29 problems

Higgs branch conjecture. The Higgs branch, viewed as a holomorphic symplectic variety, is canonically isomorphic to the associated variety of the corresponding VOA:

Let $\mathcal{T}$ be a four-dimensional $\mathcal{N}=2$ superconformal field theory, let $\mathbb{V}(\mathcal{T})$ be its associated vertex operator algebra, and let a surface defe…

Fixed-order MLDE conjecture. For any given 4d ${\cal N}=2$ superconformal field theory, ${\cal I}_k(q)$ solves a modular linear differential equation of fixed order and Wronskian i…

Generalized Schur limit matching conjecture. The displayed relations are necessary for the two partition functions to be related in this way. The claim is attributed in the source…

Modified KS operator conjecture. The Macdonald index of the class of four-dimensional ${\cal N}=2$ superconformal field theories for which the modified KS operator is defined is

Consider two class $\mathcal{S}$ theories $T[\mathfrak{g}, C^{(1)}, D^{(1)}]$ and $T[\mathfrak{g}, C^{(2)}, D^{(2)}]$ on stable Riemann surfaces $C^{(1)}$ and $C^{(2)}$, with full…

The $HT$ twist of a three-dimensional $\mathcal{N}=2$ theory equipped with an $R$-symmetry is a cohomological twist on a three-dimensional theory with a holomorphic direction, and…

Unbroken U(1) gauge-group conjecture. At a generic point of the moduli space of chiral multiplets, the $\mathrm{U}(1)^g$ gauge group is unbroken.

Unbroken diagonal U(1) conjecture. The diagonal $\mathrm{U}(1)$ gauge group is unbroken in the infrared for a genus-one theory.

Elliptic-genus character conjecture. The $(0,2)$ elliptic genus can be expressed as a linear combination of characters of the corresponding chiral algebra.

Twisted holography principle. These two algebras should be Koszul dual:

Let $\mathcal{I}_{\mathcal{N}=4}$ be the Schur index, let $\mathcal{I}_{bc\beta\gamma}$ be the second non-logarithmic solution, and let $STS\,\mathcal{I}_{\mathcal{N}=4}$ denote th…

Consider a four-dimensional $\mathcal{N}=2$ supersymmetric theory with Schur index … Here the trace is over the supersymmetric states contributing to the Schur index, $F$ is fermio…

Galois-conjugacy conjecture. $\textrm{TFT}_\pm[{\cal T}_{\rm rank\;0}]$ is a Galois conjugate of $\textrm{RW}_\pm[{\cal T}_{\rm rank\;0}]$.

For a four-dimensional theory with associated vertex operator algebra $\mathcal{V}$, suppose a free field construction equips $\mathcal{V}$ with a natural filtration, and let the u…

A hyper-Kähler with torsion (HKT) metric is a Riemannian metric with the geometric structure described in the paper. The harmonic action with the constraints … produces an HKT geom…

Honda's conjecture. CSS with a bosonic (fermionic) free parameter give poles (zeroes) of the Borel transformation of the perturbative series, with locations uniquely determined by…

Let $chi[\mathcal{T}_X]$ be the chiral algebra associated with the four-dimensional theory $cmathcal{T}_X$. Let $T$ be a stress tensor, let $J_{su(2)}^A$ and $J_{su(3)}^I$ be affin…

Let $\mathcal{I}(p,q,y)$ be a superconformal index and suppose that the corresponding partition function can be written in the form of Eq., with the transformed index and exponenti…

Let $Y_7$ be a Sasaki–Einstein space, and consider $N$ coincident M2-branes placed at the tip of the Calabi–Yau cone over $Y_7$. M-theory holographic duality conjecture. The result…

The Coulomb branch of a four-dimensional $\mathcal{N}=2$ superconformal field theory is parameterized by expectation values of chiral primary operators ${\cal E}_{r,(0,0)}$, where…

Let $\mathfrak{U}$ be a half-plane web associated to data $({\cal T}^{(\mu)},Z_\mu,\underline{R},\underline{\beta})$, where ${\cal T}^{(\mu)}$ are the theories, $Z_\mu$ are their c…

Let the theories ${\cal T}^{(\mu)}$ and Interfaces $\mathfrak{I}^{(\mu,\nu)}$ be as defined in the section, and let $\underline{\rho}(\mathfrak{W})[\underline r_a]$ denote the ampl…

Let $\mathfrak{W}$ be a web of interfaces, let $\underline{R}^{\rm intfc}$ be the direct sum of the vertex complexes over all fans of theories, and let…

Let $\mathfrak{W}$ be a web whose vertices are cyclic junctions of Interfaces between theories, and let $\underline{R}_{\mu_1,\dots,\mu_n}$ be the chain complex obtained by taking…