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A<sc>bstract</sc> We propose a triality relating the Double-Scaled SYK model, SL(2,ℂ) Chern-Simons theory on a disk with an irregular singularity at the center and the outcome of “real Schur quantization” applied to SU(2) Seiberg-Witten theory with Neumann boundary conditions. We give supporting evidence for our conjecture by establishing a precise match between a general class of correlators in all three systems. 

A<sc>bstract</sc> We study anO(N) invariant surface defect in the Wilson-Fisher conformal field theory (CFT) ind= 4 –ϵdimensions. This defect is defined by mass deformation on a two-dimensional surface that generates localized disorder and is conjectured to factorize into a pair of ordinary boundary conditions ind= 3. We determine defect CFT data associated with the lightestO(N) singlet and vector operators up to the third order in theϵ-expansion, find agreements with results from numerical methods and provide support for the factorization proposal ind= 3. Along the way, we observe surprising non-renormalization properties for surface anomalous dimensions and operator-product-expansion coefficients in theϵ-expansion. We also analyze the full conformal anomalies for the surface defect. 

A<sc>bstract</sc> We introduce and study a candidate gravity dual to the double scaled SYK model in the form of an exactly soluble 2D de Sitter gravity model consisting of two spacelike Liouville CFTs with complex central charge adding up toc₊+c₋= 26. In [1] it was shown that the two-point function of physical operators in a doubled SYK model matches in the semi-classical limit with the Green’s function of a massive scalar field in 3D de Sitter space. As further evidence of the duality, we adapt a result from Zamolodchikov to compute the boundary two-point function of the 2D Liouville-de Sitter gravity model on a disk and find that it reproduces the exact DSSYK two-point function to all orders inλ=p²/N. We describe how the 2D Liouville-de Sitter gravity model arises from quantizing 3D de Sitter gravity. 

A<sc>bstract</sc> We study the partition function of 3D de Sitter gravity defined as the trace over the Hilbert space obtained by quantizing the phase space of non-rotating Schwarzschild-de Sitter spacetime. Motivated by the correspondence with double scaled SYK, we identify the Hamiltonian with the gravitational Wilson-line that measures the conical deficit angle. We express the Hamiltonian in terms of canonical variables and find that it leads to the exact same chord rules and energy spectrum as the double scaled SYK model. We use the obtained match to compute the partition function and scalar two-point function in 3D de Sitter gravity. 

A<sc>bstract</sc> In our earlier work [1], we introduced a lattice Hamiltonian for Adjoint QCD₂using staggered Majorana fermions. We found the gauge invariant space of states explicitly for the gauge group SU(2) and used them for numerical calculations of observables, such as the spectrum and the expectation value of the fermion bilinear. In this paper, we carry out a more in-depth study of our lattice model, extending it to any compact and simply-connected gauge groupG. We show how to find the gauge invariant space of states and use it to study various observables. We also use the lattice model to calculate the mixed ’t Hooft anomalies of Adjoint QCD₂for arbitraryG. We show that the matrix elements of the lattice Hamiltonian can be expressed in terms of the Wigner 6j-symbols ofG. ForG= SU(3), we perform exact diagonalization for lattices of up to six sites and study the low-lying spectrum, the fermion bilinear condensate, and the string tension. We also show how to write the lattice strong coupling expansion for ground state energies and operator expectation values in terms of the Wigner 6j-symbols. For SU(3) we carry this out explicitly and find good agreement with the exact diagonalizations, and for SU(4) we give expansions that can be compared with future numerical studies. 

