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Using the numerical modular bootstrap, we constrain the space of 1+1d CFTs with a finite non-invertible global symmetry described by a fusion category $\mathcal{C}$. We derive universal and rigorous upper bounds on the lightest $\mathcal{C}$-preserving scalar local operator for fusion categories such as the Ising and Fibonacci categories. These numerical bounds constrain the possible robust gapless phases protected by a non-invertible global symmetry, which commonly arise from microscopic lattice models such as the anyonic chains. We also derive bounds on the lightest $\mathcal{C}$-violating local operator. Our bootstrap equations naturally arise from a "slab construction", where the CFT is coupled to the 2+1d Turaev-Viro TQFT, also known as the Symmetry TFT., Comment: 28 pages + references

We classify two-dimensional purely chiral conformal field theories which are defined on two-dimensional surfaces equipped with spin structure and have central charge less than or equal to 16, and discuss their duality webs. This result can be used to confirm that the list of non-supersymmetric ten-dimensional heterotic string theories found in the late 1980s is complete and does not miss any exotic example., Comment: 28+11 pages

We explore connections among Monstrous Moonshine, orbifolds, the Kitaev chain, and topological modular forms. Symmetric orbifolds of the Monster CFT, together with further orbifolds by subgroups of Monster, are studied and found to satisfy the divisibility property, which was recently used to rule out extremal holomorphic conformal field theories. For orbifolds by cyclic subgroups of Monster, we arrive at divisibility properties involving the full McKay-Thompson series. Orbifolds by non-abelian subgroups of Monster are further considered by utilizing the data of Generalized Moonshine., Comment: 23 pages; v2: improved discussion of series divisibility, added proofs and references

We study the statistical Ising model of spins on the infinite lattice using a bootstrap method that combines spin-flip identities with positivity conditions, including reflection positivity and Griffiths inequalities, to derive rigorous two-sided bounds on spin correlators through semi-definite programming. For the 2D Ising model on the square lattice, the bootstrap bounds based on correlators supported in a 13-site diamond-shaped region determine the nearest-spin correlator to within a small window, which for a wide range of coupling and magnetic field is narrower than the precision attainable with Monte Carlo methods. We also report preliminary results of the bootstrap bounds for the 3D Ising model on the cubic lattice., Comment: 27 pages, 11 figures. v2: minor revision, references added

We propose an effective field theory (EFT) of fractional quantum Hall systems near the filling fraction $��=5/2$ that flows to pertinent IR candidate phases, including non-abelian Pfaffian, anti-Pfaffian, and particle-hole Pfaffian states (Pf, APf, and PHPf). Our EFT has a 2+1$d$ O(2)$_{2,L}$ Chern-Simons gauge theory coupled to four Majorana fermions by a discrete charge conjugation gauge field, with Gross-Neveu-Yukawa-Higgs terms. Including deformations via a Higgs condensate and fermion mass terms, we can map out a phase diagram with tunable parameters, reproducing the prediction of the recently-proposed percolation picture and its gapless topological quantum phase transitions. Our EFT captures known features of both gapless and gapped sectors of time-reversal-breaking domain walls between Pf and APf phases. Moreover, we find that Pf$\mid$APf domain walls have higher tension than domain walls in the PHPf phase. Then the former, if formed, may transition to the energetically-favored PHPf domain walls; this could, in turn, help further induce a bulk transition to PHPf., 72 pages, 10 figures, 5 tables. Many appendices. Add Sec 2.2, new remarks in Conclusion, and other clarifications. Accepted by Physical Review Research

A fusion category is called transparent if the associator involving any invertible object is the identity map. For the Haagerup-Izumi fusion rings with $G = \mathbb{Z}_{2n+1}$ (the $\mathbb{Z}_3$ case is the Haagerup fusion ring with six simple objects), the transparent ansatz reduces the number of independent $F$-symbols from order $\mathcal{O}(n^6)$ to $\mathcal{O}(n^2)$, rendering the pentagon identity practically solvable. Transparent Haagerup-Izumi fusion categories are thereby constructively classified up to $G = \mathbb{Z}_9$, recovering all known Haagerup-Izumi fusion categories to this order, and producing new ones. Transparent Haagerup-Izumi fusion categories additionally satisfying $S_4$ tetrahedral invariance are further classified up to $G = \mathbb{Z}_{15}$, and the explicit $F$-symbols for the unitary ones, including the Haagerup $\mathcal{H}_3$ fusion category, are compactly presented. The $F$-symbols for the Haagerup $\mathcal{H}_2$ fusion category are also presented. Going beyond, the transparent ansatz offers a viable course towards constructing novel fusion categories for new fusion rings., Comment: 25+9 pages, 1 table; v2: improved exposition; v3: adopted unitary gauge for pseudo-unitary fusion categories

