arXiv subjects

Carlos Cardona

Publications and source records attributed to Carlos Cardona.

At least 19 recordsLinked to original sources

arXiv2023

Scaling and Resizing Symmetry in Feedforward Networks

Weights initialization in deep neural networks have a strong impact on the speed of converge of the learning map. Recent studies have shown that in the case of random initializations, a chaos/order phase transition occur in the space of variances of random weights and biases. Experiments then had shown that large improvements can be made, in terms of the training speed, if a neural network is initialized on values along the critical line of such phase transition. In this contribution, we show evidence that the scaling property exhibited by physical systems at criticality, is also present in untrained feedforward networks with random weights initialization at the critical line. Additionally, we suggest an additional data-resizing symmetry, which is directly inherited from the scaling symmetry at criticality.

cs.LG↗

arXiv2021

Four-point correlation modular bootstrap for OPE densities

In this work we apply the lightcone bootstrap to a four-point function of scalars in two-dimensional conformal field theory. We include the entire Virasoro symmetry and consider non-rational theories with a gap in the spectrum from the vacuum and no conserved currents. For those theories, we compute the large dimension limit (h/c>>1) of the OPE spectral decomposition of the Virasoro vacuum. We then propose a kernel ansatz that generalizes the spectral decomposition beyond h/c>>1. Finally, we estimate the corrections to the OPE spectral densities from the inclusion of the lightest operator in the spectrum.

hep-th↗

arXiv2021

The neutrino gravitational memory from a core collapse supernova: phenomenology and physics potential

General Relativity predicts that the passage of matter or radiation from an asymmetrically-emitting source should cause a permanent change in the local space-time metric. This phenomenon, called the \emph{gravitational memory effect}, has never been observed, however supernova neutrinos have long been considered a promising avenue for its detection in the future. With the advent of deci-Hertz gravitational wave interferometers, observing the supernova neutrino memory will be possible, with important implications for multimessenger astronomy and for tests of gravity. In this work, we develop a phenomenological (analytical) toy model for the supernova neutrino memory effect, which is overall consistent with the results of numerical simulations. This description is then generalized to several case studies of interest. We find that, for a galactic supernova, the dimensionless strain, $h(t)$, is of order $\sim 10^{-22} - 10^{-21}$, and develops over a typical time scale that varies between $\sim 0.1 - 10$ s, depending on the time-evolution of the anisotropy of the neutrino emission. The characteristic strain, $h_c(f)$, has a maximum at a frequency $f_{max} \sim {\mathcal O}(10^{-1}) - {\mathcal O}(1)$ Hz. The detailed features of the time- and frequency-structure of the memory strain will inform us of the matter dynamics near the collapsed core, and allow to distinguish between different stellar collapse scenarios. Next generation gravitational wave detectors like DECIGO and BBO will be sensitive to the neutrino memory effect for supernovae at typical galactic distances and beyond; with Ultimate DECIGO exceeding a detectability distance of 10 Mpc.

astro-ph.HE↗

arXiv2021

Instability of a uniform electric field in pure non-Abelian Yang-Mills theory

We study the Schwinger process in a uniform non-Abelian electric field using a dynamical approach in which we evolve an initial quantum state for gluonic excitations. We evaluate the spectral energy density and number density in the excitations as functions of time. The total energy density has an ultraviolet divergence which we argue gets tamed due to asymptotic freedom, leading to $g^4E^4t^4$ growth, where $g$ is the coupling and $E$ the electric field strength. We also find an infrared divergence in the number density of excitations whose resolution requires an effect such as confinement.

hep-th↗

arXiv2020

Virasoro blocks at large exchange dimension

In this paper, we analyze Virasoro conformal blocks in the limit when the operator exchange dimension is taking to be large in comparison with the other parameters dependence of the block. We do this by using Zamolodchikov's recursion relations. We found a dramatically simplified solution at leading order in an inverse power expansion in large exchange conformal dimension in terms of a quasi-modular form in an Eisenstein series representation. We compare this solution with existing results obtained previously by using AGT correspondence.

hep-th↗

arXiv2019

Correlation functions at the bulk point singularity from the gravitational eikonal S-matrix

