arXiv subjects

Dorin Weissman

Publications and source records attributed to Dorin Weissman.

At least 19 recordsLinked to original sources

arXiv2026

Exploring continuous beta-ensembles: A Python implementation for random matrix spectral statistics

We present an open-source Python package for sampling the Gaussian, Circular, and Laguerre $\beta$-ensembles of random matrix theory. The package implements the Dumitriu-Edelman and Killip-Nenciu constructions, allowing efficient generation of random spectra for general $\beta > 0$. In addition to spectrum generation, it includes tools for the analysis of spectral statistics, from standard nearest-neighbor spacings and spacing ratios to non-adjacent $k$-spacings and the spectral form factor. These tools can be applied to generic spectral data, allowing users to compare them with and fit them to $\beta$-ensemble predictions. In this note, we review the $\beta$-ensembles, describe the package interface, and illustrate its use through several numerical experiments motivated by applications to quantum chaos. Our numerical results include an analysis of $\beta$ as a continuous fitting parameter in spacing ratio statistics, an examination of the numerical evidence for the conjectured $k$-spacing ratio distributions, and a study of the spectral form factor for general values of $\beta$.

nlin.CD↗

arXiv2026

Multi-dimensional chaos II: String scattering amplitudes, curve repulsion, and RMT

Multi-dimensional chaos refers to processes described by erratic functions of several dynamical variables. In this letter we analyze the string scattering amplitudes of highly-excited states and ground states. We show that the amplitudes, which depend on a scattering angle and a polarization angle, are characterized by two sets of non-intersecting curves associated with the vanishing of the derivatives with respect to the angles. We introduce the notion of the "area eigenvalue" $A_n$ associated with the $n$-th curve. We compute the spacings $\delta_{n}= A_{n+1}-A_n$ and their ratios $r_{n}=\frac{\delta_{n+1}}{\delta_n}$. We show that the distributions of the spacing ratios take the form of the RMT Gaussian $\beta$-ensembles. The curves associated with the scattering angle tend to converge to the Gaussian Orthogonal Ensemble value of $\beta=1$ and those related to the polarization angle to the Gaussian Unitary Ensemble $\beta=2$. We also compute the ``areas form factor" associated with the areas and discover the regions of decline, ramp and plateau which characterize chaotic processes. The slope of the ramp seems to agree with the $\beta$ values extracted from the distribution of the spacing ratios.

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arXiv2025

High-Energy Pion Scattering in Holographic QCD: A Comparison with Experimental Data

Following Polchinski and Strassler [1] and our previous work [2], we study high-energy pion scattering in the holographic QCD hard-wall model. In particular, we focus on comparing our predictions for the angular dependence of $\pi^{+} \pi^{-} \to \pi^{+} \pi^{-}$ scattering with experimental data extracted from the process $\pi^{-} p \to \pi^{+} \pi^{-} n$. Having previously shown that our approach reproduces the constituent counting rule found in QCD, we now observe qualitative agreement between our predictions and the extracted data in the high-energy fixed-angle regime. We also provide predictions for all other 2-to-2 pion scattering processes. Our approach can be extended to a broader range of meson and glueball scattering processes in various holographic QCD models.

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arXiv2025

Multi-dimensional chaos I: Classical and quantum mechanics

We introduce the notion of multi-dimensional chaos that applies to processes described by erratic functions of several dynamical variables. We employ this concept in the interpretation of classical and quantum scattering off a pinball system. In the former case it is illustrated by means of two-dimensional plots of the scattering angle and of the number of bounces. We draw similar patterns for the quantum differential cross-section for various geometries of the disks. We find that the eigenvalues of the S-matrix are distributed according to the Circular Orthogonal Ensemble (COE) in random matrix theory (RMT), provided the setup be asymmetric and the wave-number be large enough. We then consider the electric potential associated with charges randomly located on a plane as a toy model that generalizes the scattering from a leaky torus. We propose several methods to analyze the distribution of spacings between the extrema of such functions. We show that these follow a repulsive Gaussian \beta-ensemble distribution even for Poisson-distributed positions of the charges. A generalization of the spectral form factor is introduced and determined. We apply these methods to the cases of a chaotic S-matrix and of the quantum pinball scattering. The spacings between nearest neighbor extrema points and ratios between adjacent spacings follow a logistic and Beta distributions correspondingly. We conjecture about a potential relation with random tensor theory.

