arXiv subjects

Jacob Sonnenschein

Publications and source records attributed to Jacob Sonnenschein.

At least 19 recordsLinked to original sources

arXiv2026

Higher-dimensional chaotic features and random matrix signatures following a local quench

We study the multidimensional erratic structure of correlation functions produced by local operator quenches in finite-volume free massive scalar field theory in dimensions 2 and 3. The basic observable is the subtracted equal-time two-point function in the locally excited state and its spatiotemporal patterns of extrema. We analyze these extrema by the multidimensional diagnostics recently introduced for chaotic scattering amplitudes and related problems: all-pair distance distributions, nearest-neighbor spacings, greedy-path spacing ratios, and the extrema form factor. For the $1+1$-dimensional local quench we find that, in the regime of small Euclidean smearing, the fitted extremum statistics move close to the $β=1$ random-matrix benchmark, while increasing the smearing scale softens the effective repulsion and moves the distributions away from the GOE-like value. For the $2+1$-dimensional local quench we find that the nearest-neighbor statistics of the refined extrema are close to, or above, the $β=1$ benchmark, and the greedy-path ratio statistics are described by even larger effective $β$ values. Finally we studied the all-pair extrema spatial form factor and found that, in the one-, two-, and three-dimensional cases, its main structure is controlled by the corresponding uniform interval, rectangle, or cuboid geometry of the extrema cloud and found the dip-ram-plateau structure in the last two cases. Thus the form factor provides a complementary global diagnostic of how the extrema fill their effective metric support, while the genuinely nontrivial local and mesoscopic organization is carried by the nearest-neighbor and greedy-path statistics.

hep-th↗

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 $δ_{n}= A_{n+1}-A_n$ and their ratios $r_{n}=\frac{δ_{n+1}}{δ_n}$. We show that the distributions of the spacing ratios take the form of the RMT Gaussian $β$-ensembles. The curves associated with the scattering angle tend to converge to the Gaussian Orthogonal Ensemble value of $β=1$ and those related to the polarization angle to the Gaussian Unitary Ensemble $β=2$. 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 $β$ values extracted from the distribution of the spacing ratios.

hep-th↗

arXiv2026

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 β-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.

hep-th↗

arXiv2026

On Chaos in QFT

In this note we explore the chaotic behavior of non-integrable QFTs and compare them to integrable ones. We choose as prototypes the double sine-Gordon and the sine-Gordon models. We analyze their discrete spectrum determined by a truncation method. We examine the map of the corresponding energy eigenvalues to the eigenvalues of the random matrix theory (RMT) Gaussian orthogonal ensemble (GOE). This is done by computing the following properties: (a) The distribution of the adjacent spacings and their ratios (b) Higher order spacings and ratios (c) Pair correlations (d) Spectral form factors and (e) Spectral rigidity. For these properties we determine the differences between the integrable and non-integrable theories and verify that the former admits a Poisson behavior and the latter GOE (apart from the spectral rigidity).

hep-th↗

arXiv2025

Nonabelian fluids and helicities

In analogy with the non-Abelian gauge helicities conserved in time for ``null fields", that we have defined previously, in this paper we first define non-Abelian fluid helicities and then total non-Abelian helicities for combined non-Abelian fluid and gauge fields. For a U(N) group the helicities considered are for both gluonic-type fluids, composed of particles in the adjoint representation, and quark-type fluids, in the $N$-dimensional Cartan subalgebra. We write down various Lagrangian formulations for the uncoupled and coupled systems. In each case we determine the equations of motion, symmetries, and a Hamiltonian formulation. Taking the velocity of the fluid in the adjoint representation, we find that in the case of the gluonic fluid, we can write a non-Abelian gluonic fluid Euler-Yang-Mills equation that conserves the defined helicities, and comes from a Lagrangian.

hep-th↗

arXiv2025

Phase transitions in an expanding medium -- hot remnants

We analyze the dynamics of a first order confinement/deconfinement phase transition in an expanding medium using an effective boundary description fitted to the holographic Witten model. We observe and analyze hot plasma remnants, which do not cool down or nucleate bubbles despite the expansion of the system. The appearance of the hot remnants, the dynamics of their shrinking and subsequent dissolution and further heating up is very robust and persists in such diverse scenarios as boost-invariant expansion with a flat Minkowski metric and cosmological expansion in a Friedmann-Robertson-Walker spacetime.

hep-th↗

arXiv2024

Novel knotted non-abelian gauge fields

In analogy to null electromagnetic fields we define null YM fields. We show that the null non-abelian $SU(N)$ gauge fields admit a set of $2 N^2$ conserved "helicities". We derive null YM solutions that carry finite helicities by uplifting the abelian Hopfion solution and their generalizations. Another method that we implement is to deform YM solutions which do not carry helicities into ones that have nontrivial helicities. A nontrivial non-Abelian solution with helicities is found as a wave of infinite energy. We also discuss non-abelian generalizations of the Bateman parameterization for null abelian gauge fields.

hep-th↗

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.

hep-th↗

arXiv2024

Euler fluid in 2+1 dimensions as a gauge theory, and an action for the Euler fluid in any dimension

