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  1. My question is following "Why 5D gauge theory is non-renormalizable?" Here I treat $5D$ supersymmetric gauge theories.

  2. Also I heard Non-renormalizablity of $5D$ gauge theories implies the singularities in instanton moduli space. How this can be possible? Can you give me a reliable explanation?

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  • $\begingroup$ Can you cite a reference for 5D non-renormalizability? arxiv.org/abs/hep-th/0305208 indicates non-renormalizability is known to be true only for six dimensions and higher. $\endgroup$
    – ACuriousMind
    Mar 4 '15 at 17:02
  • $\begingroup$ You can find relevant material in first about page 11. and there is some comments on second $\endgroup$
    – phy_math
    Mar 4 '15 at 17:07
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In the textbook of TASI 2009, section "Introduction to extra dimension" i can find the answer as follows.

They state that $5D$ or higher dimensional gauge coupling has a negative mass dimension, so the 5d or higher dimensional gauge theory is non-renormalizable.

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    $\begingroup$ That's a perturbative/power-counting argument, but not a proof that renormalization is impossible, I believe. Symmetries and "accidental" cancellations can make naively divergent stuff finite. $\endgroup$
    – ACuriousMind
    Mar 4 '15 at 17:18
  • $\begingroup$ Ok i try to find relevant materials dealing with cancellation of divergent terms in 5d gauge theory. As a student, i think this topic is interesting subject to study in depth. thanks for your mention. ^.^ $\endgroup$
    – phy_math
    Mar 4 '15 at 17:24

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