<p>We define the “squared amplitudes” in planar Aharony-Bergman-Jafferis-Maldacena theory, analogous to those in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></math> super-Yang-Mills (SYM) theory. Surprisingly, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>n</mi></mrow></math>-point <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi></math>-loop integrands with fixed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi><mo>≔</mo><mi>n</mi><mo>+</mo><mi>L</mi></mrow></math> are unified in a single generating function. Similar to the SYM four-point half–Bogomol’nyi-Prasad-Sommerfield correlator integrand, the generating function enjoys a hidden <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>S</mi><mi>N</mi></msub></math> permutation symmetry in the dual space, allowing us to write it as a linear combination of weight-3 planar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>f</mi></math> graphs. Remarkably, through Gram identities it can also be represented as a linear combination of “bipartite” <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>f</mi></math> graphs that manifest the important property that no odd-multiplicity amplitude exists in the theory. The generating function and these properties are explicitly checked against squared amplitudes for all <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>4</mn></math>, 6, 8. By drawing analogies with SYM, we conjecture some “graphical rules” the generating function satisfies, and exploit them to bootstrap a unique <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>10</mn></math> result, which provides new results for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi><mo>=</mo><mn>10</mn></math> squared tree amplitudes, as well as integrands for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mi>n</mi><mo>,</mo><mi>L</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo stretchy="false">)</mo><mo>,</mo><mo stretchy="false">(</mo><mn>6</mn><mo>,</mo><mn>4</mn><mo stretchy="false">)</mo></mrow></math>. Our results strongly suggest the existence of a “bipartite correlator” in Aharony-Bergman-Jafferis-Maldacena theory that unifies all squared amplitudes and satisfies physical constraints underlying these graphical rules.</p>

China

Song He

Canxin Shi

Yichao Tang

Yao-Qi Zhang

Hidden Permutation Symmetry of Squared Amplitudes in Aharony-Bergman-Jafferis-Maldacena Theory

We investigate an ensemble of boundary CFTs within the framework of a tensor model recently constructed to model 3d quantum gravity. The incorporation of CFT borders introduces new elements to the gravity theory. In particular, it leads to an open-closed extension of Virasoro TQFT, which in the classical limit gives rise to 3d gravity with tensionful end-of-the-world branes. It also provides predictions for off-shell manifolds with bordered asymptotic boundaries, such as the annulus wormhole. As an application, we construct a purely open variant of the tensor model to study a purely open bootstrap problem in the context of CFT triangulation. We also briefly discuss the extension to non-orientable CFTs.

United States

Daniel Jafferis

Liza Rozenberg

Diandian Wang

Open-closed 3d gravity as a random ensemble

In this work, we bootstrap the 4-point correlators on the 1D celestial circle using 3D symmetries in the Aharony-Bergman-Jafferis-Maldacena theory as constraints. We find that the dual inversion property is strong enough to replace the crossing symmetry condition (or cyclic invariant condition) when bootstrapping. We also give some results about the conformal block expansion coefficients which contain the spectrum. Furthermore, we extract the OPE spectrum from the multi-collinear limit since all 3-point ABJM amplitudes vanish. Although we studied a specific theory, the methods used are valid for more general cases.

Yi-Xiao Tao

The Aharony-Bergman-Jafferis-Maldacena theory on a circle

$\textit{α}$ corrections to near horizon dynamics of a Schwarzschild black hole in a large number of spacetime dimensions $\textit{D}$ are governed by the worldsheet theory composed of the cigar CFT and the classical sigma model on the sphere at the horizon, along with a timelike-Liouville theory of central charge 26 – $\textit{D}$. At leading order in weak string coupling, black hole thermodynamics is insensitive to the details of timelike Liouville theory. In this limit, we use the Lewkowycz-Maldacena-trick motivated infinitesimally off-shell closed string worldsheet formalism in [arxiv: 2310.02313] to calculate thermal entropy exactly in $\textit{α}$ . The leading term in the $\textit{α}$ → 0 limit and the first stingy correction of our result are in precise agreement with the target space Callan-Myers-Perry formula. Also, we point out a remarkable simplification at an ultra-low temperature of order $$ 1/\sqrt{\alpha^{\prime }D} $$ and show that for a certain special set of vertex operators involving modes of the $\textit{D}$ dimensional spacetime and the time-like Liouville theory, the resulting worldsheet theory is related to Virasoro minimal string.

