Communications in Mathematical Physics

, Volume 174, Issue 1, pp 137–148 | Cite as

The geometry of the quantum correction for topological σ-models

  • Davide Franco
  • Cesare Reina


The ring (Frobenius algebra) of local observables for topological σ-models on ℙ1 with values in the grassmannianG(s, n) is known to be “the same as” the quotient of the homology ring of the target space by the (inhomogeneous) ideal generated by the so-called quantum correction. While the need for a quantum correction comes from algebraic motivations in field theory, the aim of this paper is to understand its geometric meaning. The simple examples of ℙ1 → ℙn models tell us that the quantum correction comes by restriction on the boundary of the moduli spaces which allows to compute intersections on moduli spaces of lower degrees. We will check this point of view for the case of ℙ1G(s,n) models, yielding a proof of the algebraic result from physics in terms of the geometry of the σ-model itself.


Neural Network Statistical Physic Field Theory Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Davide Franco
    • 1
  • Cesare Reina
    • 1
  1. 1.SISSATriesteItaly

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