Symmetries of Thirring Models on 3D Lattices

We review some recent developments about strongly interacting relativistic Fermi theories in three spacetime dimensions. These models realize the asymptotic safety scenario and are used to describe the low-energy properties of Dirac materials in condensed matter physics. We begin with a general discussion of the symmetries of multi-flavor Fermi systems in arbitrary dimensions. Then we review known results about the critical flavor number $N_\mathrm{crit}$ of Thirring models in three dimensions. Only models with flavor number below $N_\mathrm{crit}$ show a phase transition from a symmetry-broken strong-coupling phase to a symmetric weak-coupling phase. Recent simulations with chiral fermions show that $N_\mathrm{crit}$ is smaller than previously extracted with various non-perturbative methods. Our simulations with chiral SLAC fermions reveal that for four-component flavors $N_\mathrm{crit}=0.80(4)$. This means that all reducible Thirring models with $\Nr=1,2,3,\dots$ show no phase transition with order parameter. Instead we discover footprints of phase transitions without order parameter. These new transitions are probably smooth and could be used to relate the lattice Thirring models to Thirring models in the continuum. For a single irreducible flavor, we provide previously unpublished values for the critical couplings and critical exponents.

General bounds on holographic complexity

We prove a positive volume theorem for asymptotically AdS spacetimes: the maximal volume slice has nonnegative vacuum-subtracted volume, and the vacuum-subtracted volume vanishes if and only if the spacetime is identically pure AdS. Under the Complexity=Volume proposal, this constitutes a positive holographic complexity theorem. The result features a number of parallels with the positive energy theorem, including the assumption of an energy condition that excludes false vacuum decay (the AdS weak energy condition). Our proof is rigorously established in broad generality in four bulk dimensions, and we provide strong evidence in favor of a generalization to arbitrary dimensions. Our techniques also yield a holographic proof of Lloyd’s bound for a class of bulk spacetimes. We further establish a partial rigidity result for wormholes: wormholes with a given throat size are more complex than AdS-Schwarzschild with the same throat size.

Active Brownian motion with speed fluctuations in arbitrary dimensions: exact calculation of moments and dynamical crossovers

We consider the motion of an active Brownian particle with speed fluctuations in d-dimensions in the presence of both translational and orientational diffusion. We use an Ornstein–Uhlenbeck process for active speed generation. Using a Laplace transform approach, we describe and use a Fokker–Planck equation-based method to evaluate the exact time dependence of all relevant dynamical moments. We present explicit calculations of several such moments and compare our analytical predictions against numerical simulations to demonstrate and analyze the dynamical crossovers, determined by the orientational persistence of activity, speed fluctuation and relaxation. The kurtosis of displacement shows positive and negative deviations from a Gaussian behavior at intermediate times depending on the dominance of speed and orientational fluctuations, respectively.

Higher-dimensional Calabi–Yau varieties with dense sets of rational points

We construct higher-dimensional Calabi–Yau varieties defined over a given number field with Zariski dense sets of rational points. We give two elementary constructions in arbitrary dimensions as well as another construction in dimension three which involves certain Calabi–Yau threefolds containing an Enriques surface. The constructions also show that potential density holds for (sufficiently) general members of the families.

The Progress of Black Holes: Principles & Physical Detection Technology

Humans have been trying to explain black holes since the 19th century, using theoretical understanding and observations of the universe. Incandescent body thermal radiation has been the focus of extensive theoretical and experimental research for over a century. This paper will discuss the concept of a black hole and use information retrieval to generate a panoramic image of it. The content illustrates black holes from three different perspectives: description of black holes using mathematical methods and data, models, and detection. A black hole is a controversial object, and no one knows for sure what it is. Indeed, multiple numerical simulations have been carried out to investigate the critical behaviors of black holes with various geometrical configurations in arbitrary dimensions. We will sum up the black hole knowledge so far and discuss the recent progress in terms of black hole exploration, i.e., shed light for future black holes model construction and detection.

AdS black brane solution surrounded by quintessence in massive gravity and KSS bound

In this paper, the Einstein AdS black brane solution in the presence of quintessence in context of massive gravity is introduced. The ratio of shear viscosity to entropy density for this solution violates the KSS bound by applying the Dirichlet boundary and regularity conditions on the horizon for [Formula: see text]. Our result shows that this value is independent of quintessence in any arbitrary dimensions.