Scheme-Independent Calculations of Physical Quantities in an ${\cal N}=1$ Supersymmetric Gauge Theory

Thomas A. Ryttov, Robert Shrock

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We consider an asymptotically free, vectorial, N ¼ 1 supersymmetric gauge theory with gauge group G
and Nf pairs of chiral superfields in the respective representations R and R¯ of G, having an infrared fixed
point (IRFP) of the renormalization group at αIR. We present exact results for the anomalous dimensions of
various (gauge-invariant) composite chiral superfields γΦprod at the IRFP and prove that these increase
monotonically with decreasing Nf in the non-Abelian Coulomb phase of the theory and that schemeindependent
expansions for these anomalous dimensions as powers of an Nf-dependent variable, Δf,
exhibit monotonic and rapid convergence to the exact γΦprod throughout this phase. We also present a
scheme-independent calculation of the derivative of the beta function, dβ=dαjα¼αIR , denoted β0
IR, up to
fÞ for general G and R, and, for the case G ¼ SUðNcÞ, R ¼ F, we give an analysis of the properties of
IR calculated to OðΔ4
Original languageEnglish
Article number105018
JournalPhysical Review D
Issue number10
Number of pages25
Publication statusPublished - 2017


  • hep-th
  • hep-lat
  • hep-ph

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