Tadpoles and commutative spectral triples

Bruno Iochum (1, 2) , Cyril Levy (1, 2)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332

Using the Chamseddine--Connes approach of the noncommutative action on spectral triples, we show that there are no tadpoles of any order for compact spin manifolds without boundary, and also consider a case of a chiral boundary condition. Using pseudodifferential techniques, we track zero terms in spectral actions.

Mots clés: Spectral triples; pseudodifferential calculus; noncommutative integral; Wodzicki residue

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Bruno Iochum, Cyril Levy. Tadpoles and commutative spectral triples. Journal of Noncommutative Geometry, 2011, 5 (3), pp.299-329. ⟨10.4171/JNCG/77⟩. ⟨hal-00372626v2⟩