Abstract
In the mid-seventies’ t Hooft introduced a clever device to keep track of SU(N)-group theoretic factors in the perturbative expansion of gauge field models.1 The goal was to find an approximation in the large N (planar) limit. A similar approximation for vector-valued fields singles out one-loop graphs, easily handled, and provides an interesting model in a number of problems—for instance, critical phenomena. Alas, in the case of gauge theories apart from phenomenological applications, the scheme was not very successful, since the leading terms still involve the computation of infinitely many perturbative terms. The story is recorded in a 1979 report by S. Coleman2 entitled “1/N.”
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References
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Itzykson, C., Zuber, J.B. (1992). Combinatorics of Mapping Class Groups and Matrix Integration. In: Teitelboim, C., Zanelli, J. (eds) Quantum Mechanics of Fundamental Systems 3. Series of the Centro de Estudios Científicos de Santiago. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3374-0_7
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DOI: https://doi.org/10.1007/978-1-4615-3374-0_7
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