arXiv subjects

Dennis le Plat

Publications and source records attributed to Dennis le Plat.

16 recordsLinked to original sources

arXiv2026

From Fredholm Determinants to AdS/CFT Observables: A Universal Strong-Coupling Framework

We investigate the trans-series structure of the cusp anomalous dimension of $\mathcal{N}=4$ supersymmetric Yang-Mills theory and the dynamically generated mass gap of the $\mathrm{O}(6)$ sigma model at strong 't Hooft coupling. We consider the one-parameter deformation of the cusp anomalous dimension, known as the tilted cusp, and review its strong-coupling expansion obtained through its representation in terms of Fredholm determinants with a matrix Bessel kernel. The advantage of this deformation is that the non-perturbative scales separate naturally, revealing structures that remain hidden in the physical limit. Motivated by this observation, we introduce the tilted mass gap, which reduces to the physical $\mathrm{O}(6)$ mass gap at a special value of the deformation parameter and exhibits a deep connection with the tilted cusp. This formulation allows us to determine the complete strong-coupling trans-series and resurgence structure of the $\mathrm{O}(6)$ mass gap, while extending and proving conjectured relations between successive non-perturbative corrections. Building on the underlying Fredholm determinant representation, we construct an Alien calculus that generates all non-perturbative sectors of these AdS/CFT observables directly from their perturbative expansions. Finally, we derive an exact all-orders relation between the strong-coupling trans-series of the $\mathrm{O}(6)$ mass gap and the cusp anomalous dimension of planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory.

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arXiv2026

The full strong coupling expansion of the cusp anomalous dimension and the O(6) mass gap

We present the full transseries of the strong-coupling expansion of the cusp anomalous dimension in N=4 super Yang-Mills theory. This quantity admits an exact representation as a ratio of two determinants with particularly simple strong-coupling expansions. Nonperturbative contributions are classified by partitions into distinct odd integers and obey a universal structure, with Stokes constants that can be computed iteratively. We also determine the full transseries of the O(6) mass gap as a function of the 't Hooft coupling. In the AdS/CFT string description, this mass gap fixes the dynamically generated scale of the O(6) sigma model governing the sphere fluctuations, and we establish its full nonperturbative relation to the cusp anomalous dimension.

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arXiv2025

Revisiting the tensionless limit of pure-Ramond-Ramond AdS3/CFT2

We revisit the numerical solution of the mirror TBA equations for pure--Ramond-Ramond strings on $AdS_3\times S^3\times T^4$ in the tensionless limit. Our analysis uses the recently-proposed modification of the dressing factors which account for non-trivial exchange relations of the massless modes. At leading order in the tension, the dynamics is driven by the massless excitations associated to $T^4$ modes and their superpartners, but it is non-relativistic and interacting unlike what happens in the symmetric-product orbifold CFT of $T^4$.

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arXiv2025

Three-point functions from integrability in $\mathcal{N}=2$ orbifold theories

Besides solving the spectral problem of $\mathcal{N}=4$ Super-Yang-Mills (SYM) theory, integrability also provides us with tools to compute the structure constants of the theory, most prominently through the hexagon formalism. We show that, with minor modifications, this formalism can also be applied to orbifolds of $\mathcal{N}=4$ SYM theory, which are integrable theories in their own right. To substantiate this claim, we test our results against a direct gauge-theory calculation at tree-level. We focus here on a family of $\mathcal{N}=2$ supersymmetric $\mathbb{Z}_M$-orbifold theories. BPS correlators in these theories have recently been investigated with independent localisation techniques and a structural matching with wrapping corrections in the hexagon formalism was observed. Together with our weak-coupling evidence, this suggests that a full determination of the structure constants of orbifold theories at finite coupling may be within reach.

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arXiv2025

Universality in the resurgence of generalized Tracy-Widom distributions

We analyze determinants associated with Bessel kernels and generic symbol functions, which govern a class of observables across all values of the 't Hooft coupling in supersymmetric gauge theories. Previous approaches, based on integro-differential equations, have provided systematic strong-coupling expansions for the logarithms of these determinants, expressed through the moments of the symbol. The resulting asymptotic series, once completed with non-perturbative terms, allowed the leading resurgence relations to be tested. In this Letter we focus directly on the determinants themselves, and we uncover a strikingly simple non-perturbative structure: all trans-series corrections share a universal form, while the moments transform in a direct and intuitive way. This simplicity points to an underlying organizing principle for the non-perturbative dynamics of gauge theory observables.

