arXiv subjects

Luis F. Alday

Publications and source records attributed to Luis F. Alday.

At least 37 records · Page 2Linked to original sources

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.

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arXiv2023

AdS Virasoro-Shapiro from single-valued periods

We determine the full $1/\sqrtλ$ correction to the flat-space Wilson coefficients which enter the AdS Virasoro-Shapiro amplitude in $\mathcal{N}=4$ SYM theory at strong coupling. The assumption that the Wilson coefficients are in the ring of single-valued multiple zeta values, as expected for closed string amplitudes, is surprisingly powerful and leads to a unique solution to the dispersive sum rules relating Wilson coefficients and OPE data obtained in [1]. The corresponding OPE data fully agrees with and extends the results from integrability. The Wilson coefficients to order $1/\sqrtλ$ can be summed into an expression whose structure of poles and residues generalises that of the Virasoro-Shapiro amplitude in flat space.

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arXiv2022

M-theory on $AdS_4\times S^7$ at 1-loop and beyond

We study graviton scattering on $AdS_4\times S^7$, which is dual to the stress tensor multiplet four-point function in the maximally supersymmetric 3d $U(N)_1\times U(N)_{-1}$ ABJM theory. We compute 1-loop corrections to this holographic correlator coming from Witten diagrams with supergravity $R$ and higher derivative $R^4$ vertices, up to contact term ambiguities, and find that the flat space limit matches the corresponding terms in the 11d M-theory S-matrix. We then use supersymmetric localization to show that all the 1-loop contact terms vanish, as was previously observed for the $AdS_4\times S^7/\mathbb{Z}_2$ theory dual to $U(N)_2\times U(N)_{-2}$ ABJM. Finally, we use the recent localization results of Gaiotto and Abajian, as inspired by twisted M-theory, to compute all the short OPE coefficients in correlators of the stress tensor multiplet and the next lowest half-BPS operator, which we find saturate the bootstrap bounds on these mixed correlators for all $N$.

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arXiv2022

AdS Virasoro-Shapiro from dispersive sum rules

We consider the four-point correlator of the stress-energy tensor in ${\cal N}=4$ SYM, to leading order in inverse powers of the central charge, but including all order corrections in $1/λ$. This corresponds to the AdS version of the Virasoro-Shapiro amplitude to all orders in the small $α'$/low energy expansion. Using dispersion relations in Mellin space, we derive an infinite set of sum rules. These sum rules strongly constrain the form of the amplitude, and determine all coefficients in the low energy expansion in terms of the CFT data for heavy string operators, in principle available from integrability. For the first set of corrections to the flat space amplitude we find a unique solution consistent with the results from integrability and localisation.

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arXiv2022

Pure anti-de Sitter supergravity and the conformal bootstrap

We consider graviton scattering in maximal supergravity on Anti-de Sitter space (AdS) in $d+1$ dimensions for $d=3,4,\text{and $6$}$ with no extra compact spacetime factor. Holography suggests that this theory is dual to an exotic maximally supersymmetric conformal field theory (CFT) in $d$ dimensions whose only light single trace operator is the stress tensor. This contrasts with more standard cases like Type IIB string theory on $AdS_5\times S^5$ dual to $\mathcal{N}=4$ Super-Yang-Mills, where the CFT has light single trace operators for each Kaluza-Klein mode on $S^5$. We compute the 1-loop correction to the pure AdS$_{d+1}$ theory in a small Planck length expansion, which is dual to the large central charge expansion in the CFT. We find that this correction saturates the most general non-perturbative conformal bootstrap bounds on this correlator in the large central charge regime for $d=3,4,6$, while the 1-loop correction to CFTs with string/M-theory duals all lie inside the allowed region.

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arXiv2022

Super Gluon Five-Point Amplitudes in AdS Space

We present the tree-level five-point amplitude of the lowest KK mode of SYM on AdS$_5$$\times$S$^3$, dual to the correlator of the flavor current multiplet in the dual 4d ${\cal N}=2$ SCFT. Its color and kinematical structure is particularly simple and resembles that of the flat-space gluon amplitude.

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arXiv2022

ABJM at Strong Coupling from M-theory, Localization, and Lorentzian Inversion

We study the stress tensor multiplet four-point function in the 3d maximally supersymmetric ABJ(M) theory with Chern-Simons level $k=2$, which in the large $N$ limit is holographically dual to weakly coupled M-theory on $AdS_4\times S^7/\mathbb{Z}_2$. We use the Lorentzian inversion to compute the 1-loop correction to this holographic correlator coming from Witten diagrams with supergravity $R$ and the first higher derivative correction $R^4$ vertices, up to a finite number of contact terms that contribute to low spins where the inversion formula does not converge. We find a precise match with the corresponding terms in the 11d M-theory S-matrix by taking the flat space limit, which is not sensitive to these contact terms. We then conjecturally fix these contact terms by analytically continuing the inversion formula below its expected range of convergence, and verify this conjecture using supersymmetric localization. Finally, we compare some of the 1-loop CFT data to non-perturbative in $N$ bounds from the numerical conformal bootstrap, which we compute at unprecedently high accuracy, and find that the 1-loop corrections saturate the bounds in the large $N$ regime, which extends the previously observed match at tree level.

