Chirally Symmetric Phase of Supersymmetric Gluodynamics

TL;DR

In pure SUSY gluodynamics, the discrete chiral symmetry $Z_{2T(G)}$ and the gluino condensate $\langle \lambda\lambda\rangle$ drive the standard picture of gaugino condensation, but inconsistencies arise from a Witten index mismatch and a discrepancy between strong- and weak-coupling condensate calculations. The authors amend the Veneziano-Yankielowicz effective Lagrangian by introducing an integer-valued Lagrange multiplier $n$ to enforce topological charge quantization, restoring $Z_N$ invariance and revealing a condensate-free vacuum. The corrected potential supports $N$ $Z_N$-related vacua plus a condensate-free minimum at $\langle S\rangle=0$, and they interpret a strong/weak coupling mismatch as evidence for this extra vacuum, with the possibility of massless bound states in that phase. If realized, this condensate-free phase would reshape the IR dynamics of SUSY gauge theories, impacting SUSY QCD branches, Seiberg duality, and Witten-index accounting across different gauge groups.

Abstract

We argue that supersymmetric gluodynamics (theory of gluons and gluinos) has a condensate-free phase. Unlike the standard phase, the discrete axial symmetry of the Lagrangian is unbroken in this phase, and the gluino condensate does not develop. Extra unconventional vacua are supersymmetric and are characterized by the presence of (bosonic and fermionic) massless bound states. A set of arguments in favor of the conjecture includes: (i) analysis of the effective Lagrangian of the Veneziano-Yankielowicz type which we amend to properly incorporate all symmetries of the model; (ii) consideration of an unsolved problem with the Witten index; (iii) interpretation of a mismatch between the strong-coupling and weak coupling instanton calculations of the gluino condensate detected previously. Impact on Seiberg's results is briefly discussed.