Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
arxiv(2024)
摘要
Geometric engineering is a collection of tools developed to establish
dictionaries between local singularities in string theory and (supersymmetric)
quantum fields. Extended operators and defects, as well as their higher quantum
numbers captured by topological symmetries, can be encoded within geometric
engineering dictionaries. In this paper we revisit and clarify aspects of these
techniques, with special emphasis on 't Hooft anomalies, interpreted from the
SymTFT perspective as obstructions to the existence of Neumann boundary
conditions. These obstructions to gauging higher symmetries are captured via
higher link correlators for the SymTFT on spheres. In this work, we give the
geometric engineering counterpart of this construction in terms of higher links
of topological membranes. We provide a consistency check in the context of 5D
SCFTs with anomalous 1-form symmetries, where we give two independent
derivations of the anomaly in terms of higher links, one purely field
theoretical and the other purely geometrical. Along the way, we also recover
the construction of non-invertible duality defects in 4D 𝒩=4 SYM
from a geometric engineering perspective.
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