arXiv subjects

Inês Aniceto

Publications and source records attributed to Inês Aniceto.

At least 19 recordsLinked to original sources

arXiv2026

Topological Recursion and Quantum Path Signatures

We introduce a non-commutative Laplace transform between functionals on path space and formal series in a tensor algebra, under which a natural convolution of path functionals becomes an algebraic product of series. Applying it to a random unitary matrix-valued path development - the quantum path signature - we show that the governing planar loop equations take a non-commutative spectral form. We then extend the loop equations to a $1/N$ genus expansion, organised by topological recursion, and obtain a hierarchy of integral equations on path space for the corrections.

math-ph↗

arXiv2026

Which Saddles Contribute? The South-East Rule for Multidimensional Integrals

In this paper, we introduce and demonstrate a simple geometric algorithm to determine which critical points, both complex as well as real, contribute to the asymptotic evaluation of multiple integrals with exponential integrands of the form $e^{ikf(\boldsymbol{x})}$ over $\mathbb R^d$, for finite $d\ge 1$ and $f$ is analytic. In so doing, the algorithm removes the need to compute the flows of $-\text{Re} (i\nabla f)$ in $\mathbb C^d$ that is required to identify such relevant critical points in Picard-Lefschetz approaches to the derivation of such asymptotic expansions. By contrast, our algorithm relies on the combination of three simple features: the values of $f$ at all the critical points plotted in the complex Borel plane, the concept of adjacency between such points derived from algebraic resurgence/hyperasymptotic approaches and the new result here of a geometric "South-East" rule. The algorithm incorporates functions $f$ that remain bounded or unbounded on $\mathbb R^d$. We illustrate this new approach with both pedagogical and advanced examples, and draw conclusions as to its importance for resolving issues associated with Wick rotations and its implications for path integrals. This is a significant step towards a systematic way of identifying instanton contributions in real-time path integrals.

math-ph↗

arXiv2026

Analytic approaches to perturbations of strongly coupled Yang-Mills plasma

We study perturbations of Yang-Mills plasma, represented by scalar quasinormal modes of AdS black branes, as functions of the wave number $q$ in the entire range from zero to infinity. At finite $q$, these modes can be computed by classical spectral methods based on truncating the boundary value problem. We show that this truncation admits a natural analytic interpretation in terms of quantum Seiberg--Witten periods in the Nekrasov--Shatashvili limit, with the spectral condition organised as an instanton expansion around small values of the counting parameter. The physical black-brane problem corresponds to evaluating this series at a finite value of the counting parameter, and the Seiberg--Witten formulation provides a systematic way to analyse when the truncation is under control. In particular, it reveals that, as $q$ or the mode number $N$ increases, the physical point approaches the boundary of the domain of convergence of the instanton expansion, limiting the validity of the truncation approach. We overcome this limitation through an exact WKB analysis in which $q^{-1}$ acts as the expansion parameter. The resulting exact quantisation conditions, expressed in terms of period integrals and the associated Stokes geometry, incorporate both perturbative and non-perturbative corrections. The resummed quasinormal modes remain accurate far beyond the strict large-$q$ regime and can be analytically continued all the way to $q=0$, notably by using the Seiberg--Witten approach, providing a consistent description of the QNM spectrum.

hep-th↗

arXiv2026

The resurgence of errors in the localization of $\mathcal{N} = 2$ superconformal Yang-Mills

We give a physical interpretation for the analytic continuation of the partition function of superconformal SU$(2)$ $\mathcal{N}=2$ gauge theory on the four-sphere to all values of the Yang-Mills coupling. We show that a well-motivated 2d construction associates two-dimensional unstable instantons to the 4d complex saddles which appear as singularities in the integrand of the supersymmetric localization expression. The construction is based on the chiral algebra subsector, and aligns with the alternative Higgs branch localization.