Indranil Halder

Stretched horizon, replica trick and off-shell winding condensate, and all that

We give further evidence that the matrix-tensor model studied in [1] is dual to AdS gravity including the sum over topologies. This provides a 3D version of the duality between JT gravity and an ensemble of random Hamiltonians, in which the matrix and tensor provide random CFT data subject to a potential that incorporates the bootstrap constraints. We show how the Feynman rules of the ensemble produce a sum over all 3-manifolds and how surgery is implemented by the matrix integral. The partition functions of the resulting 3d gravity theory agree with Virasoro TQFT (VTQFT) on a fixed, hyperbolic manifold. However, on non-hyperbolic geometries, our 3d gravity theory differs from VTQFT, leading to a difference in the eigenvalue statistics of the associated ensemble. As explained in [1], the Schwinger-Dyson (SD) equations of the matrix-tensor integral play a crucial role in understanding how gravity emerges in the limit that the ensemble localizes to exact CFT’s. We show how the SD equations can be translated into a combinatorial problem about 3-manifolds.

United Kingdom

Gabriel Wong

3d gravity as a random ensemble

We investigate the correlators of three single-trace operators in Aharony-Bergman-Jafferis-Maldacena (ABJM) theory from the perspective of integrable boundary states. Specifically, we focus on scenarios where two operators are 1/3-BPS and the entire correlation function is considered within the twisted-translated frame. The correlator can be expressed as the overlap between a boundary state and a Bethe state. It is found that the boundary state formed by the two 1/3-BPS operators is integrable when the number of Wick contractions between the non-BPS operator and one of the 1/3-BPS operators is 0 or 1. We compute the overlaps for the proven integrable cases utilizing the symmetries and the coordinate Bethe ansatz.

Jun-Bao Wu

Peihe Yang

Three-point functions in Aharony-Bergman-Jafferis-Maldacena theory and integrable boundary states

A key issue in both the field of quantum chaos and quantum gravity is an effective description of chaotic conformal field theories (CFTs), that is CFTs that have a quantum ergodic limit. We develop a framework incorporating the constraints of conformal symmetry and locality, allowing the definition of ensembles of ‘CFT data’. These ensembles take on the same role as the ensembles of random Hamiltonians in more conventional quantum ergodic phases of many-body quantum systems. To describe individual members of the ensembles, we introduce the notion of approximate CFT, defined as a collection of ‘CFT data’ satisfying the usual CFT constraints approximately, i.e. up to small deviations. We show that they generically exist by providing concrete examples. Ensembles of approximate CFTs are very natural in holography, as every member of the ensemble is indistinguishable from a true CFT for low-energy probes that only have access to information from semi-classical gravity. To specify these ensembles, we impose successively higher moments of the CFT constraints. Lastly, we propose a theory of pure gravity in AdS3 as a random matrix/tensor model implementing approximate CFT constraints. This tensor model is the maximum ignorance ensemble compatible with conformal symmetry, crossing invariance, and a primary gap to the black-hole threshold. The resulting theory is a random matrix/tensor model governed by the Virasoro 6j-symbol.

Italy

Switzerland

Alexandre Belin

Netherlands

Jan Boer

CERN

Pranjal Nayak

Julian Sonner

Approximate CFTs and random tensor models

We conjecture a two-dimensional conformal field theory built out of a linear dilaton and a compact βγ system deformed by winding condensates on each of the compact cycles. In particular, explicit expressions of the residues of the correlation functions are provided. As a worldsheet theory, it describes a stringy black hole in AdS3 (supported by the Kalb-Ramond flux) at the Hawking-Page temperature. It is expected to be connected to the Horowitz-Polchinski-like solution near the Hagedorn temperature of thermal AdS3 and Euclidean BTZ blackhole as we vary the temperature.

Double winding condensate CFT

We define and compute the leading sphere diagram contribution to the entropy of the BTZ black hole supported by Kalb-Ramond flux in bosonic string theory. In a winding condensate description, integrating exactly over the constant mode for the radial direction of AdS3 reduces the problem to one of the correlation functions of winding operators in the free theory. The volume of the residual PSL(2,ℂ) gauge group of the sphere is canceled by the action of conformal transformations on the winding interaction insertions. We formulate a precise version of the replica trick in terms of (infinitesimally) non-integer winding condensates to produce the entropy of the BTZ black hole. The resulting entropy can be calculated from the one-point function of a non-local operator on the worldsheet.

Thermal Bekenstein-Hawking entropy from the worldsheet

We consider bosonic string theory on AdS3 supported by Kalb-Ramond flux. It is well known that the α′ exact worldsheet theory is described by the SL(2,R) WZW model. In this note we perform checks of an α′ exact dual description proposed in [arXiv:2104.07233] involving a winding condensate on a free theory background. We give the explicit map of vertex operators for normalizable states on both sides of the duality and demonstrate the equivalence of their two and three point functions by direct computation. The duality is of strong-weak nature in α′.