11 problems

Let a 7-brane set be equivalent when it describes the same physics as another set, and consider the corresponding brane webs in the three-leg case. For a junction with charges…

S-duality conjecture. S-duality relates supergroup superquiver gauge theories by rotating their brane-web diagrams by $90$ degrees. In particular, supergroup ordinary gauge theory…

Signature-independence conjecture. The partition function $Z$ does not depend on the signatures of the NS5-branes surrounding the stack of D4-branes (or D5-branes), nor on the orde…

DeWolfe–Zwiebach conjecture. Inequivalent sets of 7-branes are characterised by the total monodromy $M_{\operatorname{tot}}$ and the asymptotic charge invariant $\ell$.

Termination conjecture. The expansion of $\widetilde{Z}_\nu(P,Q)$ by $Q$ terminates at the order $Q^{|\nu|}$. This finite-order behavior has been observed for various choices of…

Termination conjecture. The expansion by $Q$ of $Z_\nu(P,Q)$ terminates at the order $Q^{|\nu|}$ for any $\nu$. The observed finite termination removes the apparent divergences in…

Let two web diagrams be related by a flip transition, and let $\rho_i$ be the parameter of the segment at which the flip is performed. Vanishing-parameter flip conjecture. If…

A web diagram associates a vertex operator algebra to its configuration of five-branes and D3-branes. A flip transformation is the transition obtained by sliding five-branes in the…

Weighted path conjecture. The parameter $\bar{v}_1$ is given by

Let $A_1$ be a vertex of type 1 in the $(N,M)$ web, and let $\mathcal{P}(A_1,\tfrac{M}{k})$ be the path with $\tfrac{M}{k}$ vertical lines and $\tfrac{M}{k}-1$ horizontal lines lea…

Let $N$, $M$, and $k$ be positive parameters for which the $(N,M)$ and $(\tfrac{MN}{k},k)$ webs are defined, and let a generic labelling assign parameters to the lines and vertices…