hep-th↗

arXiv2025

Borel-Padé exponential asymptotics for the discrete nonlinear Schrödinger model with next-to-nearest neighbour interactions

In the present work we study discrete nonlinear Schr{ö}dinger models combining nearest (NN) and next-nearest (NNN) neighbor interactions, motivated by experiments in waveguide arrays. While we consider the more experimentally accessible case of positive ratio $μ$ of NNN to NN interactions, we focus on the intriguing case of competing such interactions $(μ<0)$, where stationary states can exist only for $-1/4 < μ< 0$. We analyze the key eigenvalues for the stability of the pulse-like stationary (ground) states, and find that such modes depend exponentially on the coupling parameter $\eps$, with suitable polynomial prefactors and corrections that we analyze in detail. Very good agreement of the resulting predictions is found with systematic numerical computations of the associated eigenvalues. This analysis uses Borel-Padé exponential asymptotics to determine Stokes multipliers in the solution; these multipliers cannot be obtained using standard matched asymptotic expansion approaches as they are hidden beyond all asymptotic orders, even near singular points. By using Borel-Padé methods near the singularity, we construct a general asymptotic template for studying parametric problems which require the calculation of subdominant Stokes multipliers.

nlin.PS↗

arXiv2024

An algebraic study of parametric Stokes phenomena

We investigate geometric aspects of co-equational parametric resurgence, by studying physical problems whose formal asymptotic solutions give rise to Borel transforms lying on an algebraic curve. This perspective allows us to elucidate concepts unique to parametric resurgence such as singularity structures, (virtual) turning points and the higher-order Stokes phenomenon. We construct examples as solutions to Borel plane partial differential equations using an algebraic curve ansatz before turning to the general analytic structure of co-equational resurgence problems, where we provide a systematic description of analytic continuation and Stokes constants through a Borel plane inner-outer matching procedure.

math-ph↗

arXiv2024

An analytic approach to the RTA Boltzmann attractor

We reformulate the Boltzmann equation in the relaxation time approximation undergoing Bjorken flow in terms of a novel partial differential equation for the generating function of the moments of the distribution function. This is used to obtain an approximate analytic description of this system's far-from-equilibrium attractor via a series expansion at early times. This expansion possesses a finite radius of convergence and can be analytically continued to late times. We find that this procedure reproduces the known values of shear viscosity and other transport coefficients to high accuracy. We also provide a simple approximate analytic expression that describes the attractor in the entire domain of interest for studies of quark-gluon plasma dynamics.

nucl-th↗

arXiv2022

The late to early time behaviour of an expanding plasma: hydrodynamisation from exponential asymptotics

We use exponential asymptotics to match the late time temperature evolution of an expanding, conformally invariant fluid to its early time behaviour. We show that the rich divergent transseries asymptotics at late times can be used to interpolate between the two regimes with exponential accuracy using the well-established methods of hyperasymptotics, Borel resummation and transasymptotics. This approach is generic and can be applied to any interpolation problem involving a local asymptotic transseries expansion as well as knowledge of the solution in a second region away from the expansion point. Moreover, we present global analytical properties of the solutions such as analytic approximations to the locations of the square-root branch points, exemplifying how the summed transseries contains within itself information about the observable in regions with different asymptotics.

hep-th↗

arXiv2020

Capturing the cascade: a transseries approach to delayed bifurcations

Transseries expansions build upon ordinary power series methods by including additional basis elements such as exponentials and logarithms. Alternative summation methods can then be used to "resum" series to obtain more efficient approximations, and have been successfully widely applied in the study of continuous linear and nonlinear, single and multidimensional problems. In particular, a method known as transasymptotic resummation can be used to describe continuous behaviour occurring on multiple scales without the need for asymptotic matching. Here we apply transasymptotic resummation to discrete systems and show that it may be used to naturally and efficiently describe discrete delayed bifurcations, or "canards", in singularly-perturbed variants of the logistic map which contain delayed period-doubling bifurcations. We use transasymptotic resummation to approximate the solutions, and describe the behaviour of the solution across the bifurcations. This approach has two significant advantages: it may be applied in systematic fashion even across multiple bifurcations, and the exponential multipliers encode information about the bifurcations that are used to explain effects seen in the solution behaviour.