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arXiv2024

High-Energy Fixed-Angle Meson Scattering and the Constituent Counting Rule in Holographic QCD

We investigate the high-energy fixed-angle scattering of pions and $\rho$-mesons in a bottom-up holographic QCD model. To this end, we generalise the approach of Polchinski and Strassler arXiv:hep-th/0109174 to write an ansatz for meson scattering amplitudes based on superstring scattering amplitudes in asymptotically AdS space. We demonstrate that our generalisation of the Polchinski--Strassler proposal is necessary to describe $\rho$-meson scattering consistently with the Nambu--Goldstone boson equivalence theorem. Our results for pion and $\rho$-meson scattering amplitudes are in agreement with the constituent counting rule found in QCD. Moreover, our proposal for 2-to-2 scattering amplitudes provides a method for computing scattering angle dependence.

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arXiv2024

A black hole effective theory for strongly interacting matter

We establish a new tool for studying strongly coupled matter: an effective theory of black holes in gravity, which maps to a hydrodynamic description of field theories via the gauge-gravity duality. Our approach is inspired by previously known effective theories found in the limit of high number of dimensions. We argue that the new approach can accurately describe phase transitions in a wide class of theories, such as the Yang-Mills and other nearly critical field theories. As an application, we analyze the interface between confining and deconfining phases in holographic Yang-Mills theory.

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arXiv2024

From spectral to scattering form factor

We propose a novel indicator for chaotic quantum scattering processes, the scattering form factor (ScFF). It is based on mapping the locations of peaks in the scattering amplitude to random matrix eigenvalues, and computing the analog of the spectral form factor (SFF). We compute the spectral and scattering form factors of several non-chaotic systems. We determine the ScFF associated with the phase shifts of the leaky torus, closely related to the distribution of the zeros of Riemann zeta function. We compute the ScFF for the decay amplitude of a highly excited string states into two tachyons. We show that it displays the universal features expected from random matrix theory - a decline, a ramp and a plateau - and is in general agreement with the Gaussian unitary ensemble. It also shows some new features, owning to the special structure of the string amplitude, including a "bump" before the ramp associated with gaps in the average eigenvalue density. The "bump" is removed for highly excited string states with an appropriate state dependent unfolding. We also discuss the SFF for the Gaussian $β$- ensemble, writing an interpolation between the known results of the Gaussian orthogonal, unitary, and symplectic ensembles.

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arXiv2023

Measuring chaos in string scattering processes

We analyze the amplitudes of one highly excited string (HES) state with two or three tachyons in open bosonic string theory. We argue that these processes are chaotic by showing that the spacing ratios of successive peaks in the angular dependence of the amplitudes are distributed as predicted by the $β$-ensemble of random matrix theory (RMT). We show how the continuous parameter $β$ depends on the level and helicity of the scattered HES state. We derive the scattering amplitude of an HES and three tachyons and show that it takes the form of the Veneziano amplitude times a dressing factor, and that the dressing is chaotic as a function of the scattering angle, in the sense that its spacing ratios match with RMT predictions.

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arXiv2023

Measure for chaotic scattering amplitudes

We propose a novel measure of chaotic scattering amplitudes. It takes the form of a log-normal distribution function for the ratios $r_n={δ_n}/{δ_{n+1}}$ of (consecutive) spacings $δ_n$ between two (consecutive) peaks of the scattering amplitude. We show that the same measure applies to the quantum mechanical scattering on a leaky torus as well as to the decay of highly excited string states into two tachyons. Quite remarkably the $r_n$ obey the same distribution that governs the non-trivial zeros of Riemann zeta function.

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arXiv2022

Supersymmetric Quantum Chiral Higher Spin Gravity

We study quantum properties of supersymmetric N=1 and N=4 extensions of the four dimensional bosonic Chiral Higher Spin Gravities (HiSGRAs). We discuss the spectra, the classical actions and define the Feynman rules in N=1 and N=4 superspaces in the light-front gauge. Using these Feynman rules, we compute tree and one-loop amplitudes for these systems. A dimensional reduction to a system with N=2 supersymmetry and with massive higher spin fields is performed and quantum properties of this system are discussed.

