arXiv subjects

Veronica Fantini

Publications and source records attributed to Veronica Fantini.

14 recordsLinked to original sources

arXiv2026

Modular resurgent structures for vectors

Building on prior results [1], we introduce vector-valued modular resurgent series, whose components exhibit a single infinite tower of singularities in the Borel plane, trivial secondary resurgent series, and Stokes constants given by linear combinations of the coefficients of a vector of $L$-functions. We extend the paradigm of modular resurgence to this setting, emphasizing the role of the Stokes constants and the interplay between the associated vectors of $q$-series and Dirichlet series, and describing the resulting symmetry relating canonical pairs of vector-valued modular resurgent series. Moreover, we conjecture that certain vectors of $q$-series with modular resurgent asymptotics are vector-valued quantum modular forms and can be reconstructed via median resummation. Finally, we show that vectors of $q$-Pochhammer symbols, previously considered in [2], and Eichler integrals of vector-valued modular forms of weight $1/2$ and $3/2$ can be studied within the framework of vector-valued modular resurgence. While the first case amounts to a convenient repackaging of scalar modular resurgence, the second involves a non-trivial representation of the modular group and therefore illustrates the necessity of the vector-valued framework; we establish its modular resurgent structure in general, and work it out in full detail for the unary theta series, whose Eichler integrals are the false theta functions of quantum topology.

math.NT↗

arXiv2026

5d Schwarzschild-Tangherlini spacetime: MST-like formalism for a Reduced Confluent Heun Equation

We study the five-dimensional Schwarzschild-Tangherlini solution, with particular attention to its geodesic structure and massless scalar perturbations. In the probe limit, we present two applications. First, we compute the scattering angle for unbound geodesics showing both post-Newtonian and post-Minkowskian type expansions, and succeeding in resumming the resulting series in terms of hypergeometric functions. Second, we derive the Lyapunov exponent for deviations from a critical circular orbit, which is relevant to the eikonal estimation of quasinormal modes. We then investigate the dynamics of massless scalar $(s=0)$ perturbations, for which the radial equation becomes a Reduced Confluent Heun equation. In this $d=5$ Schwarzschild-Tangherlini case we develop an original extension of the standard Mano-Suzuki-Takasugi (MST) formalism and validate the construction by computing the renormalized angular-momentum parameter $\nu$, whose value agrees with an independent determination based on the quantum Seiberg-Witten formalism. Finally, we analyze the energy flux from circular orbits, obtaining post-Newtonian results through 2.5PN order.

gr-qc↗

arXiv2025

Modular resurgence, $q$-Pochhammer symbols, and quantum operators from mirror curves

Building on the results of [1,2], we study the resurgence of $q$-Pochhammer symbols and determine their summability and quantum modularity properties. We construct a new, infinite family of pairs of modular resurgent series from the asymptotic expansions of sums of $q$-Pochhammer symbols weighted by suitable Dirichlet characters. These weighted sums fit into the modular resurgence paradigm and provide further evidence supporting our conjectures in [1]. In the context of the topological string/spectral theory correspondence for toric Calabi-Yau threefolds, Kashaev and Mari\~no proved that the spectral traces of canonical quantum operators associated with local weighted projective planes can be expressed as sums of $q$-Pochhammer symbols. Exploiting this relation, we show that an exact strong-weak resurgent symmetry, first observed by the second author in [3] and fully formalized in [2] for local $\mathbb{P}^2$, applies to all local $\mathbb{P}^{m,n}$, albeit stripped of some of the underlying number-theoretic properties. Under some assumptions, these properties are restored when considering linear combinations of the spectral traces that reproduce the weighted sums above.

hep-th↗

arXiv2024

Summability for State Integrals of hyperbolic knots

We prove conjectures of Garoufalidis-Gu-Mari\~no that perturbative series associated with the hyperbolic knots $4_1$ and $5_2$ are resurgent and Borel summable. In the process, we give an algorithm that can be used to explicitly compute the Borel-Laplace resummation as a combination of state integrals of Andersen-Kashaev. This gives a complete description of the resurgent structure in these examples and allows for explicit computations of Stokes constants.

math.GT↗

arXiv2024

Effective-one-body waveform model for noncircularized, planar, coalescing black hole binaries II:high accuracy by improving logarithmic terms in resummations

