arXiv subjects

Luis F. Alday

Publications and source records attributed to Luis F. Alday.

At least 19 recordsLinked to original sources

arXiv2026

Soft Algebra for ${\cal N}=4$ SYM

Scattering amplitudes of $n$ particles in nonabelian gauge theories admit factorizations of the general form $\mathcal{A}_n \;=\; \mathcal{A}^{\rm soft}_n \times \mathcal{A}^{\rm hard}_n$, where $\mathcal{A}^{\rm soft}_n$ is IR divergent, while $\mathcal{A}^{\rm hard}_n$ is IR finite and encodes the higher loop corrections to scattering. We specify a particular all-orders definition of this factorization for planar ${\cal N}=4$ super Yang-Mills (SYM) and argue that the resulting $\mathcal{A}_n^{\rm hard}$ obeys an uncorrected tree-level soft theorem. Moreover it furnishes a representation of the undeformed tree-level $\cal S$-algebra generated by a tower of soft gluons. The results follow from several commonly invoked assumptions for ${\cal N}=4$ SYM, including BDS one-loop exponentiation of the splitting function and amplitude/Wilson-loop duality.

hep-th↗

arXiv2026

Walking Sudakov: From Cusp to Octagon

We study the Sudakov form factor and the four-point scattering amplitude on the Coulomb branch of planar $\mathcal{N}=4$ SYM as functions of the Coulomb-branch parameters and kinematic invariants. This setup provides a controlled probe of the interpolation between on- and off-shell regimes of infrared-sensitive quantities in gauge theories. We identify a novel scaling limit in which both observables exhibit double-logarithmic behavior governed by a walking anomalous dimension. As the mass scales are varied, this walking anomalous dimension interpolates between the cusp anomalous dimension of the on-shell regime and the octagon anomalous dimension of the off-shell regime. Based on the explicit two-loop result and the expected all-order structure, we propose an all-loop form for the walking anomalous dimension both for the form factor and for the four-point scattering amplitude. These all-loop expressions depend on new, presently unknown functions of the 't Hooft coupling.

hep-th↗

arXiv2025

From Partons to Strings: Scattering on the Coulomb Branch of $\mathcal{N}=4$ SYM

We study scattering on the Coulomb branch of planar ${\mathcal{N}}=4$ SYM at finite 't Hooft coupling. This setup defines a family of classical open-string S-matrices that smoothly interpolates between perturbative parton scattering at weak coupling and flat-space string scattering at strong coupling. We focus on the four-point amplitude, which exhibits a remarkably rich structure: nonlinear Regge trajectories, dual conformal invariance, an intricate spectrum of bound states with an accumulation point, and a two-particle cut. Dual conformal invariance relates the spectrum of Regge trajectories to the energy spectrum of the Maldacena-Wilson cusp Hamiltonian. This connection allows us to use integrability to compute the leading and subleading Regge trajectories at finite coupling, which we then input in the bootstrap analysis. At strong coupling, we use the worldsheet bootstrap to construct the first $AdS$-curvature correction to the Veneziano amplitude. We apply dispersion relations and S-matrix bootstrap techniques to derive bounds on Wilson coefficients, couplings to bound states, and the overall shape of the amplitude. We find that the $\mathcal{N}=4$ amplitude saturates the bootstrap bounds at weak coupling and nearly saturates them at strong coupling. At intermediate coupling, the amplitude traces a nontrivial path through the allowed space of observables. To characterize this path, we combine the weak- and strong-coupling information about the amplitude to construct a finite-coupling model for Wilson coefficients using a Padé approximation. The resulting model satisfies bootstrap constraints and yields sharp predictions for the finite-coupling behavior of the amplitude. We provide evidence that complete monotonicity of the scattering amplitude, previously observed perturbatively, persists at finite coupling.

hep-th↗

arXiv2025

Monodromy Relations for String Amplitudes on AdS

We consider the $AdS$ Veneziano amplitude describing the scattering of four gluons in type IIB string theory on $AdS_5 \times S^3$. We propose a set of powerful monodromy relations between different colour-ordered amplitudes. These relations arise as a consequence of the emergent world-sheet description of open string scattering on $AdS$. In flat space, they reduce to the usual monodromy relations for the Veneziano amplitude, and they hold order by order in the small curvature expansion. The relations hold for all results available in the literature, including the scattering of arbitrary KK-modes.

hep-th↗

arXiv2025

Stringy KLT Relations on $AdS$

We study the building blocks of open and closed string amplitudes on $AdS$. These are given by two infinite towers of world-sheet integrals generalising the Euler and complex beta functions respectively. We show that the open and closed building blocks are related by an $AdS$ version of the KLT relations, whose Kernel can be computed exactly. We furthermore show that the building blocks for open string amplitudes are given by Aomoto-Gelfand hypergeometric functions, and give their closed form expression up to weight four.