math.DS↗

arXiv2020

Integrable Field Theories with an Interacting Massless Sector

We present the first known integrable relativistic field theories with interacting massive and massless sectors. And we demonstrate that knowledge of the massless sector is essential for understanding of the spectrum of the massive sector. Terms in this spectrum polynomial in the spatial volume (the accuracy for which the Bethe ansatz would suffice in a massive theory) require not just Lüscher-like corrections (usually exponentially small) but the full TBA integral equations. We are motivated by the implications of these ideas for AdS/CFT, but present here only field-theory results.

hep-th↗

arXiv2019

A Primer on Resurgent Transseries and Their Asymptotics

The computation of observables in general interacting theories, be them quantum mechanical, field, gauge or string theories, is a non-trivial problem which in many cases can only be addressed by resorting to perturbative methods. In most physically interesting problems these perturbative expansions result in asymptotic series with zero radius of convergence. These asymptotic series then require the use of resurgence and transseries in order for the associated observables to become nonperturbatively well-defined. Resurgence encodes the complete large-order asymptotic behaviour of the coefficients from a perturbative expansion, generically in terms of (multi) instanton sectors and for each problem in terms of its Stokes constants. Some observables arise from linear problems, and have a finite number of instanton sectors and associated Stokes constants; some other observables arise from nonlinear problems, and have an infinite number of instanton sectors and Stokes constants. By means of two very explicit examples, and with emphasis on a pedagogical style of presentation, this work aims at serving as a primer on the aforementioned resurgent, large-order asymptotics of general perturbative expansions. This includes discussions of transseries, Stokes phenomena, generalized steepest-descent methods, Borel transforms, nonlinear resonance, and alien calculus. Furthermore, resurgent properties of transseries---usually described mathematically via alien calculus---are recast in equivalent physical languages: either a "statistical mechanical" language, as motions in chains and lattices; or a "conformal field theoretical" language, with underlying Virasoro-like algebraic structures.

hep-th↗

arXiv2018

The large proper-time expansion of Yang-Mills plasma as a resurgent transseries

We show that the late-time expansion of the energy density of $\mathcal{N}=4$ supersymmetric Yang-Mills plasma at infinite coupling undergoing Bjorken flow takes the form of a multi-parameter transseries. Using the AdS/CFT correspondence we find a gravity solution which supplements the well known large proper-time expansion by exponentially-suppressed sectors corresponding to quasinormal modes of the AdS black-brane. The full solution also requires the presence of further sectors which have a natural interpretation as couplings between these modes. The exponentially-suppressed sectors represent nonhydrodynamic contributions to the energy density of the plasma. We use resurgence techniques on the resulting transseries to show that all the information encoded in the nonhydrodynamic sectors can be recovered from the original hydrodynamic gradient expansion.

hep-th↗

arXiv2016

Resurgence in Extended Hydrodynamics

It has recently been understood that the hydrodynamic series generated by the Müller-Israel-Stewart theory is divergent, and that this large order behaviour is consistent with the theory of resurgence. Furthermore, it was observed, that the physical origin of this is the presence of a purely damped nonhydrodynamic mode. It is very interesting to ask whether this picture persists in cases where the spectrum of nonhydrodynamic modes is richer. We take the first step in this direction by considering the simplest hydrodynamic theory which, instead of the purely damped mode, contains a pair of nonhydrodynamic modes of complex conjugate frequencies. This mimics the pattern of black brane quasinormal modes which appear on the gravity side of the AdS/CFT description of \symm\ plasma. We find that the resulting hydrodynamic series is divergent in a way consistent with resurgence and precisely encodes information about the nonhydrodynamic modes of the theory.

