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arXiv · 2104.12352

Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD

Mithat Ünsal
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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.

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Mithat Ünsal. 2021-04-26. Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD. https://doi.org/10.1007/jhep03(2022)119

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