19 problems

Witten string field theory realization conjecture. The proposed $SL(K+3,\mathbb{C})$ symmetry can be obtained from Witten SFT.

Let $\mathcal{N}_{mn}^{rs}$ be the Neumann coefficients introduced for the three-string vertex in the pp-wave background, and let $\lambda$ be the deformation parameter in the full…

Let the Neumann coefficients be the coefficients defining the three-string vertex of light-cone string field theory in a maximally supersymmetric pp-wave background, expanded in th…

The authors study Witten's open string field theory (SFT), whose Neumann coefficients for surface states satisfy the Hirota equations of the dispersionless KP hierarchy, while thos…

Let $\mathcal{P}_{\mathcal{C},\lambda,h,s}=\{\mathcal{C},\lambda,h,s\}$ be a holography package consisting of a smooth cyclic $A_\infty$-category $\mathcal{C}$, an object…

Backreacted Calabi–Yau category conjecture. Given a holography package $\mathcal{P}_{\mathcal{C},\lambda,h,s}$ as above, there is a family of Calabi–Yau categories…

The construction uses L-functionals to represent one-string states; these functionals describe states in all pictures, and more, in the $(\beta,\gamma)$-model. L-functional conject…

In open-closed BCOV theory, let the dynamically generated classical interaction be the classical BCOV interaction produced by the obstruction-theoretic construction starting from f…

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…

Let ${\cal T}^N_{\vartheta}$ be the theory with parameter $N$, and let $\mathfrak{I}^{+-+}=\mathfrak{I}^{+-}\boxtimes\mathfrak{I}^{-+}$ be the rotation Interface corresponding to a…

Let ${\cal T}^N_{\vartheta}$ be the theory with parameter $N$, and let the elementary Branes be the Branes constructed from the relevant Lefschetz thimbles and the Branes…

Modular-operad isomorphism conjecture. There is a modular operad isomorphism

Let $\mathcal{QO}$ be the modular operad of surfaces of arbitrary genus with arbitrary numbers of boundary components and open ends, and let $\mathcal{A}\mathit{ss}$ be the cyclic…

For a given type II world sheet $\mathbf{\Sigma}$, consider metrics satisfying the condition that every non-trivial supercircle has length at least $2\pi$. Minimal area uniqueness…

Open–closed correspondence conjecture. This $L_\infty$-morphism should be a quasi-isomorphism in any string field theory realization of the OCHA.

Exact tension-ratio conjecture. The exact result is extremely close to the theoretical value $\sqrt{2}\pi$, with the fully non-local action evaluated using a careful numerical proc…