Effective-one-body (EOB) models are based on analytical building blocks that, mathematically, are truncated Taylor series with logarithms. These functions are usually resummed using Pad\'e approximants obtained first assuming that the logarithms are constant, and then replacing them back into the resulting rational functions. A recent study pointed out that this procedure introduces spurious logarithmic terms when the resummed functions are reexpanded. Here we update the TEOBResumS-Dal\'i waveform model for spin-aligned, noncircularized coalescing black hole binaries by systematically implementing new (still Pad\'e based) resummations for all EOB functions (that is, the metric potentials $A, D$ and the residual waveform amplitude corrections $\rho_{\ell m}$ up to $\ell=8$). Once the model is informed by 50 Numerical Relativity simulations, this new approach proves key in lowering the maximum EOB/NR unfaithfulness $\bar{F}_{\rm EOBNR}^{\rm max}$ for the $\ell=m=2$ mode (with the Advanced LIGO noise in the total mass range $10-200M_{\odot}$) over 530 spin-aligned waveforms of the Simulating eXtreme Spacetimes catalog. A median unfaithfulness equal to $3.09\times 10^{-4}$ is achieved, which is a marked improvement over the previous value, $1.06\times 10^{-3}$. The largest value, ${\rm Max}[\bar{F}^{\rm max}_{\rm EOBNR}]= 6.80\times 10^{-3}$, is found for an equal-mass, equal-spin simulation with dimensionless spins $\sim +0.998$; only five configurations have $\bar{F}^{\rm max}_{\rm EOBNR} > 5\times 10^{-3}$ (four of which equal-mass and with equal spins larger than $\sim +0.98$). Results for eccentric binaries are similarly excellent (well below $10^{-2}$ and mostly around $10^{-3}$).

gr-qc↗

arXiv2024

The Regularity of ODEs and Thimble Integrals with Respect to Borel Summation

Through Borel summation, one can often reconstruct an analytic solution of a problem from its asymptotic expansion. We view the effectiveness of Borel summation as a regularity property of the solution, and we show that the solutions of certain differential equation and integration problems are regular in this sense. By taking a geometric perspective on the Laplace and Borel transforms, we also clarify why "Borel regular" solutions are associated with special points on the Borel plane. The particular classes of problems we look at are level 1 ODEs and exponential period integrals over one dimensional Lefschetz thimbles. To expand the variety of examples available in the literature, we treat various examples of these problems in detail.

math.CA↗

arXiv2024

Modular resurgent structures

The theory of resurgence uniquely associates a factorially divergent formal power series with a collection of exponentially small non-perturbative corrections paired with a set of complex numbers known as Stokes constants. When the Borel plane displays a single infinite tower of singularities, the secondary resurgent series are trivial, and the Stokes constants are coefficients of an $L$-function, a rich analytic number-theoretic fabric underlies the resurgent structure of the asymptotic series. We propose a new paradigm of modular resurgence that focuses on the role of the Stokes constants and the interplay of the $q$-series acting as their generating functions with the corresponding $L$-functions. Guided by two pivotal examples arising from topological string theory and the theory of Maass cusp forms, we introduce the notion of modular resurgent series, which we conjecture to have specific summability properties as well as to be related to quantum modular forms.

math.NT↗

arXiv2024

Strong-weak symmetry and quantum modularity of resurgent topological strings on local $\mathbb{P}^2$

Quantizing the mirror curve to a toric Calabi-Yau threefold gives rise to quantum operators whose fermionic spectral traces produce factorially divergent formal power series in the Planck constant and its inverse. These are conjecturally captured by the Nekrasov-Shatashvili and standard topological string free energies, respectively, via the TS/ST correspondence. The resurgent structures of the first fermionic spectral trace of local $\mathbb{P}^2$ in both weak and strong coupling limits were solved exactly by the second author in [1]. Here, we argue that a full-fledged strong-weak resurgent symmetry is at play, exchanging the perturbative/non-perturbative contributions to the holomorphic and anti-holomorphic blocks in the factorization of the spectral trace. This relies on a global net of relations connecting the perturbative series and the discontinuities in the dual regimes, which is built upon the analytic properties of the $L$-functions with coefficients given by the Stokes constants and the $q$-series acting as their generating functions. Then, we show that the latter are holomorphic quantum modular forms for $\Gamma_1(3)$ and are reconstructed by the median resummation of their asymptotic expansions.

