Out-of-Time-Ordered Correlators in (T2)n/Zn(T^2)^n/\mathbb{Z}_n

In this note we continue analysing the non-equilibrium dynamics in the $(T^2)^n/\mathbb{Z}_n$ orbifold conformal field theory. We compute the out-of-time-ordered four-point correlators with twist operators. For rational $\eta \ (=p/q)$ which is the square of the compactification radius, we find that the correlators approach non-trivial constants at late time. For $n=2$ they are expressed in terms of the modular matrices and for higher $n$ orbifolds are functions of $pq$ and $n$. For irrational $\eta$, we find a new polynomial decay of the correlators that is a signature of an intermediate regime between rational and chaotic models.Comment: 20 pages, 3 figure

Semiclassical analysis of the bifundamental QCD on R2×T2\mathbb{R}^2\times T^2 with 't Hooft flux

We study the phase structure of bifundamental quantum chromodynamics (QCD(BF)), which is the $4$-dimensional $SU(N) \times SU(N)$ gauge theory coupled with the bifundamental fermion. Firstly, we refine constraints on its phase diagram from 't Hooft anomalies and global inconsistencies, and we find more severe constraints than those in previous literature about QCD(BF). Secondly, we employ the recently-proposed semiclassical approach for confining vacua to investigate this model concretely, and this is made possible via anomaly-preserving $T^2$ compactification. For sufficiently small $T^2$ with the 't Hooft flux, the dilute gas approximation of center vortices gives reliable semiclassical computations, and we determine the phase diagram as a function of the fermion mass $m$, two strong scales $\Lambda_{1},\Lambda_2$, and two vacuum angles, $\theta_1, \theta_2$. In particular, we find that the QCD(BF) vacuum respects the $\mathbb{Z}_2$ exchange symmetry of two gauge groups. Under the assumption of the adiabatic continuity, our result successfully explains one of the conjectured phase diagrams in the previous literature and also gives positive support for the nonperturbative validity of the large-$N$ orbifold equivalence between QCD(BF) and $\mathcal{N}=1$ $SU(2N)$ supersymmetric Yang-Mills theory. We also comment on problems of domain walls.Comment: 33 pages, 5 figures, small discussion adde

Degradable and Nanosegregated Elastomers with Multiblock Sequences of Biobased Aromatic Mesogens and Biofunctional Aliphatic Oligocarbonates

We have developed multiblock aromatic/aliphatic condensation polymers, comprising side-chain biofunctionalized aliphatic oligocarbonates and biobased aromatic ester triad mesogens up to 17 wt %. Nanosegregation of the aromatic mesogen-rich domains with diameters of approximately 10 nm from the soft aliphatic polymer matrix is suggested by atomic force microscopy. The polymers exhibit rubberlike properties, unlike the corresponding aliphatic polycarbonate forming viscous liquid. These properties support the interchain interactions between the aromatic mesogens, which can serve as physical cross-linking. The aromatic ester triad mesogens in the multiblock polymers significantly bolster the tolerance to organocatalytic hydrolysis and methanolysis of the polymer chains but are eventually degraded. The multiblock polymers show degradation behavior slightly faster than poly(L-lactide), whereas poly(ethylene terephthalate) remains intact under the same condition. The present study demonstrates the efficacy of aromatic ester triad mesogens incorporated into the sequences of biodegradable aliphatic polycarbonates to enhance their physical properties while retaining degradability