In large $\textit{N}$ theories with a gravity dual, generic heavy operators should be dual to black holes in the bulk. The microscopic details of such operators should then be irrelevant in the low energy theory. We look for such universality in the strong coupling limit of a very simple two matrix model — the Hoppe model. Using analytics as well as Monte Carlo simulations, we show that there exists a universal black hole regime where the eigenvalue densities are given by parabolas and the correlation functions of probes in these backgrounds are completely determined by a few parameters. An important feature of strong coupling in this model is that the matrices commute and one can define joint eigenvalue distributions which also exhibit universality. These two results extend the beautiful findings of Berenstein, Hanada and Hartnoll [1]. Not all heavy operators are universal and at strong coupling there is a sharp phase boundary between the universal and non universal regimes (Of course this should not be confused with the universality of eigenvalue spacing in matrix models). Moreover, in the non universal phase, we also find an interesting phenomenon we call Abelianization where some eigenvalues run off to infinity, reminiscent of heavy dual giant gravitons in $$ \mathcal{N}=4 $$ SYM.

United Kingdom

Andrea Guerrieri

Canada

Harish Murali

Brazil

Pedro Vieira

Universality of heavy operators in matrix models

In the bulk dual of holography, huge operators correspond to sources so heavy that they fully backreact on the space-time geometry. Here we study the correlation function of three such huge operators when they are given by 1$\textit{/}$2 BPS operators in $$ \mathcal{N}=4 $$ SYM theory, dual to IIB Strings in $\textit{AdS}$ × $\textit{S}$ . We unveil simple matrix model representations for these correlators which we can sometimes solve analytically. For general huge operators, we translate these matrix model expressions into a 1 + 1 dimensional hydrodynamical fluid problem. This fluid is integrable thus unveiling a novel integrable sector of the $\textit{AdS/CFT}$ duality in a full fledged gravitational regime, very far from the usual free string planar regime where integrability reigns supreme. We explain how an adiabatic deformation method can be developed to yield the solution to an integrable discrete formulation of these fluids — the rational Calogero-Moser Model — so we can access the general three point correlation functions of generic huge 1$\textit{/}$2-BPS operators. Everything will be done on the gauge theory side of the duality. It would be fascinating to find the holographic dual of these matrix models and fluids.

France

Vladimir Kazakov

Huge BPS operators and fluid dynamics in $$ \mathcal{N}=4 $$ SYM

<p>We introduce the notion of jets, states of collinear flux-tube excitations. We argue for the analyticity, crossing, and unitarity of the multiparticle scattering of these jets and, through the S-matrix bootstrap, place bounds on a set of finite-energy multiparticle sum rules. Such bounds define a matrioska with a smaller and smaller allowed regions as we impose more constraints. The Yang-Mills flux tube, as well as other interesting flux-tube theories recently studied through lattice simulations, lie inside a tiny island hundreds of times smaller than the most general space of allowed theories.</p>

Italy

Alexandre Homrich

Multiparticle Flux-Tube S-matrix Bootstrap

Conformal Regge theory predicts the existence of analytically continued conformal field theory data for complex spin. How could this work when there are so many more operators with large spin compared to small spin? Using planar <math><mi>N</mi><mo>=</mo><mn>4</mn></math> SYM as a test ground, we find a simple physical picture. Operators do organize themselves into analytic families but the continuation of the higher families have zeros in their structure operator product expansion constants for lower integer spins. They thus decouple. Newton’s interpolation series technique is perfectly suited to this physical problem and will allow us to explore the complex spin half-plane.

United States

David Simmons-Duffin

Multitwist Trajectories and Decoupling Zeros in Conformal Field Theory

<p>We propose a new framework for computing three-point functions in planar <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 where these correlators take the form of multiple integrals of separation of variables type. We test this formalism at weak coupling at leading and next-to-leading orders in a noncompact SL(2) sector of the theory and all the way to next-to-next-to-leading orders for a compact SU(2) sector. We find evidence that wrapping effects can also be incorporated.</p>

Carlos Bercini

Structure constants in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> supersymmetric Yang-Mills theory and separation of variables

Using integrability, we construct (to leading order in perturbation theory) the explicit form of twist-three light-ray operators in planar   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 SYM. This construction allows us to directly compute analytically continued CFT data at complex spin. We derive analytically the “magic” decoupling zeroes previously observed numerically. Using the Baxter equation, we also show that certain Regge trajectories merge together into a single unifying Riemann surface. Perhaps more surprisingly, we find that this unification of Regge trajectories is not unique. If we organize twist-three operators differently into what we call “cousin trajectories” we find infinitely more possible continuations. We speculate about which of these remarkable features of twist-three operators might generalize to other operators, other regimes and other theories.