The bulk point singularity limit of conformal correlation functions in Lorentzian signature acts as a microscope to look into local bulk physics in AdS. From it we can extract flat space scattering processes localized in AdS that ultimate should be related to corresponding observables on the conformal field theory at the boundary. In this paper we use this interesting property to propose a map from flat space s-matrix to conformal correlation functions and try it on perturbative gravitational scattering. In particular, we show that the eikonal limit of gravitation scattering maps to a correlation function of the expected form at the bulk point singularity. We also compute the inverse map recovering a previous proposal in the literature.

hep-th↗

arXiv2019

Resummation at finite conformal spin

We generalize the computation of anomalous dimension and correction to OPE coefficients at finite conformal spin considered recently in \cite{arXiv:1806.10919, arXiv:1808.00612} to arbitrary space-time dimensions. By using the inversion formula of Caron-Huot and the integral (Mellin) representation of conformal blocks, we show that the contribution from individual exchanges to anomalous dimensions and corrections to the OPE coefficients for "double-twist" operators $[\mathcal{O}_1\mathcal{O}_2]_{Δ,J}$ in $s-$channel can be written at finite conformal spin in terms of generalized Wilson polynomials. This approach is democratic {\it wrt} space-time dimensions, thus generalizing the earlier findings to cases where closed form expressions of the conformal blocks are not available.

hep-th↗

arXiv2018

Anomalous dimensions at finite conformal spin from OPE inversion

We compute anomalous dimensions of higher spin operators in Conformal Field Theory at arbitrary space-time dimension by using the OPE inversion formula of \cite{Caron-Huot:2017vep}, both from the position space representation as well as from the integral (viz. Mellin) representation of the conformal blocks. The Mellin space is advantageous over the position space not only in allowing to write expressions agnostic to the space-time dimension, but also in that it replaces tedious recursion relations in terms of simple sums which are easy to perform. We evaluate the contributions of scalar and spin exchanges in the $t-$channel exactly, in terms of higher order Hypergeometric functions. These relate to a particular exchange of conformal spin $β=Δ+J$ in the $s-$channel through the inversion formula. Our exact results reproduce the special cases for large spin anomalous dimension and OPE coefficients obtained previously in the literature.

hep-th↗

arXiv2018

OPE inversion in Mellin space

The fundamental ingredients that build the observables in conformal field theory are the spectrum of operators and the OPE coefficients, or equivalently, the two- and three-point functions of the theory. Recently an inversion formula solving the OPE coefficients by a convolution over the light-cone double-discontinuities of the correlator has been found by Simon Caron-Huot. Taking into account that the same OPE data determine the Mellin amplitude representation of the correlator, motivate us to look for an analogous inversion formula in Mellin space, which we develops partially on this paper.

hep-th↗

arXiv2017

Mellin-(Schwinger) representation of One-loop Witten diagrams in AdS

In this paper we consider Witten diagrams at one loop in AdS space for scalar $ϕ^3+ϕ^4$ theory. After using Schwinger parametrization to trivialize the space-time loop integration, we extract the Mellin-Barnes representation for the one-loop corrections to the four-particle scattering up to an integration over the Schwinger parameters corresponding to the propagators of the internal particles running into the loop. We then discuss an approach to deal with those integrals.

hep-th↗

arXiv2017

S-matrix singularities and CFT correlation functions

In this note, we explore the correspondence between four-dimensional flat space S-matrix and two-dimensional CFT proposed by Pasterski et al. We demonstrate that the factorization singularities of an n-point cubic diagram reproduces the AdS Witten diagrams if mass conservation is imposed at each vertex. Such configuration arises naturally if we consider the 4-dimensional S-matrix as a compactified massless 5-dimensional theory. This identification allows us to rewrite the massless S-matrix in the CHY formulation, where the factorization singularities are re-interpreted as factorization limits of a Riemann sphere. In this light, the map is recast into a form of 2d/2d correspondence.

hep-th↗

arXiv2016

On the linearity of Regge trajectory at large transfer energy

In this note we consider the four-point function of identical scalar operators in its Mellin representation. For CFTs, taking the large scaling dimension limit of the Mellin amplitude yields the flat-space S-matrix. Using this correspondence, and assuming that the Regge-limit of the Mellin amplitude vanishes, we prove that the resulting flat space S-matrix must have string-like linear Regge trajectory in the limit |s|>>|t|>>1. We also show that the Regge limit of Mellin amplitude is captured by the three-point coefficient of two scalars and one double trace operator in the large-spin limit. Using this, we can see that vanishing Regge behaviour occurs at small t'Hooft limit.

