Supersymmetric asymptotic safety is not guaranteed

Abstract

It was recently shown that certain perturbatively accessible, nonsupersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those of an asymptotically free (perhaps magnetic dual) extension.

Asymptotically safe grand unification

“…These findings extend the results of [36]. Nevertheless exotic theories exist passing these tests such as the theory with 274909 generations of 10, and 5161 generations of 126 (part or all of them can be 126).…”

“…1 The situation changes when considering the supersymmetric cousins of the theory investigated in [29]. It was, in fact, demonstrated in [36] that these supersymmetric cousins are unsafe, along with a much broader class of supersymmetric theories, further extending the one in [37]. The first study of asymptotically safe chiral gauge theories, some of which resembling GUT-like non-supersymmetric theories, appeared in [38] while semi-simple gauge groups in [39].…”

“…The constraint in (2.16) is stronger for asymptotically safe theories [36,37] since it requires at least one chiral superfield to have a quite sizable R charge larger than 5/3. Assuming, for example, the presence of an asymptotically safe fixed point for super QCD once asymptotic freedom is lost, i.e.…”

“…Assuming, for example, the presence of an asymptotically safe fixed point for super QCD once asymptotic freedom is lost, i.e. N f > 3N c , one discovers that R Q = R Q = 1−N c /N f assume values between 1 and 2/3 and therefore the theory violates the constraint in (2.16) [36,37] while it still respects positivity of the remaining constraints. An IR interacting fixed point, relevant for super QCD conformal window [103,104], in asymptotically free field theories, on the other hand, requires the milder condition R i < 5/3.…”

Quantum critical behavior of semisimple gauge theories

“…For instance it is not a feature of the gauge theory with either pure fermionic or scalar matter. Neither does the ultraviolet fixed point exist for the supersymmetrized version [31,32]. It is also straightforward to engineer QCD-like IR behaviour including confinement and chiral symmetry breaking.…”