In S. Giombi, I. Klebanov, F. Popov, Prakash and G. Tarnopolsky, {\it Phys. Rev.} {\bf D} 98 (2018) 10, 105005, a prismatic tensor model was introduced. We study here the diagrammatics double scaling limit of this model, using intermediate field method. explicitly exhibit next-to-leading order Feynman graphs in $1/N$ expansion. Using appropriate combinatorial tools, we further general term expansion compute $2-$point function limit.

In Gurau and Keppler 2022 (arXiv:2207.01993), a relation between orthogonal symplectic tensor models with quartic interactions was proven. this paper, we provide an alternative proof that extends to polynomial of arbitrary order. We consider order D no symmetry under permutation the indices transform in product fundamental representations O(N) Sp(N). explicitly show obey N -N duality graph by perturbation theory.

Abstract We establish two embedding theorems for tree-free groups. The first result embeds a group G acting freely and without inversions on Λ-tree X into freely, inversions, transitively in such way that by means of -equivariant isometry. second an ℝ-tree ( H ) some suitable , again -equivariantly the associated with ). referred to here belongs class groups introduced studied present authors [ 3 ]. As consequence these theorems, we find -groups their ℝ-trees are fact universal free actions....

In a recent series of papers, duality between orthogonal and symplectic random tensor models has been proven, first for quartic then with interactions arbitrary order. However, the considered so far in literature had no symmetry under permutation indices. this paper, we generalize these results tensors order which further have non-trivial Totally symmetric anti-symmetric are thus treated as particular case our result.

In this paper we show existence of a trace for functions bounded variation on Riemannian manifolds with boundary. The trace, which is in $L^\infty$, reached via $L^1$-convergence and allows an integration by parts formula. We apply these results order to well-posedness total estimates the initial boundary value problem scalar conservation law compact context vanishing viscosity method. flux function assumed be time-dependent divergence-free.

In Gurau and Keppler 2022 (arXiv:2207.01993), a relation between orthogonal symplectic tensor models with quartic interactions was proven. this paper, we provide an alternative proof that extends to polynomial of arbitrary order. We consider order D no symmetry under permutation the indices transform in product fundamental representations O(N) Sp(N). explicitly show obey N -N duality graph by perturbation theory.

Given a finite irreducible Coxeter group $W$, positive integer $d$, and types $T_1,T_2,...,T_d$ (in the sense of classification groups), we compute number decompositions $c=\si_1\si_2 cdots\si_d$ element $c$ such that $\si_i$ is in subgroup type $T_i$ $i=1,2,...,d$, factorisation "minimal" sum ranks $T_i$'s, equals rank $W$. For exceptional types, these decomposition numbers have been computed by first author. The $A_n$ Goulden Jackson, albeit using somewhat different language. We explain...