Planar Limit of Orientifold Field Theories and Emergent Center Symmetry

TL;DR

This work analyzes four-dimensional orientifold field theories on $R_3\times S_1$ and their planar relationship to ${\mathcal N}=1$ SYM. It demonstrates that a full $Z_N$ center symmetry emerges dynamically in the large-$N$ limit (a custodial symmetry) despite the Lagrangian having at most $Z_2$, leading to identical confinement dynamics and confinement–deconfinement temperatures between orientifold daughters and the SYM parent up to ${\cal O}(1/N)$. The authors show that stable $k$-strings exist in the confining phase and match SYM predictions at large $N$, while the theory exhibits both Abelian and non-Abelian confinement regimes depending on the circle size. The analysis extends to thermal and spatial compactifications, revealing that the phase structure and Polyakov-loop behavior in orientifold theories reflect their supersymmetric progenitors, offering insights into QCD-like dynamics and guiding potential lattice validations. Key mechanisms involve planar factorization, emergent center symmetry, magnetic bion effects in the 3D effective theory, and a careful treatment of large-$N$ limits in the presence of two-index fermions.

Abstract

We consider orientifold field theories (i.e. SU(N) Yang--Mills theories with fermions in the two-index symmetric or antisymmetric representations) on R3xS1 where the compact dimension can be either temporal or spatial. These theories are planar equivalent to supersymmetric Yang--Mills. The latter has Z_N center symmetry. The famous Polyakov criterion establishing confinement-deconfinement phase transition as that from Z_N symmetric to Z_N broken phase applies. At the Lagrangian level the orientifold theories have at most a Z_2 center. We discuss how the full Z_N center symmetry dynamically emerges in the orientifold theories in the limit N-->infinity. In the confining phase the manifestation of this enhancement is the existence of stable k-strings in the large-N limit of the orientifold theories. These strings are identical to those of supersymmetric Yang--Mills theories. We argue that critical temperatures (and other features) of the confinement-deconfinement phase transition are the same in the orientifold daughters and their supersymmetric parent up to 1/N corrections. We also discuss the Abelian and non-Abelian confining regimes of four-dimensional QCD-like theories.

Figures (1)

• Figure 1: $Z_N$ symmetric vacuum fields $v_k$. For definitions see Eq. (\ref{['3']}).