Searcharxiv⌕ Search

arXiv subjects

Massimo Bianchi

Publications and source records attributed to Massimo Bianchi.

At least 19 recordsLinked to original sources
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.

hep-th↗
arXiv2026

Couch-Torrence conformal inversion, supersymmetry and conserved charges for D3-branes

An asymptotically flat spacetime in $D=4$ can be mapped via Couch-Torrence conformal inversion to the geometry around an extremal non-expanding and non-rotating horizon. At the linearized level, an infinite tower of conserved Newman-Penrose charges can be found at null-infinity, while infinitely many Aretakis charges are conserved in the near-horizon. Couch-Torrence inversion allows one to establish a matching between the two sets of asymptotic charges. In this work we construct the Newman-Penrose and Aretakis scalar charges in higher-dimensional geometries of D3-branes in $D=10$ and D3-brane bound states in $D=4$ and $D=5$ and establish a precise matching between them through the inversion. By exploiting the residual unbroken supersymmetry of Type IIB supergravity, we demonstrate that it is possible to relate scalar (complex dilaton) charges to higher spin charges. In particular, we determine infinite towers of conserved asymptotic spinorial charges associated with the dilatino fluctuations, and determine the map through inversion.

hep-th↗
arXiv2026

One-loop mass corrections and decay widths of Type II heavy string states

We approach a systematic investigation of the one-loop mass corrections to (super-)string massive higher-spin states. While the imaginary part of the relevant amplitudes are finite, being related to the width of the decay of the states into two lower-mass states at tree level, the real part is generally IR-divergent and needs regularization and renormalization. We mostly focus on states of the first Regge trajectory in the NS-NS sector of Type-II string theories. We explicitly derive a closed-form expression for the integral over the insertion point, relying on properties of elliptic functions and lattice sums. We then regularize the IR divergent integral over the modular parameter of the torus, applying the $i\varepsilon$-prescription in string theory. As a result we compute the desired mass corrections up to level $N = 10$ and analyze their behavior at increasing $N$. Finally, we speculate on the existence of mixing among lower-spin states and conjecture that the one-loop mass matrix be governed by some random matrix theory.

hep-th↗
arXiv2026

One-loop mass corrections of interacting string states

The free string spectrum is highly degenerate, with a degeneracy that grows exponentially with the mass. Turning on a non-vanishing string coupling $g_s$ introduces interactions, rendering massive string states unstable and allowing them to decay into lower-mass states, with mixing constrained by Lorentz invariance. This behavior is expected already at one-loop level. The imaginary part of the one-loop mass correction is related to the width of the decay into two lower-mass states at tree level, whereas the real part is generally IR-divergent and needs regularization and renormalization. The analysis simplifies for states in the first Regge trajectory. In particular, we consider the one-loop mass corrections for these states in the NS-NS sector of Type-II string theories. We explicitly construct the related vertex operators and exploit the properties of elliptic functions in order to obtain a closed form expression for the integral over the insertion point. We further regularize the divergences of the integral over the modular parameter of the torus by means of the $i\varepsilon$-prescription in string theory. Finally we extract numerical results for the mass correction up to level $N=4$.

hep-th↗
arXiv2025

Scalar self-force effects in neutral $W$-soliton backgrounds

We investigate several geometrical and physical properties of the recently found $W$-soliton solution (neutral case). We discuss both the genuine 5d solution and its reduction to 4d and highlight similarities and differences. In both cases, we study scattering processes of massless and massive particles in the background, reconstructing the gauge-invariant scattering angle, either with exact expressions or with large-angular momentum expansion expressions, which we show how to resum in a useful form. Finally, we analyze the propagation of a test scalar field in the $W$-soliton background and compute the spectrum of Quasi Normal Modes in the case of (non-)minimal coupling and the radiated energy in the case of minimal coupling. Our result for the energy loss is fully analytic and presented in a Post-Newtonian expansion, following the approach termed gravitational self force.

gr-qc↗
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.

hep-th↗
arXiv2025

Scattering angle in a Topological Star spacetime: a self-force approach

We compute the scattering angle for a scalar neutral probe undergoing unbound motion around a Topological Star, including self-force effects. Moreover we identify the `electro-magnetic' source of the background as Papapetrou Field compatible with the isometries and characterize Topological Stars by studying their sectional curvature, geometric transport along special curves and the gravitational energy content in terms of the super-energy tensors.

gr-qc↗
arXiv2025

Probing the multipolar structure of Myers-Perry black holes with scattering amplitudes

