124 problems

Let ${\mathcal W}^k({\mathfrak s}{\mathfrak l}_{n+1|n})$ be the principal ${\mathcal W}$-algebra, a conformal extension of the ${\mathcal N}=2$ superconformal algebra with central…

Let $S_{2^n}$ be the symmetric group on $2^n$ elements, and let the magic number for a partition into supermultiplets be the common value of the intra-tet and inter-tet correlators…

Let $\mathcal{T}$ be the supertranslation algebra associated to a super-Minkowski spacetime, and consider its third Lie algebra cohomology. A 3-cocycle is Lorentz-invariant if it i…

Let the Hamiltonians in equation … for $l\geq 4$ are conserved under the bosonic flows $\partial/\partial t_k$. The conservation of these higher Hamiltonians was obtained only conj…

Mother Hamiltonian polynomial conjecture. The Mother Hamiltonian is the polynomial

Let the systems under consideration be parametrized by $\beta=-1/\alpha$, where $\alpha$ is the parameter used in their original enumeration, and let a higher $\bar{s}$-symmetry me…

Uniqueness conjecture. The system has only one conservation law defining $w$ by

Let the isospectral flows of the $N=2$ supersymmetric unconstrained matrix GNLS hierarchy be represented using the local operator ${\cal L}_z$, with dressing matrix $\Theta$ and th…

Constraint-preservation conjecture. The isospectral flows also preserve the second constraint

N=(2|2) superspace formulation conjecture. These equations are consistent with the chirality constraints

Let $\mathfrak{g}$ be a simple finite-dimensional Lie algebra over $\mathbb{C}$, let $g$ be its dual Coxeter number, and let $A=\wedge(\mathfrak{g}\oplus\mathfrak{g})/I$, where $I$…

The Hitchin spin chains and Whitham theories are considered as renormalization-group equations, with Hitchin times identified with the spatial RG scale $t\sim \log(r)$. The fast To…

Strong-coupling zero-energy eigenstate conjecture. At strong coupling, there is one and only one zero-energy eigenstate for each even value of $F$ and for each $B=F+1$ or $B=F-1$.

Let an off-shell representation of supersymmetry in any dimension be given, and let a Clifford supermodule be equipped with a filtration or, possibly, a bifiltration. Suppose moreo…

Superfield realization conjecture. For every $N$ and every topology of engineerable Adinkras, there exists a corresponding set of superderivative constraints such that the set of s…

Consider the superunitary Calogero–Moser–Sutherland model with coupling parameters $(\beta_1,\beta_2)$, whose wavefunction admits an asymptotic expansion analogous to the Hankel ex…

Let $N$ denote the number of D0-branes, and let the low-energy dynamics of D0-branes be described by dimensionally reduced supersymmetric Yang–Mills quantum mechanics. Large-$N$ M-…

Supersymmetric explanation conjecture. The observed behavior of the torsion may be understandable using some form of supersymmetry.

Let $p$ be the order of parafermionic operators in the formalism under consideration. A tuple relation conjecture states that parafermionic operators of order $p$ are characterized…

Let the elliptic case be the setting in which the type A $\mathcal{N}$-fold supercharges and the corresponding critical generalized Bender–Dunne polynomials are defined. For odd…

Critical-fraction conjecture. The critical fraction is

Let $Z_{N_f,-N_b}(\\{x_f\\}|\\{y_b\\})$ be the partition function with $N_f$ fermionic masses $\\{x_f\\}$ and $N_b$ bosonic masses $\\{y_b\\}$. For fermionic mass $x_i$ and bosonic…

Let Z_{N_f,-N_b}(\\{x_f\}|\\{y_b\\}) be the partition function with integer numbers $N_f$ of fermionic flavors and $N_b$ of bosonic flavors. For masses $x_i$ and $x_j$, let $m$ a…

Let $Z_{N_f,-N_b}$ denote the QCD partition function with $N_f$ fermionic flavors and $N_b$ bosonic flavors, and let the fermionic and bosonic partition functions form their respec…

Let an $N=1$ superconformal field theory have a maximal supersymmetry subalgebra, meaning the largest possible subalgebra in the relevant series indexed by $N$. Uniqueness conjectu…