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arXiv2022

Partonic behavior of string scattering amplitudes from holographic QCD models

We study the emergence of partonic behavior in scattering processes at large Mandelstam's variable $s$ from string amplitudes in holographic backgrounds. We generalize the approach of Polchinski and Strassler (2001) in two ways. (i) We analyze several holographic confining backgrounds in particular the hard wall model, the soft wall model and Witten's model. (ii) In addition to deriving the asymptotic behavior of the amplitudes at fixed angle and in the Regge limit, we also expand the amplitudes around their poles, integrate over the holographic direction and then re-sum the expansion. Due to dependence of the string tension on the holographic coordinate, the resulting singularities take the form of branch points rather than poles and the amplitudes display branch cuts and acquire a finite imaginary part. This may signal the failure of the PS prescription to reproduce the correct analytic structure at low energies. We also observe that the peaks are more pronounced in the region of small $s$ but fade away for large $s$. In the fixed angle approximation we find in the hard and soft wall models that ${\cal A}\sim s^{2-Δ/2}$ whereas in Witten's model ${\cal A} \sim s^{3-Δ/2}$ and ${\cal A} \sim s^{7/3-2Δ/3}$ for the 11D and 10D formulations, respectively. In the Regge regime ${\cal A}\sim {s^{2}}\,t^{-2+α}\,(\log{s/ t})^{-1+α}$ where $α$ is the power found in the fixed angle regime. Using the pole expansion the result for each model is $Re[{\cal A}] \sim s^{-1}$, $Im[{\cal A}] \sim s^α$. We compute the corresponding amplitudes for mesons using open strings and find qualitatively similar results as for closed strings.

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arXiv2021

Cubic Vertices for N=1 Supersymmetric Massless Higher Spin Fields in Various Dimensions

Using the BRST approach to higher spin field theories we develop a generic technique for constructing the cubic interaction vertices for N=1 supersymmetric massless higher spin fields on four, six and ten dimensional flat backgrounds. Such an approach allows formulation of the equations for cubic vertices including bosonic and fermionic higher spin fields, and the problem of finding the vertices is reduced to finding the consistent solutions to these equations. As a realization of this procedure, we present the particular solutions for the vertices where the fields obey some off-shell constraints. It is shown that the supersymmetry imposes additional constraints on the vertices and singles out a particular subclass of the solutions. As a concrete application of the generic scheme, we consider supersymmetric Yang-Mills-like systems in four, six and ten dimensions where the higher spin fields transform under some internal symmetry group, as well as supergravity-like systems in the same dimensions.

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arXiv2020

On the quantization of folded strings in non-critical dimensions

Classical rotating closed string are folded strings. At the folding points the scalar curvature associated with the induced metric diverges. As a consequence one cannot properly quantize the fluctuations around the classical solution since there is no complete set of normalizable eigenmodes. Furthermore in the non-critical effective string action of Polchinski and Strominger, there is a divergence associated with the folds. We overcome this obstacle by putting a massive particle at each folding point which can be used as a regulator. Using this method we compute the spectrum of quantum fluctuations around the rotating string and the intercept of the leading Regge trajectory. The results we find are that the intercepts are $a=1$ and $a=2$ for the open and closed string respectively, independent of the target space dimension. We argue that in generic theories with an effective string description, one can expect corrections from finite masses associated with either the endpoints of an open string or the folding points on a closed string. We compute explicitly the corrections in the presence of these masses.

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arXiv2020

Deciphering the recently discovered tetraquark candidates around 6.9 GeV

Recently a novel hadronic state of mass 6.9 GeV, that decays mainly to a pair of charmonia, was observed in LHCb. The data also reveals a broader structure centered around 6490 MeV and suggests another unconfirmed resonance centered at around 7240 MeV, very near to the threshold of two doubly charmed $Ξ_{cc}$ baryons. We argue in this note that these exotic hadrons are genuine tetraquarks and not molecules of charmonia. It is conjectured that they are V-baryonium tetraquarks, namely, have an inner structure of a baryonic vertex with a $cc$ diquark attached to it, which is connected by a string to an anti-baryonic vertex with a $\bar c \bar c$ anti-diquark. We examine these states as the analogs of the states $Ψ(4360)$ and $Y(4630)$/$Ψ(4660)$ which are charmonium-like tetraquarks. One way to test these claims is by searching for a significant decay of the state at 7.2 GeV into $Ξ_{cc}\overlineΞ_{cc}$. Such a decay would be the analog of the decay of the state $Y(4630)$ into to $Λ_c\overlineΛ_c$. We further argue that there should be trajectories of both orbital and radial excited states of the $X(6900)$. We predict their masses. It is possible that a few of these states have already been seen by LHCb.

hep-ph↗

arXiv2020

The scattering amplitude of stringy hadrons I: Strings with opposite charges on their endpoints