hep-th↗

arXiv2016

Massless Lüscher Terms and the Limitations of the AdS3 Asymptotic Bethe Ansatz

In AdS5/CFT4 integrability the Bethe ansatz gives the spectrum of long strings, accurate up to exponentially small corrections. This is no longer true in AdS3, as we demonstrate here by studying Luscher F-terms with a massless particle running in the loop. We apply this to the classic test of Hernandez & Lopez, in which the su(2) sector Bethe equations (including one-loop dressing phase) should match the semiclassical string theory result for a circular spinning string. These calculations did not agree in AdS3xS3xT4, and we show that the sum of all massless Luscher F-terms can reproduce the difference.

hep-th↗

arXiv2015

The Resurgence of the Cusp Anomalous Dimension

This work addresses the resurgent properties of the cusp anomalous dimension's strong coupling expansion, obtained from the integral Beisert-Eden-Staudacher (BES) equation. This expansion is factorially divergent, and its first nonperturbative corrections are related to the mass gap of the $O(6)$ $σ$-model. The factorial divergence can also be analysed from a resurgence perspective. Building on the work of Basso and Korchemsky, a transseries ansatz for the cusp anomalous dimension is proposed and the corresponding expected large-order behaviour studied. One finds non-perturbative phenomena in both the positive and negative real coupling directions, which need to be included to address the analyticity conditions coming from the BES equation. After checking the resurgence structure of the proposed transseries, it is shown that it naturally leads to an unambiguous resummation procedure, furthermore allowing for a strong/weak coupling interpolation.

hep-th↗

arXiv2015

Macroscopic (and Microscopic) Massless Modes

We study certain spinning strings exploring the flat directions of AdS3 x S3 x S3 x S1, the massless sector cousins of su(2) and sl(2) sector spinning strings. We describe these, and their vibrational modes, using the D(2,1;α)^2 algebraic curve. By exploiting a discrete symmetry of this structure which reverses the direction of motion on the spheres, and alters the masses of the fermionic modes s \to 1-s, we find out how to treat the massless fermions which were previously missing from this formalism. We show that folded strings behave as a special case of circular strings, in a sense which includes their mode frequencies, and we are able to recover this fact in the worldsheet formalism. We use these frequencies to calculate one-loop corrections to the energy, with a version of the Beisert-Tseytlin resummation.

hep-th↗

arXiv2015

Resurgent Analysis of Localizable Observables in Supersymmetric Gauge Theories

Localization methods have recently led to a plethora of new exact results in supersymmetric gauge theories, as certain observables may be computed in terms of matrix integrals. These can then be evaluated by making use of standard large N techniques, or else via perturbative expansions in the gauge coupling. Either approximation often leads to observables given in terms of asymptotic series, which need to be properly defined in order to obtain nonperturbative results. At the same time, resurgent analysis has recently been successfully applied to several problems, e.g., in quantum, field and string theories, precisely to overcome this issue and construct nonperturbative answers out of asymptotic perturbative expansions. The present work uses exact results from supersymmetric localization to address the resurgent structure of the free energy and partition function of Chern-Simons and ABJM gauge theories in three dimensions, and of N=2 supersymmetric Yang-Mills theories in four dimensions. For each case, the complete structure of Borel singularities is exactly determined, and the relation of these singularities with the large-order behavior of (multi-instanton) perturbative expansions is made fully precise.

hep-th↗

arXiv2014

An improved AFS phase for AdS3 string integrability

We propose a number of modifications to the classical term in the dressing phase for integrable strings in AdS3 x S3 x S3 x S1, and check these against existing perturbative calculations, crossing symmetry, and the semiclassical limit of the Bethe equations. The principal change is that the phase for different masses should start with a term Q_1 Q_2, like the one-loop AdS3 dressing phase, rather than Q_2 Q_3 as for the original AdS5 AFS phase.

hep-th↗