hep-th↗

arXiv2024

Effective-one-body waveform model for non-circularized, planar, coalescing black hole binaries: the importance of radiation reaction

We present an updated version of the TEOBResumS-Dali effective-one-body (EOB) waveform model for spin aligned binaries on non-circularized orbits. Recently computed 4PN (nonspinning) terms are incorporated in the waveform and radiation reaction. The model is informed by a restricted sample ($\sim60$) of spin-aligned, quasi-circular, Numerical Relativity (NR) simulations. In the quasi-circular limit, the model displays EOB/NR unfaithfulness ${\bar{F}}^{\rm max}_{\rm EOBNR}\lesssim 10^{-2}$ (with median~ $1.06\times 10^{-3}$) (with Advanced LIGO noise and in the total mass range $10-200M_\odot$) for the dominant $\ell=m=2$ mode all over the 534 spin-aligned configurations available through the Simulating eXtreme Spacetime catalog of NR waveforms. Similar figures are also obtained with the 28 public eccentric SXS simulations and good compatibility between EOB and NR scattering angles is found. The quasi-circular limit of TEOBResumS-Dali is also found to be highly consistent with the TEOBResumS-GIOTTO quasi-circular model. We then systematically explore the importance of NR-tuning {\it also} the radiation reaction of the system. When this is done, the median of the distribution of quasi-circular ${\bar{F}}^{\rm max}_{\rm EOBNR}$ is lowered to $3.92\times 10^{-4}$, though balanced by a tail up to $\sim 0.1$ for large, positive spins. The same is true for the eccentric-inspiral datasets. We conclude that an improvement of the analytical description of the spin-dependent flux (and its interplay with the conservative part) is likely to be the cornerstone to lower the EOB/NR unfaithfulness below the $10^{-4}$ level all over the parameter space, thus grazing the current NR uncertainties as well as the expected needs for next generation of GW detector like Einstein Telescope.

gr-qc↗

arXiv2023

Scattering diagrams in mirror symmetry

Since the pioneering work of Kontsevich and Soibelman [51], scattering diagrams have started playing an important role in mirror symmetry, in particular in the study of the reconstruction problem. This paper aims at introducing the main ideas on the subject describing the role of scattering diagrams in relation to the SYZ conjecture and the HMS conjecture.

math.AG↗

arXiv2023

Regular singular Volterra equations on complex domains

The inverse Laplace transform can turn a linear differential equation on a complex domain into an equivalent Volterra integral equation on a real domain. This can make things simpler: for example, a differential equation with irregular singularities can become a Volterra equation with regular singularities. It can also reveal hidden structure, especially when the Volterra equation extends to a complex domain. Our main result is to show that for a certain kind of regular singular Volterra equation on a complex domain, there is always a unique solution of a certain form. As a motivating example, this kind of Volterra equation arises when using Laplace transform methods to solve a level 1 differential equation.

math.CA↗

arXiv2023

Resurgence, Habiro elements and strange identities

We prove resurgence properties for the Borel transform of a formal power series associated to elements in the Habiro ring that come from radial limits of partial theta series via strange identities. As an application, we prove a conjecture in quantum topology due to Costin and Garoufalidis for two families of torus knots.

math.NT↗

arXiv2020

The extended tropical vertex group

In this thesis we study the relation between scattering diagrams and deformations of holomorphic pairs, building on a recent work of Chan--Conan Leung--Ma. The new feature is the extended tropical vertex group where the scattering diagrams are defined. In addition, the extended tropical vertex provides interesting applications: on one hand we get a geometric interpretation of the wall-crossing formulas for coupled $2d$-$4d$ systems, previously introduced by Gaiotto--Moore--Neitzke. On the other hand, Gromov--Witten invariants of toric surfaces relative to their boundary divisor appear in the commutator formulas, along with certain absolute invariants due to Gross--Pandharipande--Siebert, which suggests a possible connection to open/closed theories in geometry and mathematical physics.

math.AG↗

arXiv2019

Deformations of holomorphic pairs and 2d-4d wall-crossing

We show how wall-crossing formulas in coupled 2d-4d systems, introduced by Gaiotto, Moore and Neitzke, can be interpreted geometrically in terms of the deformation theory of holomorphic pairs, given by a complex manifold together with a holomorphic vector bundle. The main part of the paper studies the relation between scattering diagrams and deformations of holomorphic pairs, building on recent work by Chan, Conan Leung and Ma.

math.AG↗