Consistency of $\chi$SB in chiral Yang-Mills theory with adiabatic continuity

Abstract

We study the pattern of chiral symmetry breaking ($\chi$SB) in the $\psi \chi \eta$ model (with the chiral fermion sector containing ${\psi }^{\{ij\}}$, ${\chi }_{[ij]}$, and ${\eta }_i^A$, see [1]) on ${\mathbb{R}}^3\times S_L^1$ and derive implications to ${\mathbb{R}}^4$ physics. Center-symmetric vacua are stabilized by a double-trace deformation. With the center symmetry maintained at small $L(S^1)\ll {\Lambda }^{-1}$, i.e. at weak coupling, no phase transitions are expected in passing to large $L(S^1)\gg {\Lambda }^{-1}$ (here $\Lambda$ is the dynamical Yang-Mills scale). Starting with the small $L$-limit, we find the leading-order nonperturbative corrections in the given theory. The instanton-monopole operators induce the adjoint chiral condensate $⟨{\psi }^{\{ij\}}{\chi }_{[jk]}⟩\ne 0$ at weak coupling i.e. at $L(S^1)\ll {\Lambda }^{-1}$. Then adiabatic continuity tells us that $⟨{\psi }^{\{ij\}}{\chi }_{[jk]}⟩\ne 0$ exists on ${\mathbb{R}}^4$, in full accord with the prediction [2]. Simultaneously with $⟨{\psi }^{\{ij\}}{\chi }_{[jk]}⟩\sim {\Lambda }^3{\delta }_k^i$ the SU($N_c$) gauge symmetry is spontaneously broken at strong coupling down to its maximal Abelian subgroup.

arXiv commentMinor corrections, reference updated

References in corpus (28)

• Generalized Global Symmetries
• Theta, Time Reversal, and Temperature
• Periodic Instantons with non-trivial Holonomy
• SU(2) Calorons and Magnetic Monopoles
• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
• Monopoles and Instantons on Partially Compactified D-Branes
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• QCD-like Theories on R_3\times S_1: a Smooth Journey from Small to Large r(S_1) with Double-Trace Deformations
• Conformality or confinement: (IR)relevance of topological excitations
• Index theorem for topological excitations on R^3 * S^1 and Chern-Simons theory
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Order parameters and color-flavor center symmetry in QCD
• Conformality or confinement (II): One-flavor CFTs and mixed-representation QCD
• On Yang-Mills Theories with Chiral Matter at Strong Coupling
• Differences and similarities between fundamental and adjoint matters in SU(N) gauge theories
• Notes on Confinement on ${\mathbf{R}}^3\times {\mathbf{S}}^1$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F)
• Patterns of Symmetry Breaking in Chiral "QCD"
• Probing the dynamics of chiral SU(N) gauge theories via generalized anomalies
• Gauging 1-form center symmetries in simple $SU(N)$ gauge theories
• New Anomalies, TQFTs, and Confinement in Bosonic Chiral Gauge Theories
• Dynamics and symmetries in chiral $SU(N)$ gauge theories
• Classification of compactified $su(N_c)$ gauge theories with fermions in all representations
• A Chiral SU(N) Gauge Theory Planar Equivalent to Super-Yang-Mills
• Quantum distillation in QCD
• Dynamical Abelianization and anomalies in chiral gauge theories
• Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD