Phase transitions in tensorial group field theories: Landau-Ginzburg analysis of models with both local and non-local degrees of freedom

In the tensorial group field theory approach to quantum gravity, the theory is based on discrete building blocks and continuum spacetime is expected to emerge from their collective dynamics, possibly at criticality, via a phase transition. On a compact group of fixed volume this can be expected to be only possible in a large-volume or thermodynamic limit. Here we show how phase transitions are possible in TGFTs in two cases: a) considering the non-local group degrees of freedom on a non-compact Lie group instead of a compact one (or taking a large-volume limit of a compact group); b) in models including ℝ-valued local degrees of freedom (that can be interpreted as discrete scalar fields, often used in this context to provide a matter reference frame). After adapting the Landau-Ginzburg approach to this setting of mixed local/non-local degrees of freedom, we determine the critical dimension beyond which there is a Gaussian fixed point and a continuous phase transition which can be described by mean-field theory. This is an important step towards the realization of a phase transition to continuum spacetime in realistic TGFT models for quantum gravity.

Early Sarmatian Burials from the Chechen Republic Territory

In 2018, Kurgan 2 of Gvardeyskiye 3 Kurgany (the 3rd Gvardeiskiy Kurgans) in the Nadterechny District of the Chechen Republic was studied. In the result, nine burials were found in the Kurgan which was created during the Early Bronze Age and continued to be used in the course of the Middle and Late Bronze Age. However, the three most recent burials date back to the Early Iron Age period. The burials were localized inside the existing embankment and formed a compact group. In two cases, the burial type was not identified; nevertheless in one case, the burial was constructed in a catacomb. The grave goods are mainly presented by ceramic vessels from the workshops of the sedentary population from the foothill area of Central and Eastern North Caucasus regions. The conclusion was made that the investigated Kurgans were left by the nomadic North Caucasian steppes population of the 3rd–1st centuries BC due to the feature analysis of the Early Iron Age burial complexes.

On Idempotent Measures of Small Norm

<p>In this Master’s Thesis, we set up the groundwork for [8], a paper co-written by the author and Hung Pham. We summarise the Fourier and Fourier-Stieltjes algebras on both abelian and general locally compact groups. Let Г be a locally compact group. We answer two questions left open in [11] and [13]: 1. When Г is abelian, we prove that if ϰs ∈ B(Г) is an idempotent with norm 1 < ||ϰs|| < 4/3 then S is the union of two cosets of an open subgroup of Г. 2. For general Г, we prove that if ϰs ∈ McbA(Г) is an idempotent with norm ||ϰs||cb < 1+√2/2 , then S is an open coset in Г.</p>

On Idempotent Measures of Small Norm

<p>In this Master’s Thesis, we set up the groundwork for [8], a paper co-written by the author and Hung Pham. We summarise the Fourier and Fourier-Stieltjes algebras on both abelian and general locally compact groups. Let Г be a locally compact group. We answer two questions left open in [11] and [13]: 1. When Г is abelian, we prove that if ϰs ∈ B(Г) is an idempotent with norm 1 < ||ϰs|| < 4/3 then S is the union of two cosets of an open subgroup of Г. 2. For general Г, we prove that if ϰs ∈ McbA(Г) is an idempotent with norm ||ϰs||cb < 1+√2/2 , then S is an open coset in Г.</p>

Global Expansion of Linezolid-Resistant Coagulase-Negative Staphylococci

Coagulase-negative staphylococci (CoNS) for a long time were considered avirulent constituents of the human and warm-blooded animal microbiota. However, at present, S. epidermidis, S. haemolyticus, and S. hominis are recognized as opportunistic pathogens. Although linezolid is not registered for the treatment of CoNS infections, it is widely used off-label, promoting emergence of resistance. Bioinformatic analysis based on maximum-likelihood phylogeny and Bayesian clustering of the CoNS genomes obtained in the current study and downloaded from public databases revealed the existence of international linezolid-resistant lineages, each of which probably had a common predecessor. Linezolid-resistant S. epidermidis sequence-type (ST) 2 from Russia, France, and Germany formed a compact group of closely related genomes with a median pairwise single nucleotide polymorphism (SNP) difference of fewer than 53 SNPs, and a common ancestor of this lineage appeared in 1998 (1986–2006) before introduction of linezolid in practice. Another compact group of linezolid-resistant S. epidermidis was represented by ST22 isolates from France and Russia with a median pairwise SNP difference of 40; a common ancestor of this lineage appeared in 2011 (2008–2013). Linezolid-resistant S. hominis ST2 from Russia, Germany, and Brazil also formed a group with a high-level genome identity with median 25.5 core-SNP differences; the appearance of the common progenitor dates to 2003 (1996–2012). Linezolid-resistant S. hominis isolates from Russia demonstrated associated resistance to teicoplanin. Analysis of a midpoint-rooted phylogenetic tree of the group confirmed the genetic proximity of Russian and German isolates; Brazilian isolates were phylogenetically distant. repUS5-like plasmids harboring cfr were detected in S. hominis and S. haemolyticus.

Influence of Water Level on the Exit of Climbing Perch Anabas testudineus out of the Water and Specific Features of Its Movements

Abstract— The study presents the behavior and movement characteristics of climbing perch Anabas testudineus in the “dry maze” installation. Two types of behavior were identified in climbing perch when the water level in the starting tank decreases to the critical value: waiting (often in a compact group at the bottom of the starting tank) or exit to ashore (land) and moving (migration). Movements usually take place in a group of two to four individuals. The fish chose a tank with the water randomly and remained there until the end of the experiment. If individuals become to an empty tank, they, as a rule, leave it and continue to search for water. Thus, the search for a new waterbody is determining the terrestrial migration of climbing perch.

Compact groups with a set of positive Haar measure satisfying a nilpotent law

The following question is proposed by Martino, Tointon, Valiunas and Ventura in [4, question 1·20]: Let G be a compact group, and suppose that \[\mathcal{N}_k(G) = \{(x_1,\dots,x_{k+1}) \in G^{k+1} \;|\; [x_1,\dots, x_{k+1}] = 1\}\] has positive Haar measure in $G^{k+1}$ . Does G have an open k-step nilpotent subgroup? We give a positive answer for $k = 2$ .