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We derive model-independent quantization conditions on the axion couplings (sometimes known as the anomaly coefficients) to the standard model gauge group 1⁄2SUð3Þ × SUð2Þ × Uð1ÞY =Zq with q 1⁄4 1, 2, 3, 6. Using these quantization conditions, we prove that any QCD axion model to the right of the E=N 1⁄4 8=3 line on the jgaγγj-ma plot must necessarily face the axion domain wall problem in a postinflationary scenario. We further demonstrate the higher-group and noninvertible global symmetries in the standard model coupled to a single axion. These generalized global symmetries lead to universal bounds on the axion string tension and the monopole mass. If the axion were discovered in the future, our quantization conditions could be used to constrain the global form of the standard model gauge group. 

Bacteria under external stress can reveal unexpected emergent phenotypes. We show that the intensely studied bacteriumEscherichia colican transform into long, highly motile helical filaments poized at a torsional buckling criticality when exposed to minimum inhibitory concentrations of several antibiotics. While the highly motile helices are physically either right- or left-handed, the motile helices always rotate with a right-handed angular velocity $\overrightarrow{\omega }$, which points in the same direction as the translational velocity ${\overrightarrow{v}}_T$of the helix. Furthermore, these helical cells do not swim by a “run and tumble” but rather synchronously flip their spin $\overrightarrow{\omega }$and thus translational velocity—backing up rather than tumbling. By increasing the translational persistence length, these dynamics give rise to an effective diffusion coefficient up to 20 times that of a normalE. colicell. Finally, we propose an evolutionary mechanism for this phenotype’s emergence whereby the increased effective diffusivity provides a fitness advantage in allowing filamentous cells to more readily escape regions of high external stress.