Related papers: Fermionic Quantum Gravity
Four-dimensional random geometries can be generated by statistical models with rank-4 tensors as random variables. These are dual to discrete building blocks of random geometries. We discover a potential candidate for a continuum limit in…
We propose a quantum mechanical theory of quantum spaces described by large $N$ noncommutative geometry as a model for quantum gravity. The model admits fuzzy sphere as static solution. Over the fuzzy geometry, the quantum mechanics of the…
We investigate the Poincar\'e approach to computing 3d gravity partition functions dual to Rational CFT. For a single genus-1 boundary, we show that for certain infinite sets of levels, the SU(2)$_k$ WZW models provide unitary examples for…
Extending black-hole entropy to ordinary objects, we propose kinetic entropy tensor, based on which a quantum gravity tensor equation is established. Our investigation results indicate that if N=1, the quantum gravity tensor equation…
Let A be the algebra generated by the power series \sum n^{n-1} q^n/n! and \sum n^n q^n /n! . We prove that many natural generating functions lie in this algebra: those appearing in graph enumeration problems, in the intersection theory of…
Fermionic phase space representations are a promising method for studying correlated fermion systems. The fermionic Q-function and P-function have been defined using Gaussian operators of fermion annihilation and creation operators. The…
We show that modeling a Grassmannian as symmetric orthogonal matrices $\operatorname{Gr}(k,\mathbb{R}^n) \cong\{Q \in \mathbb{R}^{n \times n} : Q^{\scriptscriptstyle\mathsf{T}} Q = I, \; Q^{\scriptscriptstyle\mathsf{T}} = Q,\;…
We investigate the spectrum of the infinitesimal generator of the continuous time random walk on a randomly weighted oriented graph. This is the non-Hermitian random nxn matrix L defined by L(j,k)=X(j,k) if k<>j and…
In these Notes, a comprehensive description of the universal fractal geometry of conformally-invariant scaling curves or interfaces, in the plane or half-plane, is given. The present approach focuses on deriving critical exponents…
We study the growth of structures in modified gravity models where the Poisson equation and the relationship between the two Newtonian potentials are modified by explicit functions of space and time. This parameterisation applies to the…
In this paper we study stochastic dynamics which leaves quantum gravity equilibrium distribution invariant. We start theoretical study of this dynamics (earlier it was only used for Monte-Carlo simulation). Main new results concern the…
The relation between spin and statistics in quantum field theory relies on Poincar\'e invariance, a symmetry that is lost in the presence of a gravitational field, and replaced in general relativity by the principle of general covariance.…
We formulate the planar `large N limit' of matrix models with a continuously infinite number of matrices directly in terms of U(N) invariant variables. Non-commutative probability theory, is found to be a good language to describe this…
The main results for the two-dimensional quantum gravity, conjectured from the matrix model or integrable approach, are presented in the form to be compared with the world-sheet or Liouville approach. In spherical limit the integrable side…
General Relativity (GR) exists in different formulations, which are equivalent in pure gravity. Once matter is included, however, observable predictions generically depend on the version of GR. In order to quantify the resulting ambiguity,…
Spectral statistics of quantum chaotic systems are governed by random matrix universality. In many cases of interest, time-reversal symmetry selects the Gaussian Orthogonal Ensemble (GOE) as the relevant universality class. In holographic…
In this paper we study the large $N$ solution to matrix models describing the partition functions of 3d supersymmetric gauge theories on $S^3$. The model we focus on has a single $U(N)$ gauge group and fundamental fields, whose number…
The coupling between internal degrees of freedom of quantum systems and their overall motion in an external gravitational field plays a central role in multiple extensions of Einstein's equivalence principle to quantum physics. While…
In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short…
We define and study the Pfaffian state on Riemann surfaces with arbitrary metrics and an inhomogeneous magnetic field and derive its universal transport coefficients. Following a path integral approach, we compute the generating functional…