arXiv subjects

Marcus A. C. Torres

Publications and source records attributed to Marcus A. C. Torres.

15 recordsLinked to original sources

arXiv2018

Metric in the moduli of SU(2) monopoles from spectral curves and Gauss-Manin connection in disguise

We show here that from the metric of the manifold $M^0_2$ , i.e., the reduced moduli of SU(2) 2-monopoles in Yang-Mills-Higgs theory, one can recover the respective moduli of spectral curves using the method Gauss-Manin connection in disguise. This work is a step towards creating a inverse process of finding the metric of any $M^0_k$ , from spectral curves. This is a thirty years old problem that we hope to shed some light in it.

math-ph↗

arXiv2018

Manifold Ways to Darboux-Halphen System

Many distinct problems give birth to Darboux-Halphen system of differential equations and here we review some of them. The first is the classical problem presented by Darboux and later solved by Halphen concerning finding infinite number of double orthogonal surfaces in $\mathbb{R}^3$. The second is a problem in general relativity about gravitational instanton in Bianchi IX metric space. The third problem stems from the new take on the moduli of enhanced elliptic curves called Gauss-Manin connection in disguise developed by one of the authors and finally in the last problem Darboux-Halphen system emerges from the associative algebra on the tangent space of a Frobenius manifold.

math.DG↗

arXiv2017

Cluster Algebras in Kinematic Space of Scattering Amplitudes

We clarify the natural cluster algebra of type A that exists in a residual and tropical form in the kinematical space as suggested in 1711.09102 by the use of triangulations, mutations and associahedron on the definition of scattering forms. We also show that this residual cluster algebra is preserved in a hypercube (diamond) necklace inside the associahedron where cluster sub-algebras $(A_1)^n$ exist. This result goes in line with results with cluster poligarithms in 1401.6446 written in terms of $A_2$ and $A_3$ functions only and other works showing the primacy of $A$ cluster sub-algebras as data input for scattering amplitudes.

hep-th↗

arXiv2014

Angular structure of the in-medium QCD cascade

We study the angular broadening of a medium-induced QCD cascade. We derive the equation that governs the evolution of the average transverse momentum squared of the gluons in the cascade as a function of the medium length, and we solve this equation analytically. Two regimes are identified. For a medium of a not too large size, and for not too soft gluons, the transverse momentum grows with the size of the medium according to standard momentum broadening. The other regime, visible for a medium of a sufficiently large size and very soft gluons, is a regime dominated by multiple branchings: there, the average transverse momentum saturates to a value that is independent of the size of the medium. This structure of the in-medium QCD cascade is, at least qualitatively, compatible with the recent data on dijet asymmetry.

hep-ph↗

arXiv2014

Cluster algebras in scattering amplitudes with special 2D kinematics

We study the cluster algebra of the kinematic configuration space $Conf_n(\mathbb{P}^3)$ of a n-particle scattering amplitude restricted to the special 2D kinematics. We found that the n-points two loop MHV remainder function found in special 2D kinematics depend on a selection of \XX-coordinates that are part of a special structure of the cluster algebra related to snake triangulations of polygons. This structure forms a necklace of hypercubes beads in the corresponding Stasheff polytope. Furthermore in $n = 12$, the cluster algebra and the selection of \XX-coordinates in special 2D kinematics replicates the cluster algebra and the selection of \XX-coordinates of $n=6$ two loop MHV amplitude in 4D kinematics.

hep-th↗

arXiv2012

Towards Relativistic Skyrmions

We revisit baryons in the Skyrme model. Starting from static baryons in the helicity eigenstates, we generalize their wavefunctions to the non-static and relativistic regime. A new representation for gamma matrices in the soliton collective space is constructed and the corresponding Dirac equation is obtained. As an example, we draw consideration on how to apply this new representation on the calculus of vector current vacuum expectation values for baryon states of spin and isospin half and arbitrary momenta and we show how elastic form factors can be derived.

hep-th↗

arXiv2012

Production of negative parity baryons in the holographic Sakai-Sugimoto model

We extend our investigation of resonance production in the Sakai-Sugimoto model to the case of negative parity baryon resonances. Using holographic techniques we extract the generalized Dirac and Pauli baryon form factors as well as the helicity amplitudes for these baryonic states. Identifying the first negative parity resonance with the experimentally observed S_{11}(1535), we find reasonable agreement with experimental data from the JLab-CLAS collaboration. We also estimate the contribution of negative parity baryons to the proton structure functions.

