20 problems

In the case where all fluxes vanish, a twisted background is a Calabi–Yau metric together with a covariantly constant pure spinor. The associated BCOV (or Kodaira–Spencer) theory i…

Let the Courant contact model be the local $L_\infty$-algebra construction associated to the relevant Courant algebroid, and let the cubic model be the constrained-field model intr…

Let $M$ be a Kähler manifold, let $F_g^{\mathrm{BCOV}}(M)$ be the genus-$g$ BCOV quantity defined by summing the Cauchy principal value graph integrals over connected trivalent gra…

Let $X$ be a Calabi–Yau manifold. The BCOV torsion is the $C^{\infty}$ quantity obtained from the BCOV formula and the period-domain metric; in the K3 setup it is defined by … Let…

Let $M_{2n}:=\langle 2n\rangle$ and let $\check{M}_{2n}=\langle-2n\rangle\oplus U\oplus E_{8}(-1)^{\oplus2}$. Consider families of $\check{M}_{2n}$-polarized K3 surfaces whose isom…

The construction uses the previously established solution of the commutativity equation obtained from linear algebra, together with the description of the moduli space…

Let $G_{g,n}^{\mathrm{BCOV}}$ be the set of genus-$g$, $n$-leg stable graphs with the BCOV edge types and solid or dotted legs. Define $f_{g,n}^{\mathrm{BCOV}}$ as the sum over the…

Let $G_g^{\mathrm{BCOV}}$ be the set of genus-$g$ stable graphs for the quintic threefold, with solid, half-dotted-half-solid, and dotted edges. Place the propagators…

Let $H_{\mathbf B}:=\operatorname{span}\{\bar\psi,\tilde\phi\}$ be the state space, and let $G_g$ be the set of genus-$g$ stable graphs. For each $\Gamma\in G_g$, use the BCOV edge…

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 $\mathbb{C}^2=\{z_1=z_2=z_3=0\}\subset\mathbb{C}^5$ and let $r=\sqrt{|z_1|^2+|z_2|^2+|z_3|^2}$ be the radius normal to $\mathbb{C}^2$. Let…

Let $X$ be a Calabi–Yau $5$-fold, with type IIB supergravity placed in the Calabi–Yau background and its bosonic ghost field set to the covariantly constant Killing spinor $(Q,0)$.…

Let $J$ be the classical BCOV interaction defined using the coefficients obtained from integrals over $\overline{\mathcal{M}}_{0,n}$, and let $I_{0,0,*}$ be the purely closed-strin…

On $\mathbb{C}^3$, let $I$ be the previously defined classical BCOV interaction on the fields $\PV^{*,*}(\mathbb{C}^3)[[t]][2]$, and let $\widehat I$ be the classical interaction o…

Consider a single $M5$ brane on $\mathbb{R}^7\times(\mathbb{R}^4/\mathbb{Z}_N)$, located at the singular point of the $A_N$ singularity and spanning six of the seven directions in…

In three complex dimensions, let $(1,0)$ BCOV theory denote the variant of BCOV theory whose fields describe the corresponding holomorphic theory, and let the free $(1,0)$ tensor m…

Consider type IIA string theory on $\mathbb{R}^{10}$ with one $NS5$ brane on $\mathbb{R}^6\subset\mathbb{R}^{10}$, where $x_6,\ldots,x_9=0$, together with $k$ semi-infinite $D6$ br…

BCOV theory is a closed-string field theory for the topological $B$-model, formulated here on complex affine space. Type IIB supergravity is the ten-dimensional supergravity theory…

Let $\check{X}_\tau$ be the mirror elliptic curve, let $\mathcal E_{\check{X}_\tau}$ be the space of BCOV fields, and write the quantization as … For each genus $g>0$, constructing…

Let $Z_{g;n}$ be the quasi-modular-form Gromov–Witten potentials satisfying the recursion relation … Let ${\mathcal F}^{(g)}$ denote the genus-$g$ BCOV free energy, and let the BCO…