In this note we describe hadrons: mesons and baryons as strings with electric charges on their endpoints. We consider here only the neutral system with opposite charges coupled to an external constant electric and magnetic fields. We derive certain classical solutions including rotating folded open strings. We write down the mode expansion and canonically quantize the system. The OPEs associated with such strings are determined. We re-derive the non-commutativity of the zero modes and the fact that the charges modify the spacetime metric. We show that the quantum worldsheet energy momentum tensor on the boundary is affected by the endpoint charges and differs from the corresponding Noether current. We determine the generalization of the Veneziano scattering amplitude for such strings in the critical dimension. Phenomenological implications are addressed and in particular we show that the external magnetic field can be tuned so that the amplitude vanishes for particular kinematic setups. We discuss the generalization of such strings to non-critical four dimensional spacetime. In particular we renormalize the divergence of the Polchinski-Strominger effective action associated with the rotating folded string.

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arXiv2019

Excited mesons, baryons, glueballs and tetraquarks: Predictions of the Holography Inspired Stringy Hadron model

In this note we collect and summarize the predictions of the Holography Inspired Stringy Hadron (HISH) model. We list the masses and widths of predicted excited states across the spectrum, based on placing the different hadrons on the non-linear Regge trajectories of a string with massive endpoints. Our predicted states include: (i) Light, heavy-light and heavy-heavy mesons. (ii) Baryons, including charmed, doubly charmed and bottom baryons. (iii) Glueballs, together with a method to disentangle them from flavorless mesons. (iv) Genuine tetraquarks, which are not "molecules" of hadrons, and are characterized by their decay into a baryon and an anti-baryon.

hep-ph↗

arXiv2018

Quantizing the rotating string with massive endpoints

We compute leading order quantum corrections to the Regge trajectory of a rotating string with massive endpoints using semiclassical methods. We expand the bosonic string action around a classical rotating solution to quadratic order in the fluctuations and perform the canonical quantization of the resulting theory. For a rotating string in $D$ dimensions the intercept receives contributions from $D-3$ transverse modes and one mode in the plane of rotation, in addition to a contribution due to the Polchinski-Strominger term of the non-critical effective string action when $D\neq26$. The intercept at leading order is proportional to the expectation value of the worldsheet Hamiltonian of the fluctuations, and this is shown explicitly in several cases. All contributions to the intercept are considered, and we show a simple physical method to renormalize the divergences in them. The intercept converges to known results at the massless limit, and corrections from the masses are explicitly calculated at the long string limit. In the process we also determine the quantum spectrum of the string with massive endpoints, and analyze the asymmetric case of two different endpoint masses.

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arXiv2018

The decay width of stringy hadrons

In this paper we further develop a string model of hadrons by computing their strong decay widths and comparing them to experiment. The main decay mechanism is that of a string splitting into two strings. The corresponding total decay width behaves as $Γ=\frac\pi2 ATL$ where $T$ and $L$ are the tension and length of the string and $A$ is a dimensionless universal constant. We show that this result holds for a bosonic string not only in the critical dimension. The partial width of a given decay mode is given by $Γ_i/Γ=Φ_i\exp(-2πCm_{sep}^2/T)$ where $Φ_i$ is a phase space factor, $m_{sep}$ is the mass of the "quark" and "antiquark" created at the splitting point, and $C$ is a dimensionless coefficient close to unity. Based on the spectra of hadrons we observe that their (modified) Regge trajectories are characterized by a negative intercept. This implies a repulsive Casimir force that gives the string a "zero point length". We fit the theoretical decay width to experimental data for mesons on the trajectories of $ρ$, $ω$, $π$, $η$, $K^*$, $ϕ$, $D$, and $D^*_s$, and of the baryons $N$, $Δ$, $Λ$, and $Σ$. We examine both the linearity in $L$ and the exponential suppression factor. The linearity was found to agree with the data well for mesons but less for baryons. The extracted coefficient for mesons $A=0.095\pm0.015$ is indeed quite universal. The exponential suppression was applied to both strong and radiative decays. We discuss the relation with string fragmentation and jet formation. We extract the quark-diquark structure of baryons from their decays. A stringy mechanism for Zweig suppressed decays of quarkonia is proposed and is shown to reproduce the decay width of $Υ$ states. The dependence of the width on spin and flavor symmetry is discussed. We further apply this model to the decays of glueballs and exotic hadrons.

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