In this paper we parallel the construction of Tong of a gauge theory for shallow water, by writing a gauge theory for the Euler fluid in 2+1 dimensions. We then extend it to an Euler fluid coupled to electromagnetic background. We argue that the gauge theory formulation provides a topological argument for the quantization of 2+1 dimensional Euler Hopfion solution. In the process, we find a (non-gauge) action for the Euler fluid that can be extended to any dimension, including the physical 3+1 dimensions. We discuss several aspects of the ABC flow.

hep-th↗

arXiv2024

Taming the Zoo of Tetraquarks and Pentaquarks using the HISH Model

In this paper we scan over all possible charmed tetraquarks and pentaquarks. Using the holography inspired stringy hadron (HISH) model we determine the trajectories associated with each of the exotic hadron candidates. The trajectories include further exotic states with higher angular momentum or higher stringy excited states. A trajectory is a property of a genuine exotic hadron and can be used to distinguish between the latter and a molecule. We examine 71 tetraquarks and 210 pentaquarks. Few of these states have already been found but most of the predicted zoo have yet not been discovered. We analyze the strong decay processes of these exotic hadrons and compute the corresponding decay widths of part of them.

hep-ph↗

arXiv2023

Deterministic Chaos vs Integrable Models

In this work we present analytical and numerical evidences that classical integrable models possessing infinitely many degrees of freedom unexpectedly exhibit some features that are typical of chaotic systems. By studying how the conserved charges change under a small deformation of the initial conditions, we conclude that the inverse scattering map is responsible for the presence of these features, in spite of the system being integrable. We investigate this phenomenon in the explicit examples of the KdV equation and the sine-Gordon model and further provide general arguments supporting this statement.

hep-th↗

arXiv2023

CSBIon -- a charged soliton of the 3-dimensional CS + BI Abelian gauge theory

In this paper, we construct a charged soliton with a finite energy and no delta function source in a pure Abelian gauge theory. Specifically, we first consider the 3-dimensional Abelian gauge theory, with a Maxwell term and a l evel $N$ CS term. We find a static solution that carries charge $N$, angular momentum $\frac{N}{2}$ and whose radius is $N$ independent. However, this solution has a divergent energy. In analogy to the replacement of the 4 dimensional Maxwell action with the BI action, which renders the classical energy of a point charge finite, for the 3 dimensional theory which includes a CS term such a replacement leads to a finite energy for the solution of above. We refer to this soliton as a CSBIon solution, representing a finite energy version of the fundamental (sourced) charged electron of Maxwell theory in 4 dimensions. In 3 dimensions the BI+CS action has a static charged solution with finite energy and no source, hence a soliton solution. The CSBIon, similar to its Maxwellian predecessor, has a charge $N$, angular momentum proportional to $N$ and an $N$-independent radius. We also present other nonlinear modifications of Maxwell theory that admit similar solitons. The CSBIon may be relevant in various holographic scenarios. In particular, it may describe a D6-brane wrapping an $S^4$ in a compactified D4-brane background. We believe that the CSBIon may play a role in condensed matter systems in 2+1 dimensions like graphene sheets.

hep-th↗

arXiv2023

$T\bar T$ deformations and the pp wave correspondence

In this paper we consider $T\bar T$ deformations in the context of pp waves obtained from gravity duals. We propose a deformation of $AdS_5\times S^5$ similar to the deformation of the single trace $T\bar T$ deformation of $AdS_3\times S^3\times T^4$ with NS-NS flux, and study it through the Penrose limit, concluding that it must correspond to some dipole theory, probably noncommutative. We $T\bar T$ deform the worldsheet string for the $AdS_5\times S^5$ pp wave, and find a corresponding spin chain Hamiltonian. Finally, directly $T\bar T$ deforming the spin chain Hamiltonian obtained from the pp wave, we find that it corresponds to an equivalent BMN sector of the ${\cal N}=4$ SYM.

hep-th↗

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.

hep-th↗

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.

hep-th↗

arXiv2022

Fluid-electromagnetic helicities and knotted solutions of the fluid-electromagnetic equations

In this paper we consider an Euler fluid coupled to external electromagnetism. We prove that the Hopfion fluid-electromagnetic knot, carrying fluid and electromagnetic (EM) helicities, solves the fluid dynamical equations as well as the Abanov Wiegmann (AW) equations for helicities, which are inspired by the axial-current anomaly of a Dirac fermion. We also find a nontrivial knot solution with truly interacting fluid and electromagnetic fields. The key ingredients of these phenomena are the EM and fluid helicities. An EM dual system, with a magnetically charged fluid, is proposed and the analogs of the AW equations are written down. We consider a fluid coupled to a nonlinear generalizations for electromagnetism. The Hopfions are shown to be solutions of the generalized equations. We write down the formalism of fluids in 2+1 dimensions, and we dimensionally reduce the 3+1 dimensional solutions. We determine the EM knotted solutions, from which we derive the fluid knots, by applying special conformal transformations with imaginary parameters on un-knotted null constant EM fields.

hep-th↗

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.

hep-th↗

arXiv2022

A perfect fluid hydrodynamic picture of domain wall velocities at strong coupling

We show that for a range of strongly coupled theories with a first order phase transition, the domain wall or bubble velocity can be expressed in a simple way in terms of a perfect fluid hydrodynamic formula, and thus in terms of the equation of state. We test the predictions for the domain wall velocities using the gauge/gravity duality.

hep-th↗