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We consider the question of identifying the bulk space-time of the SYK model. Focusing on the signature of emergent space-time of the (Euclidean) model, we explain the need for non-local (Radon-type) transformations on external legs of $n$-point Greens functions. This results in a dual theory with Euclidean AdS signature with additional leg-factors. We speculate that these factors incorporate the coupling of additional bulk states similar to the discrete states of 2d string theory.
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The Lorentzian type IIB matrix model has been studied as a promising candidate for a nonperturbative formulation of superstring theory. In particular, the emergence of (3+1)D expanding space-time was observed by Monte Carlo studies of this model. It has been found recently, however, that the matrix configurations generated by the simulation is singular in that the submatrices representing the expanding 3D space have only two large eigenvalues associated with the Pauli matrices. This problem has been attributed to the approximation used to avoid the sign problem in simulating the model. Here we investigate the model using the complex Langevin method to overcome the sign problem instead of using the approximation. Our results indicate a clear departure from the Pauli-matrix structure, while the (3+1)D expanding behavior is kept intact.
In this paper, we theoretically investigate the time dilation and Doppler effect in curved space-time from the perspective of quantum field theory (QFT). A Coordinate Transformation which Maintains the Period of Clocks is introduced, and such coordinate transformation is named as CTMPC throughout this paper. By analogy with the Lorentz transformation in Minkowski space-time, CTMPC is a correct transformation in curved space-times in a sense that it shows the correct relation between the time measured by the two observers, moreover, Lorentz transformation is just a special case of CTMPC applied in Minkowski space-time. We demonstrate that the Coordinate Transformation which Maintains the Local Metric (CTMLM) is one CTMPC, while the mathematical forms of physics formulas in QFT will be maintained. As applications of CTMLM, the time dilation and Doppler effect with an arbitrary time-dependent relative velocity in curved space-time are analysed. For Minkowski space-time, the time dilation and Doppler effect agree with the clock hypothesis. For curved space-time, we show that even if the emitted wave has a narrow frequency range, the Doppler effect may, in general, broaden the frequency spectrum and, at the meantime, shift the frequencies values. These new findings will deepen our understanding on the nature of space-time and the Doppler effect in curved space-time, they may also provide theoretical guidance in future astronomical observations.
SYK model is a quantum mechanical model of fermions which is solvable at strong coupling and plays an important role as perhaps the simplest holographic model of quantum gravity and black holes. The present work considers a deformed SYK model and a sudden quantum quench in the deformation parameter. The system, as in the undeformed case, permits a low energy description in terms of pseudo Nambu Goldstone modes. The bulk dual of such a system represents a gravitational collapse, which is characterized by a bulk matter stress tensor whose value near the boundary shows a sudden jump at the time of the quench. The resulting gravitational collapse forms a black hole only if the deformation parameter $Deltaepsilon$ exceeds a certain critical value $Deltaepsilon_c$ and forms a horizonless geometry otherwise. In case a black hole does form, the resulting Hawking temperature is given by a fractional power $T_{bh} propto (Deltaepsilon - Deltaepsilon_c)^{1/2}$, which is reminiscent of the `Choptuik phenomenon of critical gravitational collapse.
We study a two-site Sachdev-Ye-Kitaev (SYK) model with complex couplings, and identify a low temperature transition to a gapped phase characterized by a constant in temperature free energy. This transition is observed without introducing a coupling between the two sites, and only appears after ensemble average over the complex couplings. We propose a gravity interpretation of these results by constructing an explicit solution of Jackiw-Teitelboim (JT) gravity with matter: a two-dimensional Euclidean wormhole whose geometry is the double trumpet. This solution is sustained by imaginary sources for a marginal operator, without the need of a coupling between the two boundaries. As the temperature is decreased, there is a transition from a disconnected phase with two black holes to the connected wormhole phase, in qualitative agreement with the SYK observation. The expectation value of the marginal operator is an order parameter for this transition. This illustrates in a concrete setup how a Euclidean wormhole can arise from an average over field theory couplings.
It is shown how the characteristic thermal effects that observers experience in space-times possessing an event horizon can manifest already in a simple quantum system with affine symmetry living on the real line. The derivation presented is essentially group theoretic in nature: a thermal state emerges naturally when comparing different representations of the group of affine transformations of the real line. The freedom in the choice of different notions of translation generators is the key to the Unruh effect on a line we describe.
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