hep-th↗

arXiv2025

One-loop Gluon Amplitudes in AdS

We initiate the study of one-loop gluon amplitudes in AdS space. These amplitudes were recently computed at tree level for a variety of backgrounds of the form $AdS_{d+1} \times S^3$. For concreteness, we compute the one-loop correction to the massless gluon amplitude on $AdS_5\times S^3$, which corresponds to the four-point correlator of the flavor current multiplet in the dual 4d $\mathcal{N}=2$ SCFT. This requires solving a mixing problem that involves tree-level amplitudes of arbitrarily massive Kaluza-Klein modes. The final answer has the same color structure as in flat space but the dependence on Mandelstam variables is more complicated, with logarithms replaced by polygamma functions.

hep-th↗

arXiv2024

On the $AdS_3$ Virasoro-Shapiro Amplitude

We consider tree-level scattering amplitudes for four string tachyons on $AdS_3 \times {\cal N}$ with pure NSNS fluxes. We show that in a small curvature expansion, properly defined, the amplitudes take the form of a genus zero integral given by the Virasoro-Shapiro integrand with the extra insertion of single valued multiple polylogarithms. This is the same structure as the one found for the AdS Virasoro-Shapiro amplitude in higher dimensions.

hep-th↗

arXiv2024

Flat-space limit of defect correlators and stringy AdS form factors

We study AdS form factors, given by the Mellin representation for CFT correlators of local operators in the presence of extended defects. We propose a formula for taking (and expanding around) the flat-space limit. This formula relates the flat-space form factors for particles scattering off an extended object to the high-energy limit of the Mellin amplitude, via a Borel transform. We check the validity of our proposal in a number of examples. As an application, we study the two-point function of local operators in the presence of a 't Hooft loop in 4d $\mathcal{N}=4$ SYM, and compute the first few orders of stringy corrections to the AdS form factor of gravitons scattering off a D1 brane.

hep-th↗

arXiv2024

On the Regge behaviour of the AdS Virasoro-Shapiro Amplitude

We compute the AdS Virasoro-Shapiro amplitude in the Regge limit, in terms of the CFT data of the exchanged operators in the leading Regge trajectory. To any order in the small curvature expansion, the result can be written in terms of derivatives of the flat space Virasoro-Shapiro amplitude in the Regge limit. The result also admits an integral representation involving single-valued logarithms, fully consistent with recent proposals for the full AdS Virasoro-Shapiro amplitude.

hep-th↗

arXiv2024

Carrollian Amplitudes from Holographic Correlators

Carrollian amplitudes are flat space amplitudes written in position space at null infinity which can be re-interpreted as correlators in a putative dual Carrollian CFT. We argue that these amplitudes are the natural objects obtained in the flat space limit of AdS Lorentzian boundary correlators. The flat limit is taken entirely in position space by introducing Bondi coordinates in the bulk. From the bulk perspective, this procedure makes it manifest that the flat limit of any Witten diagram is the corresponding flat space Feynman diagram. It also makes explicit the fact that the flat limit in the bulk is implemented by a Carrollian limit at the boundary. We systematically analyse tree-level two, three and four-point correlators. Familiar features such as the distributional nature of Carrollian amplitudes and the presence of a bulk point singularity arise naturally as a consequence of requiring a finite and non-trivial Carrollian limit.

hep-th↗

arXiv2024

Single-valuedness of the AdS Veneziano amplitude

We consider the Veneziano amplitude for the scattering of gluons in type IIB string theory on $AdS_5 \times S^5/\mathbb{Z}_2$ in the presence of D7 branes. On general grounds curvature corrections around flat space can be thought of as arising from the extra insertion of soft gravitons. This naturally leads to an open string world-sheet representation with the extra insertion of single-valued functions evaluated on the real line. We check that the recently obtained first curvature correction is of this form and use this new constraint to compute the second curvature correction of the AdS Veneziano amplitude.

hep-th↗

arXiv2024

The AdS Veneziano amplitude at small curvature

We compute the AdS Veneziano amplitude for type IIB gluon scattering in $AdS_5 \times S^3$ to all orders in $\alpha'$ in a small curvature expansion. This is achieved by combining a dispersion relation in the dual $4d$ $\mathcal{N}=2$ SCFT with an ansatz for the amplitude as a worldsheet integral in terms of multiple polylogarithms. The first curvature correction is fully fixed in this way and satisfies consistency checks in the high energy limit, the low energy expansion as previously fixed using supersymmetric localisation, and for the energy of massive string operators, which we independently compute using a semiclassical expansion. We also combine localisation with this first curvature correction to fix the unprotected $D^4F^4$ correction to the amplitude at finite curvature.

