14 problems

A two-dimensional $\mathcal{N}=(0,1)$ theory is a quantum field theory with the indicated supersymmetry, and TMFs are the topological modular forms associated with such theories. T…

Let $X$ be a topological space, let $\nu\in\mathbb{Z}$ be an anomaly coefficient, and consider families parametrized by $X$ of two-dimensional $\mathcal{N}=(0,1)$ supersymmetric qu…

Bremsstrahlung-function conjecture. The Bremsstrahlung function is given by

No-exotics conjecture. The Hodge diamond of $\mathcal{M}_\gamma^Q$ is diagonal for every physical quiver describing a four-dimensional supersymmetric quantum field theory, so that

Let a non-rank-zero 3d $\mathcal{N}=4$ SQFT be a three-dimensional supersymmetric quantum field theory with nonzero rank, and let its boundary VOA be obtained after a topological t…

Let $M_3$ be a weakly negative plumbed three-manifold with defects labelled by highest weights $\nu_v\vec\omega$ at nodes $v\in V_W$, and let $\hat Z_b(M_3;W_{\{\nu_v\}};\tau)$ be…

Generalization conjecture. The construction generalizes whenever all hidden symmetries of the ultraviolet Schur ring are related to symmetries of the full four-dimensional theory t…

Let $\mathcal{T}$ be a four-dimensional $\mathcal{N}=2$ field theory with Seiberg–Witten integrable system $(M,\Omega_I)$ and holomorphic Lagrangian section $S$. Let…

Let an SQFT be a $(1+1)$-dimensional quantum field theory with $\mathcal N=(0,1)$ supersymmetry, and suppose it has an associated deformation-invariant class in TMF. TMF classifica…

Let an SQFT be a $(1+1)$-dimensional quantum field theory with $\mathcal N=(0,1)$ supersymmetry, and let TMF denote the theory of Topological Modular Forms. TMF-valued invariant co…

A marginality crossing is a situation in which an operator changes between marginal and non-marginal status along the relevant deformation or renormalization-group flow under discu…

Let $\widetilde{\mathbb{C}/\mathbb{Z}}_{2}$ denote the squashed version of the $\mathbb{Z}_2$ quotient of the complex plane, and let the $SL(2,\mathbb{R})_{k}/U(1)$ coset theory be…

Generalized commutative-diagram conjecture. The commutative diagram relating line-defect Schur indices to vacuum expectation values at the $U(1)_r$-invariant vacua exists more gene…

Absence of higher-dimensional $SU(2)_R$ representations. Only representations of the form $(\boldsymbol{1},\boldsymbol{s})$ should appear in…