Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD

Abstract

The dimension of the Hilbert space of QFT scales exponentially with the volume of the space in which the theory lives, yet in supersymmetric theories, one can define a graded dimension (such as the supersymmetric index) that counts just the number of bosonic minus fermionic ground states. Can we make this observation useful in non-supersymmetric QFTs in four dimensions? In this work, we construct symmetry graded state sums for a variety of non-supersymmetric theories. Among the theories we consider is one that is remarkably close to QCD: Yang--Mills theory with $N_f=N_c$ fundamental Dirac fermions and one adjoint Weyl fermion, QCD(F/adj). This theory can be obtained from SQCD by decoupling scalars and carry exactly the same anomalies. Despite the existence of fundamental fermions, the theory possess an exact 0-form color-flavor center (CFC) symmetry for a particular grading/twist under which Polyakov loop is a genuine order parameters. By a two-loop analysis, we prove that CFC-symmetry remains unbroken at small $\beta$ due to grading. Chiral symmetry is spontaneously broken within the domain of validity of semi-classics on ${\mathbb{R}}^3\times S^1$ in a pattern identical to $N_f=N_c$ SQCD on ${\mathbb{R}}^4$ and the two regimes are adiabatically connected. The vacuum structures of the theory on ${\mathbb{R}}^4$ and ${\mathbb{R}}^3\times S^1$ are controlled by the same mixed 't Hooft anomaly condition, implying a remarkable persistent order.

99 pages, 15 figures

References in corpus (18)

• Generalized Global Symmetries
• 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
• Volume independence in large Nc QCD-like gauge theories
• Cardy Formulae for SUSY Theories in d=4 and d=6
• Finite size phase transitions in QCD with adjoint fermions
• Vacuum structure of bifundamental gauge theories at finite topological angles
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics
• Order parameters and color-flavor center symmetry in QCD
• Dynamics of 3D SUSY Gauge Theories with Antisymmetric Matter
• The Bi-Fundamental Gauge Theory in 3+1 Dimensions: The Vacuum Structure and a Cascade
• Some Exact Results in QCD-like Theories
• Chiral gauge dynamics and dynamical supersymmetry breaking
• Adjoint fermion zero-modes for SU(N) calorons
• Critical behavior of gauge theories and Coulomb gases in three and four dimensions
• Planar Limit of Orientifold Field Theories and Emergent Center Symmetry
• Volume independence for Yang-Mills fields on the twisted torus

Cited by in corpus (3)

• Notes on Confinement on ${\mathbf{R}}^3\times {\mathbf{S}}^1$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F)
• Consistency of $\chi$SB in chiral Yang-Mills theory with adiabatic continuity
• Two types of domain walls in $\mathcal{N}=1$ super-QCD: how they are classified and counted