We develop a bootstrap strategy to obtain the six-point function of supergravitons in $\textit{AdS}$ × $\textit{S}$ from symmetry constraints and consistency conditions. Compared to previous bootstrap algorithms, a novel feature is the use of lightcone OPEs together with the chiral algebra constraint. This makes it possible to isolate different parts of the correlator and fix them separately. Our strategy allows us to gain a refined understanding of the power of different bootstrap constraints, which is also useful for computing more general correlators.

Portugal

Vasco Gonçalves

United Kingdom

Maria Nocchi

China

Xinan Zhou

Dissecting supergraviton six-point function with lightcone limits and chiral algebra

<p>In the context of planar conformal gauge theory, we study five-point correlation functions between the interaction Lagrangian and four of the lightest single-trace, gauge-invariant scalar primaries. After performing two light-cone operator product expansions (OPEs), we express this correlator in terms of the three-point functions between two leading-twist spinning operators and the Lagrangian. For finite values of spin, we compute these structure constants in perturbation theory up to two loops in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> super Yang-Mills theory. Large values of spin are captured by null polygon kinematics, where we use dualities with null polygon Wilson loops as well as factorization properties to bootstrap the universal behavior of the structure constants at all loops. We find explicit maps that relate the Lagrangian structure constants with the leading-twist anomalous dimension. From the large-spin map, we recover the cusp anomalous dimension at strong and weak coupling, including genus-one terms.</p>

Germany

Till Bargheer

Carlos Bercini

Bruno Fernandes

Jeremy Mann

Wilson Loops with Lagrangians: Large-Spin Operator Product Expansion and Cusp Anomalous Dimension Dictionary

We evaluated all two-loop conformal integrals appearing in five-point correlation functions of protected operators of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 Super Yang-Mills in several kinematical regimes. Starting from the correlation function of the lightest operators of the theory, we were able to extract structure constants of up to two spinning operators for small and large values of spin and the tensor structure label (polarization). We conjectured an universal all-loop behaviour for the large-spin, small-polarization structure constants and comment on the subtleties of analytically continuing it from finite to large spin. We also consider correlation functions of heavier operators that get factorized in the more fundamental object called decagon. We fixed this object at two loops in general kinematics and studied its physical properties under OPE and null limits.

Two-loop five-point integrals: light, heavy and large-spin correlators

We propose and explore the Regge limit for correlation functions of five local primary operators in conformal field theories. After reviewing some features of Regge theory for flat-space scattering amplitudes, we analyze the analytic structure of conformal blocks both in position and Mellin space in the Regge limit and propose an extension of conformal Regge theory for five-point functions. As a byproduct of our analysis we also introduce a new basis of three-point correlation functions for operators with spin and the associated Euclidean conformal blocks.

Miguel Costa

Aaditya Salgarkar

Switzerland

João Boas

Conformal multi-Regge theory

We continue to explore the bootstrap approach to five-point correlation functions for IIB supergravity on AdS 5 × S 5. Building on the result of [1], we develop an improved algorithm that allows us to more efficiently compute correlators of higher Kaluza-Klein modes. The new method uses only factorization and a superconformal twist, and is entirely within Mellin space where the analytic structure of holographic correlators is simpler. Using this method, we obtain in a closed form all five-point functions of the form 〈pp222〉, extending the earlier result for p = 2. As a byproduct of our analysis, we also obtain explicit results for spinning four-point functions of higher Kaluza-Klein modes.

Brazil

Italy

Carlo Meneghelli

Ireland

Raul Pereira

Joao Boas

United States

Kaluza-Klein five-point functions from AdS5×S5 supergravity

We reduce the computation of three point function of three spinning operators with arbitrary polarizations in 𝒩 = 4 SYM to a statistical mechanics problem via the hexagon formalism. The central building block of these correlation functions is the hexagon partition function. We explore its analytic structure and use it to generate perturbative data for spinning three point functions. For certain polarizations and any coupling, we express the full asymptotic three point function in determinant form. With the integrability approach established we open the ground to study the large spin limit where dualities with null Wilson loops and integrable pentagons must appear.

Canada

Alexandre Homrich

Pedro Vieira

Spinning hexagons

We work out the map between null polygonal hexagonal Wilson loops and spinning three point functions in large N conformal gauge theories by mapping the variables describing the two different physical quantities and by working out the precise normalization factors entering this duality. By fixing all the kinematics we open the ground for a precise study of the dynamics underlying these dualities — most notably through integrability in the case of planar maximally supersymmetric Yang-Mills theory.

The Wilson loop — large spin OPE dictionary

We present the tree-level five-point amplitude of the lowest Kaluza-Klein mode of super-Yang-Mills theory on <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>5</mn></mrow></msub><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></math>, dual to the correlator of the flavor current multiplet in the dual <math><mrow><mn>4</mn><mi>d</mi></mrow></math> <math><mi>N</mi><mo>=</mo><mn>2</mn></math> superconformal field theory. Its color and kinematical structure is particularly simple and resembles that of the flat-space gluon amplitude.

Luis F. Alday

Supersymmetric Five-Point Gluon Amplitudes in AdS Space

Higher-point functions of scalar operators are a rich observable in CFTs, as they contain OPE data involving multiple spinning operators. We derive the lightcone blocks for five- and six-point functions in the snowflake channel and use them to bootstrap these correlators in the lightcone limit. As a result we determine the large spin expansion of OPE coefficients involving two or three spinning operators. We verify our results by comparing to the block decomposition of higher-point functions in generalized free theory and in theories with a cubic coupling.

António Antunes

Lightcone bootstrap at higher points

We initiate an exploration of the conformal bootstrap for <math><mi>n</mi><mo>&gt;</mo><mn>4</mn></math> point correlation functions. Here we bootstrap correlation functions of the lightest scalar gauge invariant operators in planar non-Abelian conformal gauge theories as their locations approach the cusps of a null polygon. For that we consider consistency of the OPE in the so-called snowflake channel with respect to cyclicity transformations which leave the null configuration invariant. For general non-Abelian gauge theories this allows us to strongly constrain the OPE structure constants of up to three large spin <math><msub><mi>J</mi><mi>j</mi></msub></math> operators (and large polarization quantum number <math><msub><mi>l</mi><mi>j</mi></msub></math>) to all loop orders. In <math><mrow><mi>N</mi><mo>=</mo><mn>4</mn></mrow></math> we fix them completely through the duality to null polygonal Wilson loops and the recent origin limit of the hexagon explored by Basso, Dixon, and Papathanasiou.