hep-ph↗

arXiv2012

Generalized baryon form factors and proton structure functions in the Sakai-Sugimoto model

We investigate the production of positive parity baryon resonances in proton electromagnetic scattering within the Sakai-Sugimoto model. The latter is a string model for the non-perturbative regime of large $N_c$ QCD. Using holographic techniques we calculate the generalized Dirac and Pauli form factors that describe resonance production. We use these results to estimate the contribution of resonance production to the proton structure functions. Interestingly, we find an approximate Callan-Gross relation for the structure functions in a regime of intermediate values of the Bjorken variable.

hep-ph↗

arXiv2012

Electromagnetic scattering of vector mesons in the Sakai-Sugimoto model

In this proceeding we review some of our recent results for the vector meson electromagnetic form factors and structure functions in the Sakai-Sugimoto model. The latter is a string model that describes many features of the non-perturbative regime of Quantum Chromodynamics in the large $N_c$ limit.

hep-th↗

arXiv2012

Relativistic baryons in the Skyrme model revisited

We investigate and revisit certain aspects of relativistic baryons in the Skyrme model. Starting from static baryons in the helicity eigenstates, we generalize their wavefunctions to the non-static and relativistic regime. A new representation for gamma matrices in the SU(2) collective space is constructed and the corresponding Dirac equation is obtained. Furthermore, we extend the analysis of Adkins et al. concerning vector current vacuum expectation values for baryon states to arbitrary momenta and calculate baryon elastic form factors in a general framework exhibiting vector meson dominance.

hep-th↗

arXiv2011

Scalar and vector mesons of flavor chiral symmetry breaking in the Klebanov-Strassler background

Recently, Dymarsky, Kuperstein and Sonnenschein constructed an embedding of flavor D7- and anti-D7-branes in the Klebanov-Strassler geometry that breaks the supersymmetry of the background, yet is stable. In this article, we study in detail the spectrum of vector mesons in this new model of flavor chiral symmetry breaking and commence an analytical analysis of the scalar mesons in this setup.

hep-th↗

arXiv2010

Deep inelastic scattering for vector mesons in holographic D4-D8 model

We study deep inelastic scattering for vector and axial vector mesons in the holographic D4-D8 brane model. We consider tree level contributions with one particle in the final hadronic state. We obtain the unpolarized structure functions F1 and F2 for the rho and a1 mesons for q2 < 80 GeV2 and 0.2 < x < 1. We find that the ratio F2/(2xF1) is approximately equal to one for some ranges of x and q2, satisfying the Callan-Gross relation.

hep-th↗

arXiv2010

Pion and Vector Meson Form Factors in the Kuperstein-Sonnenschein holographic model

We study phenomenological aspects of the holographic model of chiral symmetry breaking recently introduced by Kuperstein and Sonnenschein (KS). As a first step, we calculate the spectrum of vector and axial-vector mesons in the KS model. We numerically compute various coupling constants of the mesons and pions. Our analysis indicates that vector meson dominance is realized in this model. The pion, vector meson and axial-vector meson form factors are obtained and studied in detail. We find good agreement with QCD results. In particular, the pion form factor closely matches available experimental data.

hep-th↗

arXiv2009

Scattering vector mesons in D4/D8 model

We review in this proceedings some recent results for vector meson form factors obtained using the holographic D4-D8 brane model. The D4-D8 brane model, proposed by Sakai and Sugimoto, is a holographic dual of a semi-realistic strongly coupled large N_c QCD since it breaks supersymmetry and incorporates chiral symmetry breaking. We analyze the vector meson wave functions and Regge trajectories as well.

hep-th↗

arXiv2009

Form factors of vector and axial-vector mesons in holographic D4-D8 model

We calculate elastic and non-elastic electromagnetic form factors for vector and axial-vector mesons in the holographic D4-D8 brane model. We obtain the mass spectrum and Regge trajectories for these particles. From the elastic form factors we extract the electric radius, the magnetic and quadrupole moments. Form factors for transverse and longitudinal polarizations are also obtained. We find superconvergence sum rules for the vector and axial-vector meson couplings that determine the asymptotic behavior of the form factors at large momentum transfer. Our results show good agreement with other holographic models and QCD.

hep-th↗