Duality anomalies in linearized gravity

Classical linearized gravity admits a dual formulation in terms of a higher-rank tensor field. However, proposing a prescription for the instanton sectors of linearized gravity and its dual, we show that they may be . The duality anomaly is obtained by resolving the dual graviton theories into vector-valued <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>p</a:mi></a:math>-form electrodynamics and is controlled by three topological invariants: the Reidemeister torsion, Ray-Singer torsion, and twisted Euler characteristic. Under the proposed instanton prescription, the duality anomaly vanishes for an odd number of spacetime dimensions as a consequence of the celebrated Cheeger-Müller theorem. In the presence of a gravitational <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>θ</c:mi></c:math>-term, the partition function is a modular form in direct analogy to Abelian S-duality for Maxwell theory.