A<sc>bstract</sc> We employ a probabilistic mesoscopic description to draw conceptual and quantitative analogies between Brownian motion and late-time fluctuations of thermal correlation functions in generic chaotic systems respecting ETH. In this framework, thermal correlation functions of ‘simple’ operators are described by stochastic processes, which are able to probe features of the microscopic theory only in a probabilistic sense. We apply this formalism to the case of semiclassical gravity in AdS₃, showing that wormhole contributions can be naturally identified as moments of stochastic processes. We also point out a ‘Matryoshka doll’ recursive structure in which information is hidden in higher and higher moments, and which can be naturally justified within the stochastic framework. We then re-interpret the gravitational results from the boundary perspective, promoting the OPE data of the CFT to probability distributions. The outcome of this study shows that semiclassical gravity in AdS can be naturally interpreted as a mesoscopic description of quantum gravity, and a mesoscopic holographic duality can be framed as a moment-vs.-probability-distribution duality. 

A<sc>bstract</sc> We propose a new model of low dimensional de Sitter holography in the form of a pair of double-scaled SYK models at infinite temperature coupled via an equal energy constraintH_L=H_R. As a test of the duality, we compute the two-point function between two dressed SYK operators$$ {\mathcal{O}}_{\Delta } $$ $O_{\text{∆}}$that preserve the constraint. We find that in the largeNlimit, the two-point function precisely matches with the Green’s function of a massive scalar field of mass squaredm²= 4∆(1 – ∆) in a 3D de Sitter space-time with radiusR_dS/G_N= 4πN/p². In this correspondence, the SYK time is identified with the proper time difference between the two operators. We introduce a candidate gravity dual of the doubled SYK model given by a JT/de Sitter gravity model obtained via a circle reduction from 3D Einstein-de Sitter gravity. We comment on the physical meaning of the finite de Sitter temperature and entropy. 

A<sc>bstract</sc> We discuss a no-boundary proposal for a subregion of the universe. In the classical approximation, this density matrix involves finding a specific classical solution of the equations of motion with no boundary. Beyond the usual no boundary condition at early times, we also have another no boundary condition in the region we trace out. We can find the prescription by starting from the usual Hartle-Hawking proposal for the wavefunction on a full slice and tracing out the unobserved region in the classical approximation. We discuss some specific subregions and compute the corresponding solutions. These geometries lead to phenomenologically unacceptable probabilities, as expected. We also discuss how the usual Coleman de Luccia bubble solutions can be interpreted as a possible no boundary contribution to the density matrix of the universe. These geometries lead to local (but not global) maxima of the probability that are phenomenologically acceptable. 

A<sc>bstract</sc> It has been proposed that the Ginzburg-Landau description of the non-unitary conformal minimal modelM(3, 8) is provided by the Euclidean theory of two real scalar fields with third-order interactions that have imaginary coefficients. The same lagrangian describes the non-unitary modelM(3, 10), which is a product of two Yang-Lee theoriesM(2, 5), and the Renormalization Group flow from it toM(3, 8). This proposal has recently passed an important consistency check, due to Y. Nakayama and T. Tanaka, based on the anomaly matching for non-invertible topological lines. In this paper, we elaborate the earlier proposal and argue that the two-field theory describes theDseries modular invariants of bothM(3, 8) andM(3, 10). We further propose the Ginzburg-Landau descriptions of the entire class ofDseries minimal modelsM(q, 3q– 1) andM(q, 3q+ 1), with odd integerq. They involve$$ \mathcal{PT} $$ $\mathrm{PT}$symmetric theories of two scalar fields with interactions of orderqmultiplied by imaginary coupling constants. 

A<sc>bstract</sc> We compute the tree-level connected six-point function of identical scalar fluctuations of the AdS₂string worldsheet dual to the half-BPS Wilson line in planar$$ \mathcal{N} $$ $N$= 4 Super Yang-Mills. The calculation can be carried out analytically in the conformal gauge approach, where the boundary reparametrization mode of the string plays a crucial role. We also study the analytic continuation of the six-point function to an out-of-time-order configuration, which is related to a 3-to-3 scattering amplitude in flat space. As a check of our results, we also numerically compute the six-point function using the Nambu-Goto action in static gauge, finding agreement with the conformal gauge answer.