Planar Diagram Field Theories

  • Gerard ’t Hooft
Part of the NATO ASI Series book series (NSSB, volume 115)


In this compilation of lectures field theories are considered which consist of N component fields qi interacting with NxN component matrix fields Aij with internal (local or global) symmetry group SU(N) or S0 (N). The double expansion in 1/N and \({{\tilde g}^2}\) = Ng2 can be formulated in terms of Feynman diagrams with a planarity structure. If the mass is sufficiently large and \({{\tilde g}^2}\) sufficiently small then the (extremely non-trivial) expansion in \({{\tilde g}^2}\) at lowest order in 1/N is Borel summable. Exact limits on the behavior of the Borel integrand for the \({{\tilde g}^2}\) expansion are derived.


Gauge Theory Green Function Difference Equation Symmetry Point Feynman Rule 
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Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • Gerard ’t Hooft
    • 1
  1. 1.Institute for Theoretical PhysicsUtrechtThe Netherlands

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