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arXiv2021

Modular invariant holographic correlators for $\mathcal{N}=4$ SYM with general gauge group

We study the stress tensor four-point function for $\mathcal{N}=4$ SYM with gauge group $G=SU(N)$, $SO(2N+1)$, $SO(2N)$ or $USp(2N)$ at large $N$. When $G=SU(N)$, the theory is dual to type IIB string theory on $AdS_5\times S^5$ with complexified string coupling $τ_s$, while for the other cases it is dual to the orbifold theory on $AdS_5\times S^5/\mathbb{Z}_2$. In all cases we use the analytic bootstrap and constraints from localization to compute 1-loop and higher derivative tree level corrections to the leading supergravity approximation of the correlator. We give perturbative evidence that the localization constraint in the large $N$ and finite complexified coupling $τ$ limit can be written for each $G$ in terms of Eisenstein series that are modular invariant in terms of $τ_s\proptoτ$, which allows us to fix protected terms in the correlator in that limit. In all cases, we find that the flat space limit of the correlator precisely matches the type IIB S-matrix. We also find a closed form expression for the $SU(N)$ 1-loop Mellin amplitude with supergravity vertices. Finally, we compare our analytic predictions at large $N$ and finite $τ$ to bounds from the numerical bootstrap in the large $N$ regime, and find that they are not saturated for any $G$ and any $τ$, which suggests that no physical theory saturates these bootstrap bounds.

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arXiv2021

Gluon Scattering in AdS from CFT

We present a systematic study of holographic correlators in a vast array of SCFTs with non-maximal superconformal symmetry. These theories include 4d $\mathcal{N}=2$ SCFTs from D3-branes near F-theory singularities, 5d Seiberg exceptional theories and 6d E-string theory, as well as 3d and 4d phenomenological models with probe flavor branes. We consider current multiplets and their generalizations with higher weights, dual to massless and massive super gluons in the bulk. At leading order in the inverse central charge expansion, connected four-point functions of these operators correspond to tree-level gluon scattering amplitudes in AdS. We show that all such tree-level four-point amplitudes in all these theories are fully fixed by symmetries and consistency conditions and explicitly construct them. Our results encode a wealth of SCFT data and exhibit various interesting emergent structures. These include Parisi-Sourlas-like dimensional reductions, hidden conformal symmetry and an AdS version of the color-kinematic duality.

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arXiv2021

6d (2,0) and M-theory at 1-loop

We study the stress tensor multiplet four-point function in the 6d maximally supersymmetric $(2,0)$ $A_{N-1}$ and $D_N$ theories, which have no Lagrangian description, but in the large $N$ limit are holographically dual to weakly coupled M-theory on $AdS_7\times S^4$ and $AdS_7\times S^4/\mathbb{Z}_2$, respectively. We use the analytic bootstrap to compute the 1-loop correction to this holographic correlator coming from Witten diagrams with supergravity $R$ and the first higher derivative correction $R^4$ vertices, which is the first 1-loop correction computed for a non-Lagrangian theory. We then take the flat space limit and find precise agreement with the corresponding terms in the 11d M-theory S-matrix, some of which we compute for the first time using two-particle unitarity cuts.

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arXiv2021

All Holographic Four-Point Functions in All Maximally Supersymmetric CFTs

We present a constructive derivation of holographic four-point correlators of arbitrary half-BPS operators for all maximally supersymmetric conformal field theories in $d>2$. This includes holographic correlators in 3d ${\cal N}=8$ ABJM theories, 4d ${\cal N}=4$ SYM theory and the 6d ${\cal N}=(2,0)$ theory, dual to tree-level amplitudes in 11D supergravity on $AdS_4 \times S^7$, 10D supergravity on $AdS_5 \times S^5$ and 11D supergravity on $AdS_7 \times S^4$, respectively. We introduce the concept of Maximally R-symmetry Violating (MRV) amplitude, which corresponds to a special configuration in the R-symmetry space. In this limit the amplitude drastically simplifies, but at the same time the entire polar part of the full amplitude can be recovered from this limit. Furthermore, for a specific choice of the polar part, contact terms can be shown to be absent, by using the superconformal Ward identities and the flat space limit.

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arXiv2020

On the Spectrum of Pure Higher Spin Gravity

We study the spectrum of pure massless higher spin theories in $AdS_3$. The light spectrum is given by a tower of massless particles of spin $s=2,\cdots,N$ and their multi-particles states. Their contribution to the torus partition function organises into the vacuum character of the ${\cal W}_N$ algebra. Modular invariance puts constraints on the heavy spectrum of the theory, and in particular leads to negative norm states, which would be inconsistent with unitarity. This negativity can be cured by including additional light states, below the black hole threshold but whose mass grows with the central charge. We show that these states can be interpreted as conical defects with deficit angle $2π(1-1/M)$. Unitarity allows the inclusion of such defects into the path integral provided $M \geq N$.

