34 problems

Let $B$ be a connected $3$-coloured graph with $2n$ vertices, and consider the quartic rank-three tensor model. Equal leading cumulants conjecture. The supplied source span begins…

Let $M_1,\ldots,M_q$ be melonic, connected $3$-coloured graphs, with $q\in\mathbb{Z}_{>0}$. Define … For each $i$, let $p_i$ satisfy $2p_i=\#V(M_i)$. Strong conjecture. … The right…

Let $B$ be a connected $3$-coloured graph. For $q\in\mathbb{Z}_{>0}$ and $i_1,\ldots,i_q\in\{1,2,3\}$, define … where $V_i$ denotes the quartic pillow invariant of colour $i$, and…

Let $Z_{3\text{d gravity}}(M_3;c,\vec{q})$ be the pure three-dimensional gravity partition function of a connected three-manifold $M_3$ appearing in the ensemble expansion, and let…

Kronecker-construction conjecture. Under these circumstances, the construction of the Kronecker coefficient can be simplified; however, this simplification may not hold for every t…

Factorial-growth conjecture. The dominant term should include either or both factors

Let $P_{abc}$ be a unital tensor that admits a covering system of partial algebras. A pointwise decomposition is a positive tensor rank decomposition … such that every factor $p^i$…

Let $P_{abc}$ be a unital symmetric real tensor, meaning that its indices are symmetric and its unit conditions are $P_{1ab}=P_{a1b}=P_{ab1}=\delta_{ab}$. A positive tensor rank de…

Higher-rank tensor asymptotic conjecture. The fixed $m=1$ sector is the dominant order, and

Uniqueness conjecture. If these properties hold for all finite $m$, then $F(n)=Z_3(n)$. The claim concerns whether the full hierarchy of asymptotic expansions uniquely determines t…

In tensor models with tetrahedral interactions, chain-of-tadpoles graphs can produce arbitrarily high powers of $D$ and obstruct the large-$D$ limit. Klebanov–Tarnopolsky conjectur…

Consider a tensor model in a large $N'$ limit dominated by melonic interactions, whose continuum limit corresponds to the branched-polymer phase. An interacting fixed point with se…

The tensor-model renormalization-group analysis uses beta functions for the interaction couplings and considers a non-perturbative approximation including the full non-polynomial s…

Consider a broader class of non-random models with Hamiltonians $H_X$ that are strongly extensive. Extensivity equivalence conjecture. Theorem 4 should generalize to such models in…

In a conformal theory, let $h$ be a scaling dimension and let the associated operator have a vacuum expectation value. A complex scaling dimension lies on the line…

Tensor models may contain interactions and other structures that distinguish the tensor colors, while their continuum limits are described by universal scaling regimes. Color-indis…

Tensor models are combinatorial models whose theory spaces consist of interactions and couplings, and a continuum limit is obtained from an appropriate critical point or scaling re…

Consider the isocolored fixed point with tetrahedral interaction, whose fixed-point values and critical exponents are computed in the sixth-order truncation. Three-dimensional quan…

Consider the cyclic melonic fixed point of a tensor model, and choose the regulator parameter $r=1/2$, for which $[g_{4,1}^{2,1}]=-1$. Two-dimensional quantum-gravity universality…

In a tensor model, let multitrace interactions be operators such as $(T_{abc}T_{abc})^n$, which can be generated by renormalization and may have enhanced symmetry. Continuum-limit…

Let $p$ be the rank of the Coxeter group $B_p$, and let rank-$p$ tensor boundary models be the tensor sigma-models whose fundamental field has tensor degree $p$. Coxeter $B_p$ tens…

The proposed Coxeter higher-spin theories are associated with free boundary conformal fields carrying tensorial higher-spin currents. Coxeter higher-spin holography conjecture. The…

A tensor model has a low-energy spectrum organized by Kronecker coefficients, and the high-energy phase begins at levels of the form $n=N+n'+1$, with $n'=0,1,\dots$. A multi-matrix…

Let $r$ be the tensor rank, and restrict the rank-$r$ tensors to an irreducible subspace. Consider a complete $(r+1)$-valent interaction. Higher-rank extension conjecture. The cons…

A tensor model is built from a tensor with special permutation symmetries, such as complete symmetry with traces removed or antisymmetry, and one studies its perturbative expansion…