Ultraviolet divergences in non-renormalizable supersymmetric theories

Abstract

We present a pedagogical review of our current understanding of the ultraviolet structure of N = (1,1) 6D supersymmetric Yang-Mills theory and of N = 8 4D supergravity. These theories are not renormalizable, they involve power ultraviolet divergences and, in all probability, an infinite set of higher-dimensional counterterms that contribute to on-mass-shell scattering amplitudes. A specific feature of supersymmetric theories (especially, of extended supersymmetric theories) is that these counterterms may not be invariant off shell under the full set of supersymmetry transformations. The lowest-dimensional nontrivial counterterm is supersymmetric on shell. Still higher counterterms may lose even the on-shell invariance. On the other hand, the full effective Lagrangian, generating the amplitudes and representing an infinite sum of counterterms, still enjoys the complete symmetry of original theory. We also discuss simple supersymmetric quantum-mechanical models that exhibit the same behaviour.

26 pages, 3 figures. Invited contribution in the conference "Supersymmetry and Quantum Symmetries" (Dubna, July 2015). Few typos corrected. To be published in Phys. Part. Nucl. Lett

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• Higher time-derivative theories from space-time interchanged integrable field theories
• On gauge dependence of the one-loop divergences in $6D$, $\mathcal{N}=(1,0)$ and $\mathcal{N}=(1,1)$ SYM theories
• Softly broken conformal symmetry with quantum gravitational corrections
• On the two-loop divergences in 6D, $\mathcal{N}=(1,1)$ SYM theory
• Nonlinear evolution of disturbances in higher time-derivative theories
• Quantisations of exactly solvable ghostly models
• Higher-dimensional invariants in $6D$ super Yang-Mills theory
• Lie symmetries and ghost-free representations of the Pais-Uhlenbeck model