Dynamics of the conformal mode and simplicial gravity

Catterall, Simon; Mottola, Emil; Bhattacharya, Tanmoy

doi:10.1016/s0920-5632(99)85205-0

Cited by 3 publications

(5 citation statements)

References 6 publications

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“…In the context of Euclidean DT quantum gravity, combined theories of gravity and various matter field theories have been studied extensively, in both three and four dimensions [120,121,122]. Surprisingly little new insight was gained from comparing the phase diagram with matter to that without matter 33 . At least perturbatively this may be understood from the fact that adding matter to the action will from a gravitational point of view mainly lead to a shift in the bare gravitational coupling constant.…”

Section: Discussionmentioning

confidence: 99%

“…As long as we stay with Euclidean signature we can use tools and techniques from statistical field theory and the theory of critical phenomena when searching for fixed 7 The fact that the behaviour of the conformal factor is captured correctly, even in the context of dynamical lattices, is nicely illustrated in two dimensions [33]. The formalism of dynamical triangulations (DT), which provides a regularization of two-dimensional Euclidean Einstein-Hilbert quantum gravity coupled to conformal matter, can be used to calculate the conformal factor for each configuration in the (discretized) path integral.…”

Section: Causal Dynamical Triangulations 101mentioning

confidence: 99%

“…The result can be compared to the continuum theory (quantum Liouville theory), and good agreement is found. As described in [33], one even has an analogy to the entropy-driven Kosterlitz-Thouless phase transition described below, namely, the condensation of spikes at the c = 1 barrier of Euclidean two-dimensional quantum gravity coupled to conformal field theory.…”

Section: Causal Dynamical Triangulations 101mentioning

confidence: 99%

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Nonperturbative quantum gravity

et al. 2012

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Asymptotic safety describes a scenario in which general relativity can be quantized as a conventional field theory, despite being nonrenormalizable when expanding it around a fixed background geometry. It is formulated in the framework of the Wilsonian renormalization group and relies crucially on the existence of an ultraviolet fixed point, for which evidence has been found using renormalization group equations in the continuum."Causal Dynamical Triangulations" (CDT) is a concrete research program to obtain a nonperturbative quantum field theory of gravity via a lattice regularization, and represented as a sum over spacetime histories. In the Wilsonian spirit one can use this formulation to try to locate fixed points of the lattice theory and thereby provide independent, nonperturbative evidence for the existence of a UV fixed point.We describe the formalism of CDT, its phase diagram, possible fixed points and the "quantum geometries" which emerge in the different phases. We also argue that the formalism may be able to describe a more general class of Hořava-Lifshitz gravitational models.

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Section: Discussionmentioning

confidence: 99%

Section: Causal Dynamical Triangulations 101mentioning

confidence: 99%

Section: Causal Dynamical Triangulations 101mentioning

confidence: 99%

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Nonperturbative quantum gravity

et al. 2012

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“…no gravitational action is used to weight the configurations. To couple matter we just dress the vertices with c m free scalar fields coupled by the usual Gaussian action using the scalar Laplacian (11). A combined heat bath and overrelaxation algorithm was used to simulate the scalars.…”

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confidence: 99%

The conformal mode in 2D simplicial gravity

Catterall

Mottola

1999

Physics Letters B

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We verify that summing 2D DT geometries correctly reproduces the Polyakov action for the conformal mode, including all ghost contributions, at large volumes. The Gaussian action is reproduced even for c m = 10, well into the branched polymer phase, which confirms the expectation that the DT measure is indeed correct in this regime as well Introduction. In the last decade there has been considerable progress in our understanding of two dimensional quantum gravity (2DQG). The key element that has made this progress possible is the recognition that the trace anomaly requires the effective action of 2DQG to be augmented by a well-defined nonlocal term [1],

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“…This is the viewpoint taken by the asymptotic safety program [9][10][11][12][13][14] which employs functional renormalization group methods to search for new fixed points in quantum general relativity. It is also common to lattice approaches such as causal and Euclidean dynamical triangulations [15][16][17][18][19][20][21]. The latter have revealed some intriguing aspects of quantum gravity like the emergence of fractal structure at the Planck scale [16,18].…”

Section: Introductionmentioning

confidence: 98%

Tensor network formulation of two-dimensional gravity

2020

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We show how to formulate a lattice gauge theory whose naive continuum limit corresponds to twodimensional (Euclidean) quantum gravity including a positive cosmological constant. More precisely the resultant continuum theory corresponds to gravity in a first-order formalism in which the local frame and spin connection are treated as independent fields. Recasting this lattice theory as a tensor network allows us to study the theory at strong coupling without encountering a sign problem. In two dimensions this tensor network is exactly soluble and we show that the system has a series of critical points that occur for pure imaginary coupling and are associated with first order phase transitions. We then augment the action with a Yang-Mills term which allows us to control the lattice spacing and show how to apply the tensor renormalization group to compute the free energy and look for critical behavior. Finally we perform an analytic continuation in the gravity coupling in this extended model and show that its critical behavior in a certain scaling limit depends only on the topology of the underlying lattice. We also show how the lattice gauge theory can be naturally generalized to generate the Polyakov or Liouville action for two dimensional quantum gravity.

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Dynamics of the conformal mode and simplicial gravity

Cited by 3 publications

References 6 publications

Nonperturbative quantum gravity

Nonperturbative quantum gravity

The conformal mode in 2D simplicial gravity

Tensor network formulation of two-dimensional gravity

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