14830356
Exact Free Energies of Statistical Systems on Random Networks
Statistical systems on random networks can be formulated in terms of partition functions expressed with integrals by regarding Feynman diagrams as random networks. We consider the cases of random networks with bounded but generic degrees of vertices, and show that the free energies can be exactly evaluated in the thermodynamic limit by the Laplace method, and that the exact expressions can in principle be obtained by solving polynomial equations for mean fields. As demonstrations, we apply our method to the ferromagnetic Ising models on random networks. The free energy of the ferromagnetic Ising model on random networks with trivalent vertices is shown to exactly reproduce that of the ferromagnetic Ising model on the Bethe lattice. We also consider the cases with heterogeneity with mixtures of orders of vertices, and derive the known formula of the Curie temperature.
119121074
Causal dynamical triangulation with extended interactions in 1+1 dimensions
Abstract We study the Causal Dynamical Triangulation (CDT) with extended interactions in 1 + 1 dimensions applying the method in the non-critical String Field Theory (SFT) constructed by Ishibashi and Kawai. For this model, we solve Schwinger–Dysonʼs Equation (SDE) for disk amplitude perturbatively, and find a matrix model in the continuum limit reproducing the SDE in the non-critical SFT approach as the loop equation.
118586207
New multicritical matrix models and multicritical 2d CDT
Abstract We define multicritical CDT models of 2d quantum gravity and show that they are a special case of multicritical generalized CDT models obtained from the new scaling limit, the so-called “classical” scaling limit, of matrix models. The multicritical behavior agrees with the multicritical behavior of the so-called branched polymers.
119234990
Interpreting canonical tensor model in minisuperspace
Abstract Canonical tensor model is a theory of dynamical fuzzy spaces in arbitrary space–time dimensions. Examining its simplest case, we find a connection to a special case of minisuperspace model of general relativity in arbitrary dimensions. This is a first step in interpreting variables in canonical tensor model based on the known language of general relativity.
116895105
n-DBI Gravity: A Short Overview
We present a model of gravity motivated by the Dirac–Born–Infeld type conformal scalar theory it yields when the Universe is conformally flat. We show that, if the Universe is permeated by a perfect fluid of radiation, the theory naturally predicts two eras of accelerated expansion mediated by a radiation dominated epoch, with a large hierarchy between the two effective cosmological constants, thus providing an alternative inflation scenario. This theory, dubbed n-DBI gravity, contains a preferred unit vector field, everywhere time-like, which breaks diffeomorphism invariance and gives rise to an extra scalar degree of freedom. We analyze the dynamics of this mode and conclude that it is free from some of the pathologies found in similar models, namely the issues of vanishing lapse short distance instability and strong coupling. We also show that the standard black holes of General Relativity are solutions of this theory.
118614910
On the scalar graviton in n-DBI gravity
n-DBI gravity is a gravitational theory which yields near de Sitter inflation spontaneously at the cost of breaking Lorentz invariance by a preferred choice of foliation. We show that this breakdown endows n-DBI gravity with one extra physical gravitational degree of freedom: a scalar graviton. Its existence is established by Dirac’s theory of constrained systems. Firstly, studying scalar perturbations around Minkowski spacetime, we show that there exists one scalar degree of freedom and identify it in terms of the metric perturbations. Then, a general analysis is made in the canonical formalism, using ADM variables. It is useful to introduce an auxiliary scalar field, which allows recasting n-DBI gravity in an Einstein-Hilbert form but in a Jordan frame. Identifying the constraints and their classes we confirm the existence of an extra degree of freedom in the full theory, besides the two usual tensorial modes of the graviton. We then argue that, unlike the case of (the original proposal for) Hoyrava-Lifschitz gravity, there is no evidence that the extra degree of freedom originates pathologies, such as vanishing lapse, instabilities and strong self-coupling at low energy scales.
118547294
Potential analysis in holographic Schwinger effect
A bstractWe analyze electrostatic potentials in the holographic Schwinger effect. The potential barrier for the pair production is estimated by a static potential consisting of static mass energies, an electric potential from an external electric-field, and the Coulomb potential between a particle and an antiparticle. Given that the Coulomb potential is supposed to be evaluated by the minimal surface attaching on the conformal boundary as usual, the critical field, where the potential barrier vanishes, exhibits a deviation of 30% from the one obtained from the Dirac-Born-Infeld (DBI) action. We reconsider this issue by reexamining the Coulomb-potential part, which is evaluated by the classical action of a string solution attaching on a probe D3-brane sitting at an intermediate position in the bulk AdS. Then the resulting critical-field completely agrees with the DBI result. This agreement gives rise to a strong support for the holographic scenario. We also discuss the finite-temperature case and the temperature-dependent critical-field also agrees with the DBI result.
119114995
Holographic description of the Schwinger effect in electric and magnetic field
A bstractWe consider a generalization of the holographic Schwinger effect proposed by Semenoff and Zarembo to the case with constant electric and magnetic fields. There are two ways to turn on magnetic fields, i) the probe D3-brane picture and ii) the string world-sheet picture. In the former picture, magnetic fields both perpendicular and parallel to the electric field are activated by a Lorentz transformation and a spatial rotation. In the latter one, the classical solutions of the string world-sheet corresponding to circular Wilson loops is generalized to contain two additional parameters encoding the presence of magnetic fields.
119213971
Holographic Schwinger effect in confining phase
A bstractWe consider the Schwinger effect in confining phase by using a holographic setup. The potential analysis is performed for the confining D3-brane and D4-brane back-grounds. We find the critical electric field above which there is no potential barrier and the system becomes unstable catastrophically. An intriguing point is that no Schwinger effect occurs when the electric field is smaller than the confining string tension.