We discuss the scattering of massive scalar probes off Myers-Perry black holes in the Kerr-Schild gauge. Extending the analysis performed recently for Kerr(-Newman) black holes, we show that the Kerr-Schild gauge allows to write down the tree-level scattering amplitude for Myers-Perry black holes in analytic form. For generic values of the angular momenta, Myers-Perry solutions have a richer multipolar structure compared to their four-dimensional counterparts, because they are characterized by the presence of stress multipoles, together with the more familiar mass and current multipoles. By focusing on the five-dimensional case, we derive the leading eikonal phase from the scattering amplitude and we give an explicit expression for two limiting scenari, namely when the two angular momenta are the same, so that the mass multipoles vanish but still the solution has a non-vanishing stress quadrupole and a current dipole, and when one of the two angular momenta is zero, and correspondingly the stress multipoles vanish similar to the Kerr case.

hep-th↗
arXiv2025

Rotating Topological Stars

We construct a three-parameter family of smooth and horizonless rotating solutions of Einstein-Maxwell theory with Chern-Simons term in five dimensions and discuss their stringy origin in terms of three-charge brane systems in Type IIB and M-theory. The general solution interpolates smoothly between Kerr and static Topological Star geometries. We show that for specific choices of the parameters and quantized values of the angular momentum the geometry terminates on a smooth five-dimensional cap, and it displays neither ergoregion nor closed timelike curves. We discuss the propagation of particles and waves showing that geodetic motion is integrable and the radial and angular propagation of scalar perturbations can be separated and described in terms of two ordinary differential equations of confluent Heun type.

hep-th↗
arXiv2024

Source multipoles and energy-momentum tensors for spinning black holes and other compact objects in arbitrary dimensions

Working in momentum space and at linear order in the gravitational coupling, we derive the most general class of energy-momentum tensors associated with a given multipolar structure of the spacetime in arbitrary dimensions, and built out of a mass and an angular momentum, at any order in the spin expansion. In this formalism, we are able to derive directly the full multipolar structure of any solution from the multipole expansion of the energy-momentum tensor, in complete analogy to Newtonian gravity. In particular, we identify the recurrence relations that allow obtaining the multipolar structure of the Kerr and the Myers-Perry black hole solutions, defining source multipoles in a General Relativity context for the first time. For these solutions, we are able to resum the energy-momentum tensor in momentum space at all orders in the angular momentum, and compute its real-space version. In the Kerr case we exactly obtain the matter source found by Israel, namely an equatorial, pressureless thin disk rotating at superluminal speed. For Myers-Perry in five dimensions, the matter distribution is a three-ellipsoid in four spatial dimensions with nontrivial stresses. Remarkably, for any dimensions, the matter configuration is a lower-dimensional distribution which has the same singularity structure as the fully non-linear black-hole solution. Our formalism underscores the advantage of working in momentum space to generate nontrivial matter sources for non-linear spacetimes, and could be used to construct regular non-exotic matter configurations that source spinning black hole solutions or horizonless compact objects with the same multipolar structure as black holes.

gr-qc↗
arXiv2024

Gauge theory meets cosmology

We reconsider linear perturbations around general Friedmann - Lemaitre - Robertson - Walker (FLRW) cosmological backgrounds. Exploiting gauge freedom involving only time reparametrizations, we write down classical background solutions analytically, for an arbitrary number of fluid components. We then show that the time evolution of scalar and tensor adiabatic perturbations are governed by Schr\"odinger-like differential equations of generalized Heun type. After recovering known analytic results for a single-component fluid, we discuss more general situations with two and three different fluid components, with special attention to the combination of radiation, matter and vacuum energy, which is supposed to describe the $\Lambda$CDM model. The evolution of linear perturbations of a flat $\Lambda$CDM universe is described by a two-transient model, where the transitions from radiation to matter and matter to vacuum energy are governed by a Heun equation and a Hypergeometric equation, respectively. We discuss an analytic approach to the study of the general case, involving generalized Heun equations, that makes use of (quantum) Seiberg-Witten curves for ${\cal N}=2$ supersymmetric gauge theories and has proven to be very effective in the analysis of Black-Hole, fuzzball and ECO perturbations.