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arXiv2025

The complete trans-series for conserved charges in the Lieb-Liniger model

We determine the complete trans-series solution for the (non-relativistic) moments of the rapidity density in the Lieb-Liniger model. The trans-series is written explicitly in terms of a perturbative basis, which can be obtained from the already known perturbative expansion of the density by solving several ordinary differential equations. Unknown integration constants are fixed from Volin's method. We have checked that our solution satisfies the analytical consistency requirements including the newly derived resurgence relations and agrees with the high precision numerical solution. Our results also provides the full analytic trans-series for the capacitance of the coaxial circular plate capacitor.

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arXiv2024

Anomalous dimensions from the $\mathcal{N}=4$ SYM hexagon

We consider the correlator $\langle \mathcal{L} \mathcal{K} \tilde{ \mathcal{K}} \rangle $ of the Lagrange operator of $\mathcal{N}=4$ super Yang-Mills theory and two conjugate two-excitation operators in an $su(2)$ sector. We recover the planar one-loop anomalous dimension of the renormalised operators from this hexagon computation.

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arXiv2023

More on the tensionless limit of pure-Ramond-Ramond AdS3/CFT2

In a recent letter we presented the equations which describe tensionless limit of the excited-state spectrum for strings on $AdS_3\times S^3\times T^4$ supported by Ramond-Ramond flux, and their numerical solution. In this paper, we give a detailed account of the derivation of these equations from the mirror TBA equations proposed by Frolov and Sfondrini, discussing the contour-deformation trick which we used to obtain excited-state equations and the tensionless limit. We also comment at length on the algorithm for the numerical solution of the equations in the tensionless limit, and present a number of explicit numerical results, as well as comment on their interpretation.

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arXiv2023

The Tensionless Limit of Pure-Ramond-Ramond AdS3/CFT2

Despite impressive advances in the AdS3/CFT2 correspondence, the setup involving Ramond-Ramond backgrounds, which is related to the D1-D5 system of branes, remained relatively poorly understood. We use the Mirror TBA equations recently constructed by Frolov and Sfondrini to study the spectrum of pure Ramond-Ramond $AdS_3\times S^3\times T^4$ strings. We find that the leading-order contribution to the anomalous dimensions at small tension is due to the gapless worldsheet excitations, i.e. to the $T^4$ bosons and their superpartners, whose interactions are nontrivial.

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arXiv2023

Double excitations in the AdS(5)/CFT(4) integrable system and the Lagrange operator

It is argued that the integrable model for the planar spectrum of the AdS/CFT correspondence can accommodate for the full spectrum of excitations $D^{α\dot α}, ϕ^{[IJ]}, ψ^I, \bar ψ_I, F^{αβ}, \tilde F^{\dot α\dot β}$ (with $I,J \in 1 \ldots 4$) if double excitations are allowed for all three raising operators of the internal $SU(4)$ symmetry. We present a tree-level analysis of related creation amplitudes in the nested Bethe ansatz as well as in the original level-1 picture in which excitations of various flavours scatter by a true $S$-matrix. In the latter case, the creation amplitudes for all double excitations we encounter take a perfectly universal form. Building on these ideas we work out Bethe solutions and states relevant in the mixing problem concerning the on-shell Lagrangian of ${\cal N} = 4$ super Yang-Mills theory. Owing to the very existence of double excitations, the chiral Yang-Mills field strength tensor can be represented by the four fermions $\{ψ^{31}, ψ^{32}, ψ^{41}, ψ^{42}\}$ moving on a spin chain of length two. Our analysis remains restricted to leading order in the coupling, where the conformal eigenstate corresponding to the on-shell Lagrangian only comprises the pure Yang-Mills action. It should eventually be possible to augment our analysis to higher loop orders by incorporating coupling corrections in the relevant ingredients from the Bethe ansatz. Finally, it was recently realised how structure constants for operators containing the hitherto hidden half of the excitations can be computed by the hexagon formalism. We use this for a first test of our conjecture for the on-shell Lagrangian, namely that its three-point function with two half-BPS operators of equal length ought to vanish.

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arXiv2022

Higher-rank sectors in the hexagon formalism and marginal deformations

The hexagon approach provides an integrability framework for the computation of structure constants in $\mathcal{N}=4$ super Yang--Mills theory in four dimensions. Three-point functions are cut into two hexagonal patches, on which the excitations of the long-range Bethe ansatz of the spectrum problem scatter. To this end, the Bethe states representing the operators also need to be cut into two parts. In rank-one sectors such entangled states are fairly straightforward to construct so that most applications of the method have so far been restricted to this simplest case. In this article we construct entangled states for operators in $psu(1,1|2)$ sectors, importing a minimum of information from the nested Bethe ansatz. The idea is successfully tested against free field theory for a sample set of correlators with up to three higher-rank operators. Further, we take a look at the same correlators in the presence of marginal deformations of the theory. While a systematic modification of the hexagon procedure remains out of reach for now, in practical applications the undeformed amplitudes are surprisingly efficient, especially for a certain one-parameter deformation.

