPS su(2) monopoles with C_3
cyclic symmetry. The symmetry means that the genus 4 spectral curve covers a
(Toda) spectral curve of genus 2. A well adapted homology basis is presented
enabling the theta functions and monopole data of the genus 4 curve to be given
in terms of genus 2 data. The Richelot correspondence, a generalization of the
arithmetic mean, is used to solve for this genus 2 curve. Results of other
approaches are compared.Comment: 34 pages, 16 figures. Revision: Abstract added and a few small
change
Non-perturbative renormalization group analysis of nonlinear spiking networks
The critical brain hypothesis posits that neural circuits may operate close
to critical points of a phase transition, which has been argued to have
functional benefits for neural computation. Theoretical and computational
studies arguing for or against criticality in neural dynamics largely rely on
establishing power laws or scaling functions of statistical quantities, while a
proper understanding of critical phenomena requires a renormalization group
(RG) analysis. However, neural activity is typically non-Gaussian, nonlinear,
and non-local, rendering models that capture all of these features difficult to
study using standard statistical physics techniques. Here, we overcome these
issues by adapting the non-perturbative renormalization group (NPRG) to work on
(symmetric) network models of stochastic spiking neurons. By deriving a pair of
Ward-Takahashi identities and making a ``local potential approximation,'' we
are able to calculate non-universal quantities such as the effective firing
rate nonlinearity of the network, allowing improved quantitative estimates of
network statistics. We also derive the dimensionless flow equation that admits
universal critical points in the renormalization group flow of the model, and
identify two important types of critical points: in networks with an absorbing
state there is Directed Percolation (DP) fixed point corresponding to a
non-equilibrium phase transition between sustained activity and extinction of
activity, and in spontaneously active networks there is a \emph{complex valued}
critical point, corresponding to a spinodal transition observed, e.g., in the
Lee-Yang model of Ising magnets with explicitly broken symmetry. Our
Ward-Takahashi identities imply trivial dynamical exponents in
both cases, rendering it unclear whether these critical points fall into the
known DP or Ising universality classes
Comment on ''Understanding the Area Proposal for Extremal Black Hole Entropy''
A. Ghosh and P. Mitra made the proposal how to explain the area law for the
entropy of extreme black holes in some model calculations. I argue that their
approach implicitly operates with strongly singular geometries and says nothing
about the contribution of regular metrics of extreme black holes into the
partition function.Comment: 5 pages, ReVTeX, no figures. Expanded from the journal version to
include response to Ghosh and Mitra Reply
Temperature Dependence of Interlayer Magnetoresistance in Anisotropic Layered Metals
Studies of interlayer transport in layered metals have generally made use of
zero temperature conductivity expressions to analyze angle-dependent
magnetoresistance oscillations (AMRO). However, recent high temperature AMRO
experiments have been performed in a regime where the inclusion of finite
temperature effects may be required for a quantitative description of the
resistivity. We calculate the interlayer conductivity in a layered metal with
anisotropic Fermi surface properties allowing for finite temperature effects.
We find that resistance maxima are modified by thermal effects much more
strongly than resistance minima. We also use our expressions to calculate the
interlayer resistivity appropriate to recent AMRO experiments in an overdoped
cuprate which led to the conclusion that there is an anisotropic, linear in
temperature contribution to the scattering rate and find that this conclusion
is robust.Comment: 8 pages, 4 figure
Renormalization group trajectories from resonance factorized S-matrices
We propose and investigate a large class of models possessing resonance
factorized S-matrices. The associated Casimir energy describes a rich pattern
of renormalization group trajectories related to flows in the coset models
based on the simply laced Lie Algebras. From a simplest resonance S-matrix,
satisfying the ``-property'', we predict new flows in non-unitary
minimal models.Comment: (7 pages) (no figures included
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