Using supersymmetric localization, we compute the partition function and some protected correlators of the polarized IKKT matrix model. Surprisingly, we find that the original IKKT model is different from polarized IKKT in the limit of vanishing mass deformation. We study different regimes of the localization results and recover the electrostatic problem which defines the gravity dual.

Switzerland

Shota Komatsu

Adrien Martina

Joao Penedones

Antoine Vuignier

France

Xiang Zhao

Einstein gravity from a matrix integral. Part II

We construct backreacted geometries dual to the supersymmetric mass deformation of the IKKT matrix model. They are Euclidean type IIB supergravity solutions given in terms of an electrostatic potential, having SO(7) × SO(3) isometry and 16 supersymmetries. Quantizing the fluxes, we find that the supergravity solutions are in one-to-one correspondence with fuzzy sphere vacua of the matrix model.

Einstein gravity from a matrix integral. Part I

We revisit the Berenstein-Maldacena-Nastase (BMN) conjecture relating M-theory on a PP-wave background and Matrix Quantum Mechanics (MQM) of $\textit{N}$ × $\textit{N}$ matrices. In particular, we study the BMN MQM at strong coupling and finite $\textit{N}$ and derive an effective Hamiltonian that describes non-relativistic free particles in a harmonic trap. The energy spectrum predicted by this Hamiltonian matches the supergravity excitation spectrum around the PP-wave background, if we further assume the existence of bound states. Our derivation is based on the strong coupling expansion of the wavefunction and supersedes the naive path integral approach that can lead to incorrect results, as we demonstrate in a simple toy model. We conclude with open questions about various regimes of the theory when we vary the size of the matrices, the coupling and the temperature.

Noé Suchel

Gravity from quantum mechanics of finite matrices

<p>We study the decomposition of the Hilbert space of quantum field theory in (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></math>)-dimensional de Sitter spacetime into unitary irreducible representations (UIRs) of its isometry group <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SO</mi><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><mi>d</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></math>. First, we consider multiparticle states in free theories starting from the tensor product of single-particle UIRs. Second, we study conformal multiplets of a bulk conformal field theory with symmetry group <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SO</mi><mo stretchy="false">(</mo><mn>2</mn><mo>,</mo><mi>d</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></math>. Our main tools are the Harish-Chandra characters and the numerical diagonalization of the (truncated) quadratic Casimir of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SO</mi><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><mi>d</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></math>. We introduce a continuous density that encodes the spectrum of irreducible representations contained in a reducible one of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SO</mi><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><mi>d</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></math>. Our results are complete for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mo>=</mo><mn>1</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mo>=</mo><mn>2</mn></math>. In higher dimensions, we rederive and extend several results previously known in the literature. Our work provides the foundation for future nonperturbative bootstrap studies of quantum field theory in de Sitter spacetime.</p>

Netherlands

Kamran Salehi Vaziri

United States

Zimo Sun

Hilbert space of quantum field theory in de Sitter spacetime

We study correlation functions of the bulk stress tensor and boundary operators in Quantum Field Theories (QFT) in Anti-de Sitter (AdS) space. In particular, we derive new sum rules from the two-point function of the stress tensor and its three-point function with two boundary operators. In AdS2, this leads to a bootstrap setup that involves the central charge of the UV limit of the bulk QFT and may allow to follow a Renormalization Group (RG) flow non-perturbatively by continuously varying the AdS radius. Along the way, we establish the convergence properties of the newly discovered local block decomposition of the three-point function.

Marco Meineri

Taro Spirig

Renormalization group flows in AdS and the bootstrap program

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

Canada

Italy

Andrea Guerrieri

Harish Murali

Brazil

Pedro Vieira

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

We study quantum field theory on a de Sitter spacetime dS d+1 background. Our main tool is the Hilbert space decomposition in irreducible unitary representations of its isometry group SO(d + 1, 1). As the first application of the Hilbert space formalism, we recover the Källen-Lehmann spectral decomposition of the scalar bulk two-point function. In the process, we exhibit a relation between poles in the corresponding spectral densities and the boundary CFT data. Moreover, we derive an inversion formula for the spectral density through analytical continuation from the sphere and use it to find the spectral decompisiton for a few examples. Next, we study the conformal partial wave decomposition of the four-point functions of boundary operators. These correlation functions are very similar to the ones of standard conformal field theory, but have different positivity proper- ties that follow from unitarity in de Sitter. We conclude by proposing a non-perturbative conformal bootstrap approach to the study of these late-time four-point functions, and we illustrate our proposal with a concrete example for QFT in dS2.

Matthijs Hogervorst

Kamran Vaziri

Towards the non-perturbative cosmological bootstrap

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 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.

Joao Silva

Alexander Zhiboedov

Nonperturbative Mellin amplitudes: existence, properties, applications

We set up a scattering experiment of matter against an impurity which separates two generic one-dimensional critical quantum systems. We compute the flux of reflected and transmitted energy, thus defining a precise measure of the transparency of the interface between the related two-dimensional conformal field theories. If the largest symmetry algebra is Virasoro, we find that the reflection and transmission coefficients are independent of the details of the initial state, and are fixed in terms of the central charges and of the two-point function of the displacement operator. The situation is more elaborate when extended symmetries are present. Positivity of the total energy flux at infinity imposes bounds on the coefficient of the two-point function of the displacement operator, which controls the free-energy cost of a small deformation of the interface. Finally, we study out-of-equilibrium steady states of a critical system connecting two reservoirs at different temperatures. In the absence of extended symmetries, our result implies that the energy flux across an impurity is proportional to the difference of the squared temperatures and controlled by the reflection coefficient.

Antonin Rousset

Colliders and conformal interfaces

We consider constraints on the S-matrix of any gapped, Lorentz invariant quantum field theory in 3+1 dimensions due to crossing symmetry, analyticity and unitarity. We extremize cubic couplings, quartic couplings and scattering lengths relevant for the elastic scattering amplitude of two identical scalar particles. In the cases where our results can be compared with the older S-matrix literature they are in excellent agreement. We also extremize a cubic coupling in 2+1 dimensions which we can directly compare to a universal bound for a QFT in AdS. This paper generalizes our previous 1+1 dimensional results of [1] and [2].