30 problems

Seiberg's deformation conjecture. Any quantum field theories with the same symmetry $G$ and the same anomaly ${\mathbf{Z}}_{d+1}$ can be deformed to each other by adding degrees of…

Let $\mathbf Q(\mathrm{pt})$ be the spectrum of quantum cellular automata governing lattice anomalies, and let $\mathbf{4Vect}^{\times}$ be the spectrum of invertible objects and m…

Full twisted eta-invariant conjecture. The full set of twisted $\eta$-invariants of the Dirac operator modulo $1$, collected into this function on the set of orbi-bundles…

Let $S^5/{\mathbb Z}_N$ be the boundary of the orbifold construction, and let $\beta$, $\gamma$, $\widetilde{\delta}_k$, and $\widetilde{\epsilon}_k$ denote the anomaly coefficient…

Let $\mathscr{S}\mathscr{W}$ be the generalized cohomology theory associated to the categorical obstruction, and let $I_\mathbb{Z}M\mathrm{Spin}$ denote the theory classifying 't H…

Let $k$ be as in the paper, let $x_1$ and $y$ specify the twist, and let $\alpha_{\mathrm{DW}}$ and $\alpha_{\mathrm{GW}}$ be the Dijkgraaf–Witten and Gu–Wen classes in…

Let $\Sigma^2\xrightarrow{\iota}X^6\xrightarrow{\pi}X^4$ be a fibration with monodromy representation $\rho:\pi_1(X^4)\to\operatorname{Sp}(2g,\mathbb{Z})$. Assume twisted Stiefel–W…

A lattice system is equipped with a symmetry and an associated anomaly, and its possible quantum phases of matter are those that can emerge in the lattice system. Emergibility hypo…

Let $\mathcal{M}$ be a bulk internal manifold, let $\mathfrak{g}(\mathcal{M})$ be its generalized Kac–Moody current algebra, and let its cohomological 2-cocycles be computed from b…

Pontryagin-dual anomaly classification conjecture. The classification is conjectured to be

Anomaly classification conjecture. The anomaly is classified by

Anomaly obstruction conjecture. A nonzero 2d anomaly index should obstruct the existence of $G$-invariant invertible 2d states.

Let a $d$-dimensional superconformal field theory, with $d$ even, be placed on a space with topology … Let $I_{d+2}$ denote its anomaly polynomial, and let the integral below be th…

Trivial-anomaly conjecture. For the orbifold of the $d=128$ Barnes–Wall lattice VOA by $E(7)$, $\omega$ is trivial. A trivial anomaly is necessary for constructing a holomorphic ex…

Let $\rho(x,y)$ be the conformal factor of a two-dimensional metric … with $\triangle=\partial_x^2+\partial_y^2$, satisfying the Liouville equation … Liouville theory is a classica…

Non-perturbative Noether theorem. If $\cT$ has $X$-symmetry, then there exists a factorizing line bundle $\mc{L}$ on the prefactorization space $X_c$ and a map of prefactorization…

SPT-cobordism conjecture. The particular loop spectrum that appears is the Anderson dual of the Thom spectrum.

Let $G$ be a non-abelian gauge group, let $\mathcal{A}$ be the space of gauge fields, and let $Psi(A)$ denote a section of the fermionic Fock-space bundle over $\mathcal{A}$. Let…

Let the bosonic $\mathds{CP}^{n-1}$ model be a sigma model whose integrability is obstructed by known anomalies, and consider models with vanishing chiral anomalies. Bykov's anomal…

Branch–frame independence conjecture. Independence of the branch structure of the spacetime complex for lattice models implies independence of the frame structure of the spacetime…

Let $\mathcal{C}$ be a fermionic topological order with anyon quantum dimensions $d_a$, total quantum dimension $\mathcal{D}$, U(1) charges $Q_a$, and modular data $S_{a,b}$. Let…

Let $X$ be a parameter space, and let $\nu\oplus k\in (I_\mathbb{Z}\Omega^\text{spin})^4(X)$ be the anomaly of a 2d spin $\mathcal{N}=(0,1)$ supersymmetric theory. Twisted Segal–St…

Let $G$ be a symmetry group, let $\nu$ be the gravitational anomaly, and let $k$ be the 't Hooft anomaly, with $\nu\oplus k\in (I_\mathbb{Z}\Omega^\text{spin})^4(BG)$. For a simple…

Anomaly-freeness conjecture for 2d fermionic topological orders. All 2d fermionic topological orders are anomaly-free.

Let $Z(\beta)$ be a generic finite-temperature path integral defined using a thermal circle $S^1_{\beta}$, and let $N_0$ denote the number of zero modes along that circle. Write…