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arXiv2021

Integrable bootstrap for AdS3/CFT2 correlation functions

We propose an integrable bootstrap framework for the computation of correlation functions for superstrings in $AdS_3\times S^3\times T^4$ backgrounds supported by an arbitrary mixture or Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz fluxes. The framework extends the "hexagon tessellation" approach which was originally proposed for $AdS_5\times S^5$ and for the first time it demonstrates its applicability to other (less supersymmetric) setups. We work out the hexagon form factor for two-particle states, including its dressing factors which follow from those of the spectral problem, and we show that it satisfies non-trivial consistency conditions. We propose a bootstrap principle, slightly different from that of $AdS_5\times S^5$, which allows to extend the form factor to arbitrarily many particles. Finally, we compare its predictions with some correlation functions of protected operators. Possible applications of this construction include the study of wrapping corrections, of higher-point correlation functions, and of non-planar corrections.

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arXiv2019

Multi-particle finite-volume effects for hexagon tessellations

Correlation functions of gauge-invariant composite operators in N=4 super Yang-Mills theory can be computed by integrability using triangulations. The elementary tile in this process is the hexagon, which should be glued by appropriately inserting resolutions of the identity involving virtual ("mirror") magnons. We consider this problem for five-point functions of protected operators. At one-loop in the 't Hooft coupling, it is necessary to glue three adjacent tiles which involves two virtual magnons scattering among each other. We show that the result can be simplified by using an adapted mirror rotation and employing appropriate summation techniques. The mirror-particle contributions then yield hyperlogarithms of weight two. Finally, we use these results to investigate braiding prescriptions introduced in earlier work on the problem.

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arXiv2019

Polylogarithms from the bound state S-matrix

Higher-point functions of gauge invariant composite operators in N=4 super Yang-Mills theory can be computed via triangulation. The elementary tile in this process is the hexagon introduced for the evaluation of structure constants. A glueing procedure welding the tiles back together is needed to return to the original object. In this note we present work in progress on n-point functions of BPS operators. In this case, quantum corrections are entirely carried by the glueing procedure. The lowest non-elementary process is the glueing of three adjacent tiles by the exchange of two single magnons. This problem has been analysed before. With a view to resolving some conceptional questions and to generalising to higher processes we are trying to develop an algorithmic approach using the representation of hypergeometric sums as integrals over Euler kernels.

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arXiv2018

Positivity of hexagon perturbation theory

The hexagon-form-factor program was proposed as a way to compute three- and higher-point correlation functions in $\mathcal{N}=4$ super-symmetric Yang-Mills theory and in the dual AdS$_5\times$S$^5$ superstring theory, by exploiting the integrability of the theory in the 't Hooft limit. This approach is reminiscent of the asymptotic Bethe ansatz in that it applies to a large-volume expansion. Finite-volume corrections can be incorporated through Lüscher-like formulae, though the systematics of this expansion is largely unexplored so far. Strikingly, finite-volume corrections may feature negative powers of the 't Hooft coupling $g$ in the small-$g$ expansion, potentially leading to a breakdown of the formalism. In this work we show that the finite-volume perturbation theory for the hexagon is positive and thereby compatible with the weak-coupling expansion for arbitrary $n$-point functions.

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arXiv2017

Colour-dressed hexagon tessellations for correlation functions and non-planar corrections

We continue the study of four-point correlation functions by the hexagon tessellation approach initiated in 1611.05436 and 1611.05577. We consider planar tree-level correlation functions in $\mathcal{N} = 4$ supersymmetric Yang-Mills theory involving two non-protected operators. We find that, in order to reproduce the field theory result, it is necessary to include $SU(N)$ colour factors in the hexagon formalism; moreover, we find that the hexagon approach as it stands is naturally tailored to the single-trace part of correlation functions, and does not account for multi-trace admixtures. We discuss how to compute correlators involving double-trace operators, as well as more general $1/N$ effects; in particular we compute the whole next-to-leading order in the large-$N$ expansion of tree-level BMN two-point functions by tessellating a torus with punctures. Finally, we turn to the issue of "wrapping", Lüscher-like corrections. We show that $SU(N)$ colour-dressing reproduces an earlier empirical rule for incorporating single-magnon wrapping, and we provide a direct interpretation of such wrapping processes in terms of $\mathcal{N}=2$ supersymmetric Feynman diagrams.

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