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 $\phi^3$ model of Ising magnets with explicitly broken symmetry. Our Ward-Takahashi identities imply trivial dynamical exponents $z_\ast = 2$ 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 ``$\phi^3$-property'', we predict new flows in non-unitary minimal models.Comment: (7 pages) (no figures included