hep-th↗
arXiv2024

Scalar perturbations in a Top-Star spacetime

We discuss the dynamics of a (neutral) test particle in Topological Star spacetime undergoing scattering processes by a superposed test radiation field, a situation that in a 4D black hole spacetime is known as relativistic Poynting-Robertson effect, paving the way for future studies involving radiation-reaction effects. Furthermore, we study self-force-driven evolution of a scalar field, perturbing the Top-Star spacetime with a scalar charge current. The latter for simplicity is taken to be circular, equatorial and geodetic. To perform this study, besides solving all the self-force related problem (regularization of all divergences due to the self-field, mode sum regularization, etc.), we had to adapt the 4D Mano-Suzuki-Takasugi formalism to the present 5D situation. Finally, we have compared this formalism with the (quantum) Seiberg-Witten formalism, both related to the solutions of a Heun Confluent Equation, but appearing in different contexts in the literature, black hole perturbation theory the first, quantum curves in super-Yang-Mills theories the second.

gr-qc↗
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 $\beta$- ensemble, writing an interpolation between the known results of the Gaussian orthogonal, unitary, and symplectic ensembles.

hep-th↗
arXiv2023

Non-geometric BPS branes on T-folds

We give a detailed (microscopic) description of the geometric and non-geometric fundamental branes and their bound states in Type II superstring compactifications preserving N=6 supersymmetry. We consider general boundary states that couple to the twisted sector and compute the relevant annulus amplitudes. We check consistency of the construction by relating the transverse channel, corresponding to closed-string tree-level exchange, with the direct open-string loop channel. Focussing on the Type IIA frame, we show that D0-D4 have the expected tension for a geometric brane, while the non-geometric D2-D6 boundary states have a tension equal to $1/\sqrt{K}$ the one of a geometric brane for the $\mathbb{Z}_K$ orbifold. This is consistent with Fricke T-duality of the N=6 model.

hep-th↗
arXiv2023

A Rutherford-like formula for scattering off Kerr-Newman BHs and subleading corrections

By exploiting the Kerr-Schild gauge, we study the scattering of a massive (charged) scalar off a Kerr-Newman black hole. In this gauge, the interactions between the probe and the target involve only tri-linear vertices. We manage to write down the tree-level scattering amplitudes in analytic form, from which we can construct an expression for the eikonal phase which is exact in the spin of the black hole at arbitrary order in the Post-Minkowskian expansion. We compute the classical contribution to the cross-section and deflection angle at leading order for a Kerr black hole for arbitrary orientation of the spin. Finally, we test our method by reproducing the classical amplitude for a Schwarzschild black hole at second Post-Minkowskian order and outline how to extend the analysis to the Kerr-Newman case.

hep-th↗
arXiv2023

On the stability and deformability of top stars

Topological stars, or top stars for brevity, are smooth horizonless static solutions of Einstein-Maxwell theory in 5-d that reduce to spherically symmetric solutions of Einstein-Maxwell-Dilaton theory in 4-d. We study linear scalar perturbations of top stars and argue for their stability and deformability. We tackle the problem with different techniques including WKB approximation, numerical analysis, Breit-Wigner resonance method and quantum Seiberg-Witten curves. We identify three classes of quasi-normal modes corresponding to prompt-ring down modes, long-lived meta-stable modes and what we dub `blind' modes. All mode frequencies we find have negative imaginary parts, thus suggesting linear stability of top stars. Moreover we determine the tidal Love and dissipation numbers encoding the response to tidal deformations and, similarly to black holes, we find zero value in the static limit but, contrary to black holes, we find non-trivial dynamical Love numbers and vanishing dissipative effects at linear order. For the sake of illustration in a simpler context, we also consider a toy model with a piece-wise constant potential and a centrifugal barrier that captures most of the above features in a qualitative fashion.

gr-qc↗
arXiv2023

Charge instability of JMaRT geometries

We perform a detailed study of linear perturbations of the JMaRT family of non-BPS smooth horizonless solutions of type IIB supergravity beyond the near-decoupling limit. In addition to the unstable quasi normal modes (QNMs) responsible for the ergo- region instability, already studied in the literature, we find a new class of `charged' unstable modes with positive imaginary part, that can be interpreted in terms of the emission of charged (scalar) quanta with non zero KK momentum. We use both matched asymptotic expansions and numerical integration methods. Moreover, we exploit the recently discovered correspondence between JMaRT perturbation theory, governed by a Reduced Confluent Heun Equation, and the quantum Seiberg-Witten (SW) curve of $\mathcal{N} = 2$ SYM theory with gauge group SU(2) and $N_f = (0,2)$ flavours.

hep-th↗