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arXiv2020

Holographic Correlators at Finite Temperature

We consider weakly-coupled QFT in AdS at finite temperature. We compute the holographic thermal two-point function of scalar operators in the boundary theory. We present analytic expressions for leading corrections due to local quartic interactions in the bulk, with an arbitrary number of derivatives and for any number of spacetime dimensions. The solutions are fixed by judiciously picking an ansatz and imposing consistency conditions. The conditions include analyticity properties, consistency with the operator product expansion, and the Kubo-Martin-Schwinger condition. For the case without any derivatives we show agreement with an explicit diagrammatic computation. The structure of the answer is suggestive of a thermal Mellin amplitude. Additionally, we derive a simple dispersion relation for thermal two-point functions which reconstructs the function from its discontinuity.

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arXiv2020

All Tree-Level Correlators for M-theory on $AdS_7 \times S^4$

We present a constructive derivation of all four-point tree-level holographic correlators for eleven dimensional supergravity on $AdS_7 \times S^4$. These correlators correspond to four-point functions of arbitrary one-half BPS operators in the six-dimensional $(2,0)$ theory at large central charge. The crucial observation is that the polar part of the correlators in Mellin space is fully captured by a drastically simpler Maximally R-symmetry Violating (MRV) amplitude, while the contact part is fully fixed by superconformal Ward identities and the flat space limit.

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arXiv2020

Simplicity of AdS Supergravity at One Loop

We demonstrate the simplicity of $AdS_5\times S^5$ IIB supergravity at one loop level, by studying non-planar holographic four-point correlators in Mellin space. We develop a systematic algorithm for constructing one-loop Mellin amplitudes from tree-level data, and obtain a simple closed form answer for the $\langle \mathcal{O}_2^{SG}\mathcal{O}_2^{SG}\mathcal{O}_p^{SG}\mathcal{O}_p^{SG} \rangle$ correlators. The structure of this expression is remarkably simple, containing only simultaneous poles in the Mellin variables. We also study the flat space limit of the Mellin amplitudes, which reproduces precisely the IIB supergravity one-loop amplitude in ten dimensions. Our results provide nontrivial evidence for the persistence of the hidden conformal symmetry at one loop.

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arXiv2019

Rademacher Expansions and the Spectrum of 2d CFT

A classical result from analytic number theory by Rademacher gives an exact formula for the Fourier coefficients of modular forms of non-positive weight. We apply similar techniques to study the spectrum of two-dimensional unitary conformal field theories, with no extended chiral algebra and $c>1$. By exploiting the full modular constraints of the partition function we propose an expression for the spectral density in terms of the light spectrum of the theory. The expression is given in terms of a Rademacher expansion, which converges for spin $j \neq 0$. For a finite number of light operators the expression agrees with a variant of the Poincare construction developed by Maloney, Witten and Keller. With this framework we study the presence of negative density of states in the partition function dual to pure gravity, and propose a scenario to cure this negativity.

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arXiv2019

Loops in AdS from Conformal Field Theory

We propose and demonstrate a new use for conformal field theory (CFT) crossing equations in the context of AdS/CFT: the computation of loop amplitudes in AdS, dual to non-planar correlators in holographic CFTs. Loops in AdS are largely unexplored, mostly due to technical difficulties in direct calculations. We revisit this problem, and the dual $1/N$ expansion of CFTs, in two independent ways. The first is to show how to explicitly solve the crossing equations to the first subleading order in $1/N^2$, given a leading order solution. This is done as a systematic expansion in inverse powers of the spin, to all orders. These expansions can be resummed, leading to the CFT data for finite values of the spin. Our second approach involves Mellin space. We show how the polar part of the four-point, loop-level Mellin amplitudes can be fully reconstructed from the leading-order data. The anomalous dimensions computed with both methods agree. In the case of $ϕ^4$ theory in AdS, our crossing solution reproduces a previous computation of the one-loop bubble diagram. We can go further, deriving part of the four-point function in $ϕ^3+ϕ^4$ theory in AdS which had never been computed. In the process, we show how to analytically derive anomalous dimensions from Mellin amplitudes with an infinite series of poles, and discuss applications to more complicated cases such as the ${\cal N}=4$ super-Yang-Mills theory.

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arXiv2019

An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order $1/N^2$

We apply the methods of modern analytic bootstrap to the critical $O(N)$ model in a $1/N$ expansion. At infinite $N$ the model possesses higher spin symmetry which is weakly broken as we turn on $1/N$. By studying consistency conditions for the correlator of four fundamental fields we derive the CFT-data for all the (broken) currents to order $1/N$, and the CFT-data for the non-singlet currents to order $1/N^2$. To order $1/N$ our results are in perfect agreement with those in the literature. To order $1/N^2$ we reproduce known results for anomalous dimensions and obtain a variety of new results for structure constants, including the global symmetry central charge $C_J$ to this order.

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