Twelve undescribed sesquiterpenoids, fomitopins A-L (1-12), were isolated via bioassay-guided purification from the bracket fungus Fomitopsis pinicola (Sw.) P. Karst, and this fungus have been reported to exhibit anti-microbial and anti-inflammatory activities. The structures of 1-12 were elucidated by spectroscopic and spectrometric analyses and their absolute configurations were further confirmed by ECD simulations. Ten isolated compounds were evaluated for their anti-inflammatory potential and compound 11 exhibited the most significant inhibition of superoxide anion generation and elastase release with IC50 values of 0.81 ± 0.15 and 0.74 ± 0.12 μM. These newly purified sesquiterpenoids could be potential candidates for further anti-inflammatory studies.

In the southeastern US, substantial emissions of isoprene from deciduous trees undergo atmospheric oxidation to form secondary organic aerosol (SOA) that contributes to fine particulate matter (PM2.5). Laboratory studies have revealed that anthropogenic pollutants, such as sulfur dioxide (SO2), oxides of nitrogen (NOx), and aerosol acidity, can enhance SOA formation from the hydroxyl radical (OH)-initiated oxidation of isoprene; however, the mechanisms by which specific pollutants enhance isoprene SOA in ambient PM2.5 remain unclear. As one aspect of an investigation to examine how anthropogenic pollutants influence isoprene-derived SOA formation, high-volume PM2.5 filter samples were collected at the Birmingham, Alabama (BHM), ground site during the 2013 Southern Oxidant and Aerosol Study (SOAS). Sample extracts were analyzed by gas chromatography–electron ionization-mass spectrometry (GC/EI-MS) with prior trimethylsilylation and ultra performance liquid chromatography coupled to electrospray ionization high-resolution quadrupole time-of-flight mass spectrometry (UPLC/ESI-HR-QTOFMS) to identify known isoprene SOA tracers. Tracers quantified using both surrogate and authentic standards were compared with collocated gas- and particle-phase data as well as meteorological data provided by the Southeastern Aerosol Research and Characterization (SEARCH) network to assess the impact of anthropogenic pollution on isoprene-derived SOA formation. Results of this study reveal that isoprene-derived SOA tracers contribute a substantial mass fraction of organic matter (OM) ( ~7 to ~20 %). Isoprene-derived SOA tracers correlated with sulfate (SO42-) (r2 = 0.34, n = 117) but not with NOx. Moderate correlations between methacrylic acid epoxide and hydroxymethyl-methyl-α-lactone (together abbreviated MAE/HMML)-derived SOA tracers with nitrate radical production (P[NO3]) (r2 = 0.57, n = 40) were observed during nighttime, suggesting a potential role of the NO3 radical in forming this SOA type. However, the nighttime correlation of these tracers with nitrogen dioxide (NO2) (r2 = 0.26, n = 40) was weaker. Ozone (O3) correlated strongly with MAE/HMML-derived tracers (r2 = 0.72, n = 30) and moderately with 2-methyltetrols (r2 = 0.34, n = 15) during daytime only, suggesting that a fraction of SOA formation could occur from isoprene ozonolysis in urban areas. No correlation was observed between aerosol pH and isoprene-derived SOA. Lack of correlation between aerosol acidity and isoprene-derived SOA is consistent with the observation that acidity is not a limiting factor for isoprene SOA formation at the BHM site as aerosols were acidic enough to promote multiphase chemistry of isoprene-derived epoxides throughout the duration of the study. All in all, these results confirm previous studies suggesting that anthropogenic pollutants enhance isoprene-derived SOA formation. Published version

We study two-dimensional (4,4) superconformal field theories of central charge c=6, corresponding to nonlinear sigma models on K3 surfaces, using the superconformal bootstrap. This is made possible through a surprising relation between the BPS N=4 superconformal blocks with c=6 and bosonic Virasoro conformal blocks with c=28, and an exact result on the moduli dependence of a certain integrated BPS 4-point function. Nontrivial bounds on the non-BPS spectrum in the K3 CFT are obtained as functions of the CFT moduli, that interpolate between the free orbifold points and singular CFT points. We observe directly from the CFT perspective the signature of a continuous spectrum above a gap at the singular moduli, and find numerically an upper bound on this gap that is saturated by the $A_1$ N=4 cigar CFT. We also derive an analytic upper bound on the first nonzero eigenvalue of the scalar Laplacian on K3 in the large volume regime, that depends on the K3 moduli data. As two byproducts, we find an exact equivalence between a class of BPS N=2 superconformal blocks and Virasoro conformal blocks in two dimensions, and an upper bound on the four-point functions of operators of sufficiently low scaling dimension in three and four dimensional CFTs., Comment: 60 pages, 9 figures