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Quiver Gauge Theories: Finitude and Trichotomoty

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  • Yang-Hui He

    (Department of Mathematics, University of London, London EC1V 0HB, UK
    Merton College, University of Oxford, Oxford OX14JD, UK
    School of Physics, NanKai University, Tianjin 300071, China)

Abstract

D-brane probes, Hanany-Witten setups and geometrical engineering stand as a trichotomy of standard techniques of constructing gauge theories from string theory. Meanwhile, asymptotic freedom, conformality and IR freedom pose as a trichotomy of the beta-function behaviour in quantum field theories. Parallel thereto is a trichotomy in set theory of finite, tame and wild representation types. At the intersection of the above lies the theory of quivers. We briefly review some of the terminology standard to the physics and to the mathematics. Then, we utilise certain results from graph theory and axiomatic representation theory of path algebras to address physical issues such as the implication of graph additivity to finiteness of gauge theories, the impossibility of constructing completely IR free string orbifold theories and the unclassifiability of N < 2 Yang-Mills theories in four dimensions.

Suggested Citation

  • Yang-Hui He, 2018. "Quiver Gauge Theories: Finitude and Trichotomoty," Mathematics, MDPI, vol. 6(12), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:12:p:291-:d:186232
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