Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userImplementing holographic projections in Ponzano--Regge gravity
64
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We consider the path-sum of Ponzano-Regge with additional boundary contributions in the context of the holographic principle of Quantum Gravity. We calculate an holographic projection in which the bulk partition function goes to a semi-classical limit while the boundary state functional remains quantum-mechanical. The properties of the resulting boundary theory are discussed.
rate research
Read More
This is the first of a series of papers dedicated to the study of the partition function of three-dimensional quantum gravity on the twisted solid torus with the aim to deepen our understanding of holographic dualities from a non-perturbative quantum gravity perspective. Our aim is to compare the Ponzano-Regge model for non-perturbative three-dimensional quantum gravity with the previous perturbative calculations of this partition function. We begin by reviewing the results obtained in the past ten years via a wealth of different approaches, and then introduce the Ponzano--Regge model in a self-contained way. Thanks to the topological nature of three-dimensional quantum gravity we can solve exactly for the bulk degrees of freedom and identify dual boundary theories which depend on the choice of boundary states, that can also describe finite, non-asymptotic boundaries. This series of papers aims precisely at the investigation of the role played by the different quantum boundary conditions leading to different boundary theories. Here, we will describe the spin network boundary states for the Ponzano-Regge model on the twisted torus and derive the general expression for the corresponding partition functions. We identify a class of boundary states describing a tessellation with maximally fuzzy squares for which the partition function can be explicitly evaluated. In the limit case of a large, but finely discretized, boundary we find a dependence on the Dehn twist angle characteristic for the BMS3 character. We furthermore show how certain choices of boundary states lead to known statistical models as dual field theories-but with a twist.
We investigate the propagator of 3d quantum gravity, formulated as a discrete topological path integral. We define it as the Ponzano-Regge amplitude of the solid cylinder swept by a 2d disk evolving in time. Quantum states for a 2d disk live in the tensor products of N spins, where N is the number of holonomy insertions connecting to the disk boundary. We formulate the cylindric amplitude in terms of a transfer matrix and identify its eigen-modes in terms of spin recoupling. We show that the propagator distinguishes the subspaces with different total spin and may select the vanishing total spin sector at late time depending on the chosen cylinder boundary data. We discuss applications to quantum circuits and the possibility of experimental simulations of this 3d quantum gravity propagator.
In this paper, we investigate the AC charge transport in the holographic Horndeski gravity and identify a metal-semiconductor like transition that is driven by the Horndeski coupling. Moreover, we fit our numeric data by the Drude formula in slow relaxation cases.
We investigate the neutral AdS black-hole solution in the consistent $Drightarrow4$ Einstein-Gauss-Bonnet gravity proposed in [K. Aoki, M.A. Gorji, and S. Mukohyama, Phys. Lett. B {bf 810}, 135843 (2020)] and construct the gravity duals of ($2+1$)-dimensional superconductors with Gauss-Bonnet corrections in the probe limit. We find that the curvature correction has a more subtle effect on the scalar condensates in the s-wave superconductor in ($2+1$)-dimensions, which is different from the finding in the higher-dimensional superconductors that the higher curvature correction makes the scalar hair more difficult to be developed in the full parameter space. However, in the p-wave case, we observe that the higher curvature correction always makes it harder for the vector condensates to form in various dimensions. Moreover, we note that the higher curvature correction results in the larger deviation from the expected relation in the gap frequency $omega_g/T_capprox 8$ in both ($2+1$)-dimensional s-wave and p-wave models.
We construct the holographic p-wave superfluid in Gauss-Bonnet gravity via a Maxwell complex vector field model and investigate the effect of the curvature correction on the superfluid phase transition in the probe limit. We obtain the rich phase structure and find that the higher curvature correction hinders the condensate of the vector field but makes it easier for the appearance of translating point from the second-order transition to the first-order one or for the emergence of the Cave of Winds. Moreover, for the supercurrents versus the superfluid velocity, we observe that our results near the critical temperature are independent of the Gauss-Bonnet parameter and agree well with the Ginzburg-Landau prediction.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