Light-ray wave functions and integrability

We describe solutions of asymptotically AdS3 Einstein gravity that are sourced by the insertion of operators in the boundary CFT2, whose dimension scales with the central charge of the theory. Previously, we found that the geometry corresponding to a black hole two-point function is simply related to an infinite covering of the Euclidean BTZ black hole [1]. However, here we find that the geometry sourced by the presence of a third black hole operator turns out to be a Euclidean wormhole with two asymptotic boundaries. We construct this new geometry as a quotient of empty AdS3 realized by domes and doors. The doors give access to the infinite covers that are needed to describe the insertion of the operators, while the domes describe the fundamental domains of the quotient on each cover. In particular, despite the standard fact that the Fefferman-Graham expansion is single-sided, the extended bulk geometry contains a wormhole that connects two asymptotic boundaries. We observe that the two-sided wormhole can be made single-sided by cutting off the wormhole and gluing on a “Lorentzian cap”. In this way, the geometry gives the holographic description of a three-point function, up to phases. By rewriting the metric in terms of a Liouville field, we compute the on-shell action and find that the result matches with the Heavy-Heavy-Heavy three-point function predicted by the modular bootstrap. Finally, we describe the geometric transition between doors and defects, that is, when one or more dual operators describe a conical defect insertion, rather than a black hole insertion.

Jacob Abajian

Spain

Francesco Aprile

Robert Myers

Correlation functions of huge operators in AdS3/CFT2: domes, doors and book pages

We initiate the study of holographic correlators for operators whose dimension scales with the central charge of the CFT. Differently from light correlators or probes, the insertion of any such maximally heavy operator changes the AdS metric, so that the correlator itself is dual to a backreacted geometry with marked points at the Poincaré boundary. We illustrate this new physics for two-point functions. Whereas the bulk description of light or probe operators involves Witten diagrams or extremal surfaces in an AdS background, the maximally heavy two-point functions are described by nontrivial new geometries which we refer to as “spacetime bananas”. As a universal example, we discuss the two-point function of maximally heavy scalar operators described by the Schwarzschild black hole in the bulk and we show that its onshell action reproduces the expected CFT result. This computation is nonstandard, and adding boundary terms to the action on the stretched horizon is crucial. Then, we verify the conformal Ward Identity from the holographic stress tensor and discuss important aspects of the Fefferman-Graham patch. Finally we study a Heavy-Heavy-Light-Light correlator by using geodesics propagating in the banana background. Our main motivation here is to set up the formalism to explore possible universal results for three- and higher-point functions of maximally heavy operators.

Holography and correlation functions of huge operators: spacetime bananas

We use the S-matrix bootstrap to carve out the space of unitary, analytic, crossing symmetric and supersymmetric graviton scattering amplitudes in nine, ten and eleven dimensions. We extend and improve the numerical methods of our previous work in ten dimensions. A key new tool employed here is unitarity in the celestial sphere. In all dimensions, we find that the minimal allowed value of the Wilson coefficient α, controlling the leading correction to maximal supergravity, is very close but not equal to the minimal value realized in Superstring theory or M-theory. This small difference may be related to inelastic effects that are not well described by our numerical extremal amplitudes. Although α has a unique value in M-theory, we found no evidence of an upper bound on α in 11D.

Israel

Switzerland

Joao Penedones

Where is M-theory in the space of scattering amplitudes?

We consider correlation functions of single trace operators approaching the cusps of null polygons in a double-scaling limit where so-called cusp times <math><msubsup><mi>t</mi><mi>i</mi><mn>2</mn></msubsup><mo>=</mo><msup><mi>g</mi><mn>2</mn></msup><mi>log</mi><msubsup><mi>x</mi><mrow><mi>i</mi><mo>−</mo><mn>1</mn><mo>,</mo><mi>i</mi></mrow><mn>2</mn></msubsup><mi>log</mi><msubsup><mi>x</mi><mrow><mi>i</mi><mo>,</mo><mi>i</mi><mo>+</mo><mn>1</mn></mrow><mn>2</mn></msubsup></math> are held fixed and the ‘t Hooft coupling is small. With the help of stampedes, symbols, and educated guesses, we find that any such correlator can be uniquely fixed through a set of coupled lattice PDEs of Toda type with several intriguing novel features. These results hold for most conformal gauge theories with a large number of colors, including planar <math><mi>N</mi><mo>=</mo><mn>4</mn></math> SYM.