hep-th↗

arXiv2024

High Energy String Scattering in AdS

We study the AdS Virasoro-Shapiro amplitude in the limit of fixed-angle high energy scattering. A recent representation as a world-sheet integral allows to compute the amplitude in this regime by saddle point techniques, very much as in flat space. This result is then compared to a classical scattering computation in AdS and agreement is found. As a byproduct of this comparison we show that AdS curvature corrections exponentiate in the high energy limit.

hep-th↗

arXiv2024

Six-Point AdS Gluon Amplitudes from Flat Space and Factorization

We present a powerful new approach to compute tree-level higher-point holographic correlators. Our method only exploits the flat-space limit, where we point out a novel and important simplification, and factorization of amplitudes in AdS. In particular, it makes minimal use of supersymmetry, crucial in all previous bootstrap methods. We demonstrate our method by computing the six-point super gluon amplitude of super Yang-Mills in AdS$_5$.

hep-th↗

arXiv2023

The AdS Virasoro-Shapiro Amplitude

We present a constructive method to compute the AdS Virasoro-Shapiro amplitude, order by order in AdS curvature corrections. At kth order the answer takes the form of a genus zero world-sheet integral involving weight 3k single-valued multiple polylogarithms. The coefficients in our ansatz are fixed, order by order, by requiring: crossing symmetry; the correct supergravity limit; the correct structure of poles, determined by dispersive sum rules; and the dimensions of the first few Konishi-like operators, available from integrability. We explicitly construct the first two curvature corrections. Our final answer then reproduces all localisation results and all CFT data available from integrability, to this order, and produces a wealth of new CFT data for planar N=4 SYM at strong coupling.

hep-th↗

arXiv2023

Relations between integrated correlators in $\mathcal{N}=4$ Supersymmetric Yang--Mills Theory

Integrated correlation functions in $\mathcal{N}=4$ supersymmetric Yang--Mills theory with gauge group $SU(N)$ can be expressed in terms of the localised $S^4$ partition function, $Z_N$, deformed by a mass $m$. Two such cases are $\mathcal{C}_N=(\text{Im} τ)^2 \partial_τ\partial_{\barτ} \partial_m^2\log Z_N\vert_{m=0}$ and $\mathcal{H}_N=\partial_m^4\log Z_N\vert_{m=0}$, which are modular invariant functions of the complex coupling $τ$. While $\mathcal{C}_N$ was recently written in terms of a two-dimensional lattice sum for any $N$ and $τ$, $\mathcal{H}_N$ has only been evaluated up to order $1/N^3$ in a large-$N$ expansion in terms of modular invariant functions with no known lattice sum realisation. Here we develop methods for evaluating $\mathcal{H}_N$ to any desired order in $1/N$ and finite $τ$. We use this new data to constrain higher loop corrections to the stress tensor correlator, and give evidence for several intriguing relations between $\mathcal{H}_N$ and $\mathcal{C}_N$ to all orders in $1/N$. We also give evidence that the coefficients of the $1/N$ expansion of $\mathcal{H}_N$ can be written as lattice sums to all orders. Lastly, these large $N$ and finite $τ$ results are used to accurately estimate the integrated correlators at finite $N$ and finite $τ$.

hep-th↗

arXiv2023

On the spectrum and structure constants of short operators in N=4 SYM at strong coupling

We study short operators in planar $\mathcal{N}=4$ SYM at strong coupling, for general spin and $SO(6)$ symmetric traceless representations. At strong coupling their dimension grows like $Δ\sim 2\sqrtδ λ^{1/4}$ and their spectrum of degeneracies can be analysed by considering the massive spectrum of type II strings in flat space-time. We furthermore compute their structure constants with two arbitrary chiral primary operators. This is done by considering the four-point correlator of arbitrary chiral primary operators at strong coupling in planar $\mathcal{N}=4$ SYM, including the supergravity approximation plus the infinite tower of stringy corrections that contributes in the flat space limit. Our results are valid for generic rank $n$ symmetric traceless representations of $SO(6)$ and in particular for $n \gg 1$, as long as $n \ll λ^{1/4}$.

hep-th↗

arXiv2023

Emergent world-sheet for the AdS Virasoro-Shapiro amplitude

We construct a representation for the first AdS curvature correction to the Virasoro-Shapiro amplitude, as an integral over the Riemann sphere. The integrand is that of the Virasoro-Shapiro amplitude in flat space, with the extra insertion of a linear combination of single-valued multiple polylogarithms of weight three. The integral representation implies an elegant, manifestly single-valued representation for the Wilson coefficients of the low energy expansion.

hep-th↗