Exact Results in Non-Supersymmetric Large N Orientifold Field Theories

TL;DR

This work shows that a non-supersymmetric large-$N$ orientifold field theory, containing a Dirac fermion in the antisymmetric representation, is nonperturbatively planar equivalent to ${\cal N}=1$ SYM in a substantial bosonic sector. Through a detailed comparison of perturbative planar graphs and a nonperturbative determinant-based mapping, it obtains exact results for the daughter theory, including a bifermion condensate $\langle \lambda\lambda\rangle_k = N \Lambda^3 \exp\left(i {2\pi k \over N}\right)$, $N$ vacua, parity doublets, and a vanishing leading cosmological constant. The authors reinforce this equivalence with a string-theory picture via type 0A branes and an M-theory lift, where the M5 curve coincides with that of ${\cal N}=1$ SYM, lending support to the IR identification. The findings provide non-SUSY, large-$N$ exact results and sharpen our understanding of how planar equivalence can extend beyond perturbation theory, with implications for the spectrum and vacuum structure of non-SUSY gauge theories.

Abstract

We consider non-supersymmetric large N orientifold field theories. Specifically, we discuss a gauge theory with a Dirac fermion in the anti-symmetric tensor representation. We argue that, at large N and in a large part of its bosonic sector, this theory is non-perturbatively equivalent to N=1 SYM, so that exact results established in the latter (parent) theory also hold in the daughter orientifold theory. In particular, the non-supersymmetric theory has an exactly calculable bifermion condensate, exactly degenerate parity doublets, and a vanishing cosmological constant (all this to leading order in 1/N).

Figures (3)

• Figure 1:
• Figure 2: (a) A typical planar contribution to the vacuum polarization. (b) For ${\cal N}=1\ $ SYM. (c) For the non-SUSY theory.
• Figure 3: The type 0A brane configuration. The solid lines denote D4 branes. The dashed line denotes the orientifold 4-plane.