Fractional Skyrmion molecules in a ℂPN−1 model

We study fractional Skyrmions in a ℂP2 baby Skyrme model with a generalization of the easy-plane potential. By numerical methods, we find stable, metastable, and unstable solutions taking the shapes of molecules. Various solutions possess discrete symmetries, and the origin of those symmetries are traced back to congruencies of the fields in homogeneous coordinates on ℂP2.

Symmetries of complex analytic vector fields with an essential singularity on the Riemann sphere

We consider the family ℰ (s, r, d) of all singular complex analytic vector fields X ( z ) = Q ( z ) P ( z ) e E ( z ) ∂ ∂ z $X(z)=\frac{Q(z)}{P(z)}{{e}^{E(z)}}\frac{\partial }{\partial z}$ on the Riemann sphere where Q, P, ℰ are polynomials with deg Q = s, deg P = r and deg ℰ = d ≥ 1. Using the pullback action of the affine group Aut(ℂ) and the divisors for X, we calculate the isotropy groups Aut(ℂ) X of discrete symmetries for X ∈ ℰ (s, r, d). The subfamily ℰ (s, r, d)id of those X with trivial isotropy group in Aut(ℂ) is endowed with a holomorphic trivial principal Aut(ℂ)-bundle structure. A necessary and sufficient arithmetic condition on s, r, d ensuring the equality ℰ (s, r, d) = ℰ (s, r, d)id is presented. Moreover, those X ∈ ℰ (s, r, d) \ ℰ (s, r, d)id with non-trivial isotropy are realized. This yields explicit global normal forms for all X ∈ ℰ (s, r, d). A natural dictionary between analytic tensors, vector fields, 1-forms, orientable quadratic differentials and functions on Riemann surfaces M is extended as follows. In the presence of nontrivial discrete symmetries Γ < Aut(M), the