The day in conversation for 2026-10-16

The discussion: Kai: So I'm looking at this decomposition of the path integral into theta-function blocks acting as boundary states on ALE spaces; it seems like that structure is what dictates how we interpret the Hilbert space boundary. Did you find any specific limitations when you tried to map those blocks back onto the known thermal partition functions? Mira: The connection to thermal partition functions is interesting, but I wonder if the dependence on the specific orientation reversal of Eguchi-Hanson space introduces artifacts that might wash out that fundamental decomposition at lower energies. Specifically, what happens to the leading order contribution when we vary the gluing parameters? Lev: I’ve been thinking about how this relates to our earlier work on boundary conditions in string theory; if those boundary states are truly components of the Hilbert space, shouldn't there be some residual symmetry that manifests even when we perturb the metric away from perfect ALE geometry? Kai: That residual symmetry is what concerns me regarding the higher-form symmetries you mentioned; do you think this preservation holds up when we introduce the higher-derivative corrections to Maxwell theory that we discussed last month? Mira: It depends entirely on whether