We define Modular Linear Differential Equations (MLDE) for the level-two congruence subgroups Γθ, Γ0(2) and Γ0(2) of SL2(ℤ). Each subgroup corresponds to one of the spin structures on the torus. The pole structures of the fermionic MLDEs are investigated by exploiting the valence formula for the level-two congruence subgroups. We focus on the first and second order holomorphic MLDEs without poles and use them to find a large class of ‘Fermionic Rational Conformal Field Theories’, which have non-negative integer coefficients in the q-series expansion of their characters. We study the detailed properties of these fermionic RCFTs, some of which are supersymmetric. This work also provides a starting point for the classification of the fermionic Modular Tensor Category.

Recently, the modular linear differential equation (MLDE) for level-two congruence subgroups Γθ, Γ0(2) and Γ0(2) of SL2(ℤ) was developed and used to classify the fermionic rational conformal field theories (RCFT). Two character solutions of the second-order fermionic MLDE without poles were found and their corresponding CFTs are identified. Here we extend this analysis to explore the landscape of three character fermionic RCFTs obtained from the third-order fermionic MLDE without poles. Especially, we focus on a class of the fermionic RCFTs whose Neveu-Schwarz sector vacuum character has no free-fermion currents and Ramond sector saturates the bound hR ≥ $$ \frac{C}{24} $$ C 24 , which is the unitarity bound for the supersymmetric case. Most of the solutions can be mapped to characters of the fermionized WZW models. We find the pairs of fermionic CFTs whose characters can be combined to produce K(τ), the character of the c = 12 fermionic CFT for Co0 sporadic group.

We define Modular Linear Differential Equations (MLDE) for the level-two congruence subgroups Γ ϑ , Γ 0 (2) and Γ 0 (2) of SL 2 (Z). Each subgroup corresponds to one of the spin structures on the torus. The pole structures of the fermionic MLDEs are investigated by exploiting the valence formula for the level-two congruence subgroups. We focus on the first and second order holomorphic MLDEs without poles and use them to find a large class of 'Fermionic Rational Conformal Field Theories', which have non-negative integer coefficients in the q-series expansion of their characters. We study the detailed properties of these fermionic RCFTs, some of which are supersymmetric. This work also provides a starting point for the classification of the fermionic Modular Tensor Category.

We compute the new supersymmetric index of a large class of N=2 heterotic compactifications with torsion, corresponding to principal two-torus bundles over warped K3 surfaces with H-flux. Starting from a UV description as a (0,2) gauged linear sigma-model with torsion, we use supersymmetric localization techniques to provide an explicit expression of the index as a sum over the Jeffrey-Kirwan residues of the one-loop determinant. We finally propose a geometrical formula that gives the new supersymmetric index in terms of bundle data, regardless of any particular choice of underlying two-dimensional theory.Comment: 53 pages. Version 2 to be published in JHEP: added proof of the geometrical formula for the quartic, few minor clarifications and typos correcte

Pulmonary surfactant forms a sub-micrometer thick fluid layer that covers the surface of alveolar lumen and inhaled nanoparticles therefore come in to contact with surfactant prior to any interaction with epithelial cells. We investigate the role of the surfactant as a protective physical barrier by modeling the interactions using silica-Curosurf-alveolar epithelial cell system in vitro. Electron microscopy displays that the vesicles are preserved in the presence of nanoparticles while nanoparticle-lipid interaction leads to formation of mixed aggregates. Fluorescence microscopy reveals that the surfactant decreases the uptake of nanoparticles by up to two orders of magnitude in two models of alveolar epithelial cells, A549 and NCI-H441, irrespective of immersed culture on glass or air–liquid interface culture on transwell. Confocal microscopy corroborates the results by showing nanoparticle-lipid colocalization interacting with the cells. Our work thus supports the idea that pulmonary surfactant plays a protective role against inhaled nanoparticles. The effect of surfactant should therefore be considered in predictive assessment of nanoparticle toxicity or drug nanocarrier uptake. Models based on the one presented in this work may be used for preclinical tests with engineered nanoparticles.