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1. Field Theory of Interacting Boundary Gravitons

   https://doi.org/10.21468/SciPostPhys.13.2.038  

   Ebert, Stephen ; Hijano, Eliot ; Kraus, Per ; Monten, Ruben ; Myers, Richard M. ( January 2022 , SciPost Physics)

   Pure three-dimensional gravity is a renormalizable theory with twofree parameters labelled byG$G$and\Lambda$\Lambda$.As a consequence, correlation functions of the boundary stress tensor inAdS_3${}_3$are uniquely fixed in terms of one dimensionless parameter, which is thecentral charge of the Virasoro algebra. The same argument implies thatAdS_3${}_3$gravity at a finite radial cutoff is a renormalizable theory, but nowwith one additional parameter corresponding to the cutoff location. Thistheory is conjecturally dual to aT\overline{T}$T\overline{T}$-deformedCFT, assuming that such theories actually exist. To elucidate this, westudy the quantum theory of boundary gravitons living on a cutoff planarboundary and the associated correlation functions of the boundary stresstensor. We compute stress tensor correlation functions to two-loop order(G$G$being the loop counting parameter), extending existing tree levelresults. This is made feasible by the fact that the boundary gravitonaction simplifies greatly upon making a judicious field redefinition,turning into the Nambu-Goto action. After imposing Lorentz invariance,the correlators at this order are found to be unambiguous up to a singleundetermined renormalization parameter.

    

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2. Summing inflationary logarithms in nonlinear sigma models

   https://doi.org/10.1007/JHEP03(2022)069  

   Miao, S. P. ; Tsamis, N. C. ; Woodard, R. P. ( March 2022 , Journal of High Energy Physics)

   A bstract We consider two nonlinear sigma models on de Sitter background which involve the same derivative interactions as quantum gravity but without the gauge issue. The first model contains only a single field, which can be reduced to a free theory by a local field redefinition; the second contains two fields and cannot be so reduced. Loop corrections in both models produce large temporal and spatial logarithms which cause perturbation theory to break down at late times and large distances. Many of these logarithms derive from the “tail” part of the propagator and can be summed using a variant of Starobinsky’s stochastic formalism involving a curvature-dependent effective potential. The remaining logarithms derive from the ultraviolet and can be summed using a variant of the renormalization group based on a special class of curvature-dependent renormalizations. Explicit results are derived at 1-loop and 2-loop orders. 

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3. Quantum Melting of Spin-1 Dimer Solid Induced by Inter-chain Couplings

   Xu, Yi ; Fu, Tianfu ; Hasik, Juraj ; Nevidomskyy, Andriy H. ( September 2022 , arXivorg)

   Dimerized valence bond solids appear naturally in spin-1/2 systems on bipartite lattices, with the geometric frustrations playing a key role both in their stability and the eventual `melting' due to quantum fluctuations. Here, we ask the question of the stability of such dimerized solids in spin-1 systems, taking the anisotropic square lattice with bilinear and biquadratic spin-spin interactions as a paradigmatic model. The lattice can be viewed as a set of coupled spin-1 chains, which in the limit of vanishing inter-chain coupling are known to possess a stable dimer phase. We study this model using the density matrix renormalization group (DMRG) and infinite projected entangled-pair states (iPEPS) techniques, supplemented by the analytical mean-field and linear flavor wave theory calculations. While the latter predicts the dimer phase to remain stable up to a reasonably large interchain-to-intrachain coupling ratio r≲0.6, the DMRG and iPEPS find that the dimer solid melts for much weaker interchain coupling not exceeding r≲0.15. We find the transition into a magnetically ordered state to be first order, manifested by a hysteresis and order parameter jump, precluding the deconfined quantum critical scenario. The apparent lack of stability of dimerized phases in 2D spin-1 systems is indicative of strong quantum fluctuations that melt the dimer solid. 

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4. Continuous N\'{e}el-VBS quantum phase transition in non-local one-dimensional systems with SO(3) symmetry

   https://doi.org/10.21468/SciPostPhys.10.2.033  

   Jian, Chao-Ming ; Xu, Yichen ; Wu, Xiao-Chuan ; Xu, Cenke ( January 2021 , SciPost Physics)

   null (Ed.)

   One dimensional (1d) interacting systems with local Hamiltonianscan be studied with various well-developed analytical methods.Recently novel 1d physics was found numerically in systems witheither spatially nonlocal interactions, or at the 1d boundary of2d quantum critical points, and the critical fluctuation in thebulk also yields effective nonlocal interactions at the boundary.This work studies the edge states at the 1d boundary of 2dstrongly interacting symmetry protected topological (SPT) states,when the bulk is driven to a disorder-order phase transition. Wewill take the 2d Affleck-Kennedy-Lieb-Tasaki (AKLT) state as anexample, which is a SPT state protected by the SO(3) spinsymmetry and spatial translation. We found that the original(1+1)d boundary conformal field theory of the AKLT state isunstable due to coupling to the boundary avatar of the bulkquantum critical fluctuations. When the bulk is fixed at thequantum critical point, within the accuracy of our expansionmethod, we find that by tuning one parameter at the boundary,there is a generic direct transition between the long rangeantiferromagnetic Néel order and the valence bond solid (VBS)order. This transition is very similar to the Néel-VBStransition recently found in numerical simulation of a spin-1/2chain with nonlocal spatial interactions. Connections between ouranalytical studies and recent numerical results concerning theedge states of the 2d AKLT-like state at a bulk quantum phasetransition will also be discussed. 

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5. Finiteness of entanglement entropy in collective field theory

   https://doi.org/10.1007/JHEP12(2022)052  

   Das, Sumit R. ; Jevicki, Antal ; Zheng, Junjie ( December 2022 , Journal of High Energy Physics)

   A bstract We explore the question of finiteness of the entanglement entropy in gravitational theories whose emergent space is the target space of a holographic dual. In the well studied duality of two-dimensional non-critical string theory and c = 1 matrix model, this question has been studied earlier using fermionic many-body theory in the space of eigenvalues. The entanglement entropy of a subregion of the eigenvalue space, which is the target space entanglement in the matrix model, is finite, with the scale being provided by the local Fermi momentum. The Fermi momentum is, however, a position dependent string coupling, as is clear in the collective field theory formulation. This suggests that the finiteness is a non-perturbative effect. We provide evidence for this expectation by an explicit calculation in the collective field theory of matrix quantum mechanics with vanishing potential. The leading term in the cumulant expansion of the entanglement entropy is calculated using exact eigenstates and eigenvalues of the collective Hamiltonian, yielding a finite result, in precise agreement with the fermion answer. Treating the theory perturbatively, we show that each term in the perturbation expansion is UV divergent. However the series can be resummed, yielding the exact finite result. Our results indicate that the finiteness of the entanglement entropy for higher dimensional string theories is non-perturbative as well, with the scale provided by Newton’s constant. 

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