35 problems

Let $W$ be a D$p$-brane world-volume embedded in space-time $X$ by $\iota:W\hookrightarrow X$, and let $E\rightarrow W$ be the rank-$q$ Chan–Paton bundle. If $W$ is spin$^c$ with a…

Let $G$ act on a space covered by $G$-stable patches $U_{\alpha}$, and let $\gamma^g_{\alpha}:U_{\alpha}\to U(N)$ describe the action of $g\in G$ on a D-brane $U(N)$ gauge field. L…

In Type IIB superstring theory, consider a brane-antibrane pair with an unstable tachyonic mode. Tachyon condensation conjecture. Giving the tachyon field a suitable expectation va…

Let a non-associative deformation product on the world-volume of a curved D-brane be cyclic with respect to the Born–Infeld measure through second order in the derivative expansion…

In string theory, let the target space be a space on which D-branes can occur, and let their charges be the associated conserved charge group. K-theory classification conjecture. D…

Let $\Gamma$ and $\Gamma'$ be lattices with quadratic forms $q$ and $q'$, let $g:(\Gamma\oplus\Gamma^*,q)\to(\Gamma'\oplus{\Gamma'}^*,q')$ be a lattice isomorphism, and let…

Let $X$ be a torus with a geometric $N=2$ structure $(I,J)$, and let $C^{\mathrm{B}}_{I,J}(X)$ denote the category of B-branes and $\mathcal{D}\operatorname{Coh}_{I,J}(X)$ the deri…

Let $S$ and $T$ be smooth complex submanifolds of $X$ with intersection $S\cap T$, and let ${\cal E}$ and ${\cal F}$ be twisted holomorphic bundles on $S$ and $T$. The paper constr…

Let $\omega\in H^2(X,\mathcal{O}_X^*)$ define the $B$ field, let $i:S\hookrightarrow X$ and $j:T\hookrightarrow X$ be smooth complex submanifolds with $T\subseteq S$, and let…

Let $S$ be a smooth complex submanifold of $X$, let $i:S\hookrightarrow X$, and let ${\cal E}$ and ${\cal F}$ be twisted holomorphic bundles on $S$. The spectral sequence relating…

Let $\omega\in H^2(X,\mathcal{O}_X^*)$ define a $B$ field, let $i:S\hookrightarrow X$ be a smooth complex submanifold, and let ${\cal E}$ and ${\cal F}$ be $i^*\omega$-twisted holo…

The relevant objects are the bifundamental matter content of supersymmetric Yang–Mills theories arising from type IIB D-branes on orbifold singularities, and the modular invariant…

Let $X$ be a Calabi–Yau threefold containing a subspace $E$, let $i:E\hookrightarrow X$ be the inclusion, and let $q:E\to Z$ be the map contracting $E$ to a lower-dimensional subsp…

Let $X$ be a Calabi–Yau threefold, and let $Delta$ be the discriminant locus in the moduli space of conformal field theories. Its primary component is the component corresponding t…

Let $G$ be a finite group acting on $\mathbb{C}^d$, let $X$ be a geometric phase of a resolution of $\mathbb{C}^d/G$, and let $\rho_i$ be a one-dimensional representation of $G$. D…

Let $X$ be a Calabi–Yau threefold, let $\Delta_0$ be the primary component of the discriminant, and let a 0-brane be an object $P\in\mathbf{D}(X)$ with Chern character equal to the…

Shrinking-cylinder endpoint conjecture. The endpoint of this shrinking process is simply the $F_L$ $\mathrm{R}7$-brane itself.

Let $X$ be a spacetime and let ${\mathcal D}$ be a continuous-trace $C^{\ast}$-algebra over $X$ with ${\mathcal A}={\mathbb C}$ and twisting class…

Let ${\mathcal D}$ be a $C^{\ast}$-algebra describing a noncommutative spacetime, with the associated Topological T-duality construction and purely infinite fibers. D-brane charge…

Let a Type II string-theory spacetime background with Ramond–Ramond flux be modeled by a locally trivial $C^{\ast}$-bundle whose fiber is a stabilized strongly self-absorbing…

Let Poisson–Lie duality be described by the QP-manifold and symplectic-reduction framework, and let spectators be additional target-space fields not included in the dualised Poisso…

Let $\rho$ be a solution of the saddle equations, let ${\cal B}_\rho$ be the B-model D-brane associated with that saddle, and consider the large-$N$ expansion of correlators around…

Consider a saddle of the large-$N$ equations for a correlation function of determinant or sub-determinant operators, together with its associated spectral curve and the natural Cha…

Let $\rho$ be a solution of the saddle equations for a correlation function of sub-determinants, and let ${\cal S}_\rho$ be the associated spectral curve in $SL(2,\mathbb{C})$, obt…

Geometric support conjecture. The only additional attractor invariants correspond to D2-branes wrapped on rational curves in this extended singularity.