We study low-energy dynamics of $[SU(N)]^K$ chiral quiver gauge theories in connection with $mathcal{N}=1$ super Yang-Mills (SYM) theory, and quantum chromodynamics with bi-fundamental fermions (QCD(BF)). These theories can be obtained by $mathbb{Z}_
K$ orbifold projections of $mathcal{N}=1$ $SU(NK)$ SYM theory, but the perturbative planar equivalence does not extend nonperturbatively for $Kge 3$. In order to study low-energy behaviors, we analyze these systems using t~Hooft anomaly matching and reliable semiclassics on $mathbb{R}^3times S^1$. Thanks to t~Hooft anomaly that involves $1$-form center symmetry and discrete chiral symmetry, we predict that chiral symmetry must be spontaneously broken in the confinement phase, and there exist $N$ vacua. Theories with even $K$ possess a physical $theta$ angle despite the presence of massless fermions, and we further predict the $N$-branch structure associated with it; the number of vacua is enhanced to $2N$ at $theta=pi$ due to spontaneous $CP$ breaking. Both of these predictions are explicitly confirmed by reliable semiclassics on $mathbb{R}^3times S^1$ with the double-trace deformation. Symmetry and anomaly of odd-$K$ theories are the same as those of the ${cal N}=1$ SYM, and the ones of even-$K$ theories are same as those of QCD(BF). We unveil why there exists universality between vector-like and chiral quiver theories, and conjecture that their ground states can be continuously deformed without quantum phase transitions. We briefly discuss anomaly inflow on the domain walls connecting the vacua of the theory and possible anomaly matching scenarios.
We study 2d U(1) gauge Higgs systems with a $theta$-term. For properly discretizing the topological charge as an integer we introduce a mixed group- and algebra-valued discretization (MGA scheme) for the gauge fields, such that the charge conjugation
symmetry at $theta = pi$ is implemented exactly. The complex action problem from the $theta$-term is overcome by exactly mapping the partition sum to a worldline/worldsheet representation. Using Monte Carlo simulation of the worldline/worldsheet representation we study the system at $theta = pi$ and show that as a function of the mass parameter the system undergoes a phase transition. Determining the critical exponents from a finite size scaling analysis we show that the transition is in the 2d Ising universality class. We furthermore study the U(1) gauge Higgs systems at $theta = pi$ also with charge 2 matter fields, where an additional $Z_2$ symmetry is expected to alter the phase structure. Our results indicate that for charge 2 a true phase transition is absent and only a rapid crossover separates the large and small mass regions.
We simulate the 2d U(1) gauge Higgs model on the lattice with a topological angle $theta$. The corresponding complex action problem is overcome by using a dual representation based on the Villain action appropriately endowed with a $theta$-term. The
Villain action is interpreted as a non-compact gauge theory whose center symmetry is gauged and has the advantage that the topological term is correctly quantized so that $2pi$ periodicity in $theta$ is intact. Because of this the $theta = pi$ theory has an exact $Z_2$ charge-conjugation symmetry $C$, which is spontaneously broken when the mass-squared of the scalars is large and positive. Lowering the mass squared the symmetry becomes restored in a second order phase transition. Simulating the system at $theta = pi$ in its dual form we determine the corresponding critical endpoint as a function of the mass parameter. Using a finite size scaling analysis we determine the critical exponents and show that the transition is in the 2d Ising universality class, as expected.
