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We study superpotentials from worldsheet instantons in heterotic Calabi-Yau compactifications for vector bundles constructed from line bundle sums, monads and extensions. Within a certain class of manifolds and for certain second homology classes, we derive simple necessary conditions for a non-vanishing instanton superpotential. These show that non-vanishing instanton superpotentials are rare and require a specific pattern for the bundle construction. For the class of monad and extension bundles with this pattern, we derive a sufficient criterion for non-vanishing instanton superpotentials based on an affine Hilbert function. This criterion shows that a non-zero instanton superpotential is common within this class. The criterion can be checked using commutative algebra methods only and depends on the topological data defining the Calabi-Yau X and the vector bundle V.
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We investigate instantons on manifolds with Killing spinors and their cones. Examples of manifolds with Killing spinors include nearly Kaehler 6-manifolds, nearly parallel G_2-manifolds in dimension 7, Sasaki-Einstein manifolds, and 3-Sasakian manifolds. We construct a connection on the tangent bundle over these manifolds which solves the instanton equation, and also show that the instanton equation implies the Yang-Mills equation, despite the presence of torsion. We then construct instantons on the cones over these manifolds, and lift them to solutions of heterotic supergravity. Amongst our solutions are new instantons on even-dimensional Euclidean spaces, as well as the well-known BPST, quaternionic and octonionic instantons.
We would like to put the area law -- believed to by obeyed by entanglement entropies in the ground state of a local field theory -- to scrutiny in the presence of non-perturbative effects. We study instanton corrections to entanglement entropy in various models whose instanton effects are well understood, including $U(1)$ gauge theory in 2+1 dimensions and false vacuum decay in $phi^4$ theory, and we demonstrate that the area law is indeed obeyed in these models. We also perform numerical computations for toy wavefunctions mimicking the theta vacuum of the (1+1)-dimensional Schwinger model. Our results indicate that such superpositions exhibit no more violation of the area law than the logarithmic behavior of a single Fermi surface.
We construct the half-supersymmetric instanton solutions that are electric-magnetically dual to the recently discussed half-supersymmetric Q7-branes. We call these instantons `Q-instantons. Whereas the D-instanton is most conveniently described using the RR axion chi and the dilaton phi, the Q-instanton is most conveniently described using a different set of fields chi and T, where chi is an axionic scalar. The real part of the Q-instanton on-shell action is a function of T and the imaginary part is linear in chi. Discrete shifts of the axion chi correspond to PSL(2,Z) transformations that are of finite order. These are e.g. pure S-duality transformations relating weak and strongly coupled regimes. We argue that near each orbifold point of the quantum axion-dilaton moduli space PSL(2,Z)PSL(2,R)/SO(2) the higher order R^4 terms in the string effective action contain contributions from an infinite sum of single multiply-charged instantons with the Q-instantons corresponding to the orbifold points tau=i,rho where tau is the complex axion-dilaton field.
We discuss various aspects of multi-instanton configurations in generic multi-cut matrix models. Explicit formulae are presented in the two-cut case and, in particular, we obtain general formulae for multi-instanton amplitudes in the one-cut matrix model case as a degeneration of the two-cut case. These formulae show that the instanton gas is ultra-dilute, due to the repulsion among the matrix model eigenvalues. We exemplify and test our general results in the cubic matrix model, where multi-instanton amplitudes can be also computed with orthogonal polynomials. As an application, we derive general expressions for multi-instanton contributions in two-dimensional quantum gravity, verifying them by computing the instanton corrections to the string equation. The resulting amplitudes can be interpreted as regularized partition functions for multiple ZZ-branes, which take into full account their back-reaction on the target geometry. Finally, we also derive structural properties of the trans-series solution to the Painleve I equation.
We compute the prepotential for gauge theories descending from ${cal N}=4$ SYM via quiver projections and mass deformations. This accounts for gauge theories with product gauge groups and bifundamental matter. The case of massive orientifold gauge theories with gauge group SO/Sp is also described. In the case with no gravitational corrections the results are shown to be in agreement with Seiberg-Witten analysis and previous results in the literature.
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