String universality in six dimensions. (English) Zbl 1259.81062

Summary: In six dimensions, cancellation of gauge, gravitational, and mixed anomalies strongly constrains the set of quantum field theories, which can be coupled consistently to gravity. We show that for some classes of six-dimensional (6D) supersymmetric gauge theories coupled to gravity, the anomaly cancellation conditions are equivalent to tadpole cancellation and other constraints on the matter content of heterotic/type I compactifications on K3. In these cases, all consistent 6D supergravity theories have a realization in string theory. We find one example that may arise from a novel string compactification, and we identify a new infinite family of models satisfying anomaly factorization. We find, however, that this infinite family of models, as well as other infinite families of models previously identified by Schwarz are pathological. We suggest that it may be feasible to demonstrate that there is a string theoretic realization of all consistent 6D supergravity theories which have Lagrangian descriptions with arbitrary gauge and matter content. We attempt to frame this hypothesis of string universality as a concrete conjecture.


81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83E15 Kaluza-Klein and other higher-dimensional theories
81T50 Anomalies in quantum field theory
81V17 Gravitational interaction in quantum theory
81T20 Quantum field theory on curved space or space-time backgrounds
83E50 Supergravity
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