19 problems

Let the diagonal unitary minimal model $(D_6,A_{10})$ be deformed by the relevant operator $\phi_{\frac9{11}}$, with no other relevant operators turned on, and suppose the flow is…

In closed string theory, Ricci flow arises as a first-order world-sheet renormalization-group flow. Off-shell processes in string field theory, such as tachyon condensation, are co…

Consider the massless flow from the coset model $su(2)_{k+1}\otimes su(2)_k/su(2)_{2k+1}$ to the minimal model $M_{k+2}$. Let $\sigma_1\Phi_{1,2}$ denote the ultraviolet operator w…

Let $k$ be the coset parameter, and consider the flow from $\mathcal{M}(k+3,k+2)$ in the ultraviolet to $\mathcal{M}(3,k+2)$ in the infrared. The ultraviolet operator is…

A unitary modular fusion category is a unitary modular fusion category with central charge $\frac{110}{29}\mod 8$. For a modular fusion category $\mathcal C$ of rank $r$, define it…

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…

Massless RG-flow conjecture. This positive solution corresponds to the existing massless renormalization-group flow. Further studies using other methods are needed to confirm this…

Let two four-dimensional ${\cal N}=2$ SCFTs be related by an RG flow, and denote their VOA stress-tensor nilpotency indices by $\mathfrak{n}_{\rm UV}$ and $\mathfrak{n}_{\rm IR}$,…

An RG flow to a rational conformal field theory (RCFT) is called a rational RG flow when its endpoint is an RCFT; suppose that it admits an RG domain wall or interface, and conside…

Gaiotto's conjecture. The boundary conformal field theory $\operatorname{BCFT}(\mathbf{F}_{\text{UV}\times \text{IR}})$ produces the information of the massless renormalization-gro…

Consider an RG flow from a UV conformal field theory to an IR theory in which some interpolating fields corresponding to UV primaries have massive correlation functions, with expon…

Let $\mathcal S_\text{UV}$ be the surviving pre-modular fusion category and $\mathcal S_\text{IR}$ be its image pre-modular fusion subcategory in the infrared diagonal rational con…

Double affine Grassmannian conjecture. These hierarchies of mixed Higgs-tensor branch RG flows can be understood as semi-infinite periodic Hasse diagrams of the double affine Grass…

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 $\mathcal{D}_p$ be a conformal defect of odd dimension $p$, and let $s(\mathcal{D}_p)$ denote its defect entropy, defined as the finite, scheme-independent term in the defect f…

A 5d superconformal field theory (SCFT) is a five-dimensional $mathcal N=1$ supersymmetric conformal field theory, and a 5d Kaluza–Klein theory is an $S^1$ reduction of a six-dimen…

Let $(A_1,A_3)$ and $(A_1,D_3)$ denote the two Argyres-Douglas theories described by the distinct four-dimensional ${\mathcal N}=1$ ultraviolet Lagrangian theories in the source. I…

Let the initial closed-string model carry non-geometric $R$-flux, and let an asymmetric version of the WZW model denote a conformal field theory with asymmetric left- and right-mov…

Let a two-dimensional conformal field theory have central charge $c$. Consider gauge theories consisting of free bosons coupled to $SU(2)$ WZW models, and let a flow mean the renor…