hep-th↗

arXiv2016

CHY-Graphs on a Torus

Recently, we proposed a new approach using a punctured Elliptic curve in the CHY framework in order to compute one-loop scattering amplitudes. In this note, we further develop this approach by introducing a set of connectors, which become the main ingredient to build integrands on $\mathfrak{M}_{1,n}$, the moduli space of n-punctured Elliptic curves. As a particular application, we study the $Φ^3$ bi-adjoint scalar theory. We propose a set of rules to construct integrands on $\mathfrak{M}_{1,n}$ from $Φ^ 3$ integrands on $\mathfrak{M}_{0,n}$, the moduli space of n-punctured spheres. We illustrate these rules by computing a variety of $Φ^3$ one-loop Feynman diagrams. Conversely, we also provide another set of rules to compute the corresponding CHY-integrand on $\mathfrak{M}_{1,n}$ by starting instead from a given $Φ^ 3$ one-loop Feynman diagram. In addition, our results can easily be extended to higher loops.

hep-th↗

arXiv2016

Elliptic scattering equations

Recently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is totally algebraic. This new proposal is based on an elliptic algebraic curve embedded in a $\mathbb{C}P^2$ space. We show that for the simplest integrand, namely the ${\rm n-gon}$, our proposal indeed reproduces the expected result. By using the recently formulated $Λ-$algorithm, we found a novel recurrence relation expansion in terms of tree level off-shell amplitudes. Our results connect nicely with recent results on the one-loop formulation of the scattering equations. In addition, this new proposal can be easily stretched out to hyperelliptic curves in order to compute higher genus.

hep-th↗

arXiv2016

Cross-ratio Identities and Higher-order Poles of CHY-integrand

The evaluation of generic Cachazo-He-Yuan(CHY)-integrands is a big challenge and efficient computational methods are in demand for practical evaluation. In this paper, we propose a systematic decomposition algorithm by using cross-ratio identities, which provides an analytic and easy to implement method for the evaluation of any CHY-integrand. This algorithm aims to decompose a given CHY-integrand containing higher-order poles as a linear combination of CHY-integrands with only simple poles in a finite number of steps, which ultimately can be trivially evaluated by integration rules of simple poles. To make the method even more efficient for CHY-integrands with large number of particles and complicated higher-order pole structures, we combine the $Λ$-algorithm and the cross-ratio identities, and as a by-product it provides us a way to deal with CHY-integrands where the $Λ$-algorithm was not applicable in its original formulation.

hep-th↗

arXiv2016

Elimination and recursions in the scattering equations

We use the elimination theory to explicitly construct the (n-3)! order polynomial in one of the variables of the scattering equations. The answer can be given either in terms of a determinant of Sylvester type of dimension (n-3)! or a determinant of Bézout type of dimension (n-4)!. We present a recursive formula for the Sylvester determinant. Expansion of the determinants yields expressions in terms of Plücker coordinates. Elimination of the rest of the variables of the scattering equations is also presented.

hep-th↗

arXiv2016

Comments on the evaluation of massless scattering

The goal of this work is threefold. First, we give an expression of the most general five point integral on M_{0,n} in terms of Chebyshev polynomials. Second, we choose a special kinematics that transforms the polynomial form of the scattering equations to a linear system of symmetric polynomials. We then explain how this can be used to explicitly evaluate arbitrary point integrals on M_{0,n}. Third, we comment on the recently presented method of companion matrices and we show its equivalence to the elimination theory and an algorithm previously developed by one of the authors.

hep-th↗

arXiv2015

Asymptotic Symmetries of Yang-Mills with Theta Term and Monopoles

In this short note we suggest that the singular behavior of large gauge transformations preserving the vacuum at null infinity in Yang-Mills theory implies monopoles into the bulk, as well as that the inclusion of a theta term induces a decoupling between holomorphic and anti-holomorphic currents associated to those large gauge transformations

hep-th↗