arXiv subjects

Alexander Zhiboedov

Publications and source records attributed to Alexander Zhiboedov.

At least 37 records · Page 2Linked to original sources

arXiv2022

Gravitational Regge bounds

We review the basic assumptions and spell out the detailed arguments that lead to the bound on the Regge growth of gravitational scattering amplitudes. The minimal extra ingredient compared to the gapped case - in addition to unitarity, analyticity, subexponentiality, and crossing - is the assumption that scattering at large impact parameters is controlled by known semi-classical physics. We bound the Regge growth of amplitudes both with the fixed transferred momentum and smeared over it. Our basic conclusion is that gravitational scattering amplitudes admit dispersion relations with two subtractions. For a sub-class of smeared amplitudes, black hole formation reduces the number of subtractions to one. Finally, using dispersion relations with two subtractions we derive bounds on the local growth of relativistic scattering amplitudes. Schematically, the local bound states that the amplitude cannot grow faster than $s^2$.

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arXiv2022

Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude

We analyze constraints from perturbative unitarity and crossing on the leading contributions of higher-dimension operators to the four-graviton amplitude in four spacetime dimensions, including constraints that follow from distinct helicity configurations. We focus on the leading-order effect due to exchange by massive degrees of freedom which makes the amplitudes of interest infrared finite. In particular, we place a bound on the coefficient of the $R^3$ operator that corrects the graviton three-point amplitude in terms of the $R^4$ coefficient. To test the constraints we obtain nontrivial effective field-theory data by computing and taking the large-mass expansion of the one-loop minimally-coupled four-graviton amplitude with massive particles up to spin 2 circulating in the loop. Remarkably, we observe that the leading EFT coefficients obtained from both string and one-loop field-theory amplitudes lie in small islands. The shape and location of the islands can be derived from the dispersive representation for the Wilson coefficients using crossing and assuming that the lowest-spin spectral densities are the largest. Our analysis suggests that the Wilson coefficients of weakly-coupled gravitational physical theories are much more constrained than indicated by bounds arising from dispersive considerations of $2 \to 2$ scattering. The one-loop four-graviton amplitudes used to obtain the EFT data are computed using modern amplitude methods, including generalized unitarity, supersymmetric decompositions and the double copy.

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arXiv2022

Snowmass White Paper: The Analytic Conformal Bootstrap

The analytic conformal bootstrap is an array of techniques to characterize, constrain, and solve strongly interacting quantum field theories using symmetries, causality, unitarity, and other general principles. In the last decade, bolstered by the development of new Lorentzian methods, it has been used to solve conformal field theories at large spin; to place bounds on energy distributions, event shapes, operator product coefficients, and other observables; and to understand aspects of quantum gravity in anti-de Sitter space. We review these advances and highlight several promising areas for future exploration. Targets include developing new methods to close the gap between numerical and analytic bounds, extending the bootstrap beyond conformal fixed points, applications to quantum gravity and cosmology, and building on ties to condensed matter theory and mathematics.

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arXiv2022

On the light-ray algebra in conformal field theories

We analyze the commutation relations of light-ray operators in conformal field theories. We first establish the algebra of light-ray operators built out of higher spin currents in free CFTs and find explicit expressions for the corresponding structure constants. The resulting algebras are remarkably similar to the generalized Zamolodchikov's $W_\infty$ algebra in a two-dimensional conformal field theory. We then compute the commutator of generalized energy flow operators in a generic, interacting CFTs in $d>2$. We show that it receives contribution from the energy flow operator itself, as well as from the light-ray operators built out of scalar primary operators of dimension $Δ\leq d-2$, that are present in the OPE of two stress-energy tensors. Commutators of light-ray operators considered in the present paper lead to CFT sum rules which generalize the superconvergence relations and naturally connect to the dispersive sum rules, both of which have been studied recently.

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arXiv2021

Generalizing event shapes: In search of lost collider time

We introduce a new class of collider-type observables in conformal field theories which we call generalized event shapes. They are defined as matrix elements of light-ray operators that are sensitive to the longitudinal, or time-dependent, structure of the state produced in the collision. Generalized event shapes can be studied using both correlation functions and scattering amplitudes. They are infrared finite and smoothly transit over to the familiar event shapes. We compute them in planar ${\cal N}=4$ super-Yang-Mills theory at weak and strong coupling, and study their physical properties. We show that at strong coupling both the stringy and quantum-gravitational corrections to the energy-energy correlation exhibit longitudinal broadening that manifests itself through the presence of long-time tails in the energy flux measured by the detectors.

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arXiv2021

Probing multi-particle unitarity with the Landau equations

We consider the $2\to 2$ scattering amplitude of identical massive particles. We identify the Landau curves in the multi-particle region $16m^2 \leq s, t < 36m^2$. We systematically generate and select the relevant graphs and numerically solve the associated Landau equations for the leading singularity. We find an infinite sequence of Landau curves that accumulates at finite $s$ and $t$ on the physical sheet. We expect that such accumulations are generic for $s,t > 16m^2$. Our analysis sheds new light on the complicated analytic structure of nonperturbative relativistic scattering amplitudes.

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arXiv2021

Applications of dispersive sum rules: $ε$-expansion and holography

We use Mellin space dispersion relations together with Polyakov conditions to derive a family of sum rules for Conformal Field Theories (CFTs). The defining property of these sum rules is suppression of the contribution of the double twist operators. Firstly, we apply these sum rules to the Wilson-Fisher model in $d=4-ε$ dimensions. We re-derive many of the known results to order $ε^4$ and we make new predictions. No assumption of analyticity down to spin $0$ was made. Secondly, we study holographic CFTs. We use dispersive sum rules to obtain tree-level and one-loop anomalous dimensions. Finally, we briefly discuss the contribution of heavy operators to the sum rules in UV complete holographic theories.

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arXiv2021

Scattering from production in 2d

In 1968, Atkinson proved the existence of functions that satisfy all S-matrix axioms in four spacetime dimensions. His proof is constructive and to our knowledge it is the only result of this type. Remarkably, the methods to construct such functions used in the proof were never implemented in practice. In the present paper, we test the applicability of those methods in the simpler setting of two-dimensional S-matrices. We solve the problem of reconstructing the scattering amplitude starting from a given particle production probability. We do this by implementing two numerical iterative schemes (fixed-point iteration and Newton's method), which, by iterating unitarity and dispersion relations, converge to solutions to the S-matrix axioms. We characterize the region in the amplitude-space in which our algorithms converge, and discover a fractal structure connected to the so-called CDD ambiguities which we call "CDD fractal". To our surprise, the question of convergence naturally connects to the recent study of the coupling maximization in the two-dimensional S-matrix bootstrap. The methods exposed here pave the way for applications to higher dimensions, and expose some of the potential challenges that will have to be overcome.

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arXiv2020

Transverse spin in the light-ray OPE

We study a product of null-integrated local operators $\mathcal{O}_1$ and $\mathcal{O}_2$ on the same null plane in a CFT. Such null-integrated operators transform like primaries in a fictitious $d-2$ dimensional CFT in the directions transverse to the null integrals. We give a complete description of the OPE in these transverse directions. The terms with low transverse spin are light-ray operators with spin $J_1+J_2-1$. The terms with higher transverse spin are primary descendants of light-ray operators with higher spins $J_1+J_2-1+n$, constructed using special conformally-invariant differential operators that appear precisely in the kinematics of the light-ray OPE. As an example, the OPE between average null energy operators contains light-ray operators with spin $3$ (as described by Hofman and Maldacena), but also novel terms with spin $5,7,9,$ etc.. These new terms are important for describing energy two-point correlators in non-rotationally-symmetric states, and for computing multi-point energy correlators. We check our formulas in a non-rotationally-symmetric energy correlator in $\mathcal{N}=4$ SYM, finding perfect agreement.

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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

An Analytical Toolkit for the S-matrix Bootstrap

We revisit analytical methods for constraining the nonperturbative $S$-matrix of unitary, relativistic, gapped theories in $d \geq 3$ spacetime dimensions. We assume extended analyticity of the two-to-two scattering amplitude and use it together with elastic unitarity to develop two natural expansions of the amplitude. One is the threshold (non-relativistic) expansion and the other is the large spin expansion. The two are related by the Froissart-Gribov inversion formula. When combined with crossing and a local bound on the discontinuity of the amplitude, this allows us to constrain scattering at finite energy and spin in terms of the low-energy parameters measured in the experiment. Finally, we discuss the modern numerical approach to the $S$-matrix bootstrap and how it can be improved based on the results of our analysis.

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arXiv2020

The light-ray OPE and conformal colliders

We derive a nonperturbative, convergent operator product expansion (OPE) for null-integrated operators on the same null plane in a CFT. The objects appearing in the expansion are light-ray operators, whose matrix elements can be computed by the generalized Lorentzian inversion formula. For example, a product of average null energy (ANEC) operators has an expansion in the light-ray operators that appear in the stress-tensor OPE. An important application is to collider event shapes. The light-ray OPE gives a nonperturbative expansion for event shapes in special functions that we call celestial blocks. As an example, we apply the celestial block expansion to energy-energy correlators in N=4 Super Yang-Mills theory. Using known OPE data, we find perfect agreement with previous results both at weak and strong coupling, and make new predictions at weak coupling through 4 loops (NNNLO).

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arXiv2020

Nonperturbative Mellin Amplitudes: Existence, Properties, Applications

We argue that nonperturbative CFT correlation functions admit a Mellin amplitude representation. Perturbative Mellin representation readily follows. We discuss the main properties of nonperturbative CFT Mellin amplitudes: subtractions, analyticity, unitarity, Polyakov conditions and polynomial boundedness at infinity. Mellin amplitudes are particularly simple for large N CFTs and 2D rational CFTs. We discuss these examples to illustrate our general discussion. We consider subtracted dispersion relations for Mellin amplitudes and use them to derive bootstrap bounds on CFTs. We combine crossing, dispersion relations and Polyakov conditions to write down a set of extremal functionals that act on the OPE data. We check these functionals using the known 3d Ising model OPE data and other known bootstrap constraints. We then apply them to holographic theories.

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arXiv2019

Energy-energy correlations at next-to-next-to-leading order

We develop further an approach to computing energy-energy correlations (EEC) directly from finite correlation functions. In this way, one completely avoids infrared divergences. In maximally supersymmetric Yang-Mills theory ($\mathcal{N}=4$ sYM), we derive a new, extremely simple formula relating the EEC to a triple discontinuity of a four-point correlation function. We use this formula to compute the EEC in $\mathcal{N}=4$ sYM at next-to-next-to-leading order in perturbation theory. Our result is given by a two-fold integral representation that is straightforwardly evaluated numerically. We find that some of the integration kernels are equivalent to those appearing in sunrise Feynman integrals, which evaluate to elliptic functions. Finally, we use the new formula to provide the expansion of the EEC in the back-to-back and collinear limits.

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arXiv2019

Modular Invariance, Tauberian Theorems, and Microcanonical Entropy

We analyze modular invariance drawing inspiration from tauberian theorems. Given a modular invariant partition function with a positive spectral density, we derive lower and upper bounds on the number of operators within a given energy interval. They are most revealing at high energies. In this limit we rigorously derive the Cardy formula for the microcanonical entropy together with optimal error estimates for various widths of the averaging energy shell. We identify a new universal contribution to the microcanonical entropy controlled by the central charge and the width of the shell. We derive an upper bound on the spacings between Virasoro primaries. Analogous results are obtained in holographic 2d CFTs. We also study partition functions with a UV cutoff. Control over error estimates allows us to probe operators beyond the unity in the modularity condition. We check our results in the 2d Ising model and the Monster CFT and find perfect agreement.

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arXiv2019

Shocks, Superconvergence, and a Stringy Equivalence Principle

We study propagation of a probe particle through a series of closely situated gravitational shocks. We argue that in any UV-complete theory of gravity the result does not depend on the shock ordering - in other words, coincident gravitational shocks commute. Shock commutativity leads to nontrivial constraints on low-energy effective theories. In particular, it excludes non-minimal gravitational couplings unless extra degrees of freedom are judiciously added. In flat space, these constraints are encoded in the vanishing of a certain "superconvergence sum rule." In AdS, shock commutativity becomes the statement that average null energy (ANEC) operators commute in the dual CFT. We prove commutativity of ANEC operators in any unitary CFT and establish sufficient conditions for commutativity of more general light-ray operators. Superconvergence sum rules on CFT data can be obtained by inserting complete sets of states between light-ray operators. In a planar 4d CFT, these sum rules express (a-c)/c in terms of the OPE data of single-trace operators.

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arXiv2018

Analytic Euclidean Bootstrap

We solve crossing equations analytically in the deep Euclidean regime. Large scaling dimension $Δ$ tails of the weighted spectral density of primary operators of given spin in one channel are matched to the Euclidean OPE data in the other channel. Subleading $1\over Δ$ tails are systematically captured by including more operators in the Euclidean OPE in the dual channel. We use dispersion relations for conformal partial waves in the complex $Δ$ plane, the Lorentzian inversion formula and complex tauberian theorems to derive this result. We check our formulas in a few examples (for CFTs and scattering amplitudes) and find perfect agreement. Moreover, in these examples we observe that the large $Δ$ expansion works very well already for small $Δ\sim 1$. We make predictions for the 3d Ising model. Our analysis of dispersion relations via complex tauberian theorems is very general and could be useful in many other contexts.

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arXiv2018

Veneziano Amplitude of Vasiliev Theory

We compute the four-point function of scalar operators in CFTs with weakly broken higher spin symmetry at arbitrary 't Hooft coupling. We use the known three-point functions in these theories, the Lorentzian OPE inversion formula and crossing to fix the result up to the addition of three functions of the cross ratios. These are given by contact Witten diagrams in AdS and manifest non-analyticity of the OPE data in spin. We use Schwinger-Dyson equations to show that such terms are absent in the large $N$ Chern-Simons matter theories. The result is that the OPE data is analytic in spin up to $J=0$.

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