Compact expressions in terms of the Q-functions of the Quantum Spectral Curve are given for 3-cusped fundamental Wilson loops in the ladders limit of N = 4 Super Yang-Mills with additional scalars inserted at a cusp between uncoupled arcs. This gives some further credence to the already natural and evidenced view that the Quantum Spectral Curve in fact pertains to a wide class of observables beyond the spectrum, as well as providing additional nonperturbative ladders limit results.
The attractor equations for an arbitrary one-parameter family of Calabi-Yau manifolds are studied in the large complex structure region. These equations are solved iteratively, generating what we term an N-expansion, which is a power series in the Gromov-Witten invariants of the manifold. The coefficients of this series are associated with integer partitions. In important cases we are able to find closed-form expressions for the general term of this expansion. To our knowledge, these are the first generic solutions to attractor equations that incorporate instanton contributions. In particular, we find a simple closed-form formula for the entropy associated to rank two attractor points, including those recently discovered. The applications of our solutions are briefly discussed. Most importantly, we are able to give an expression for the Wald entropy of black holes that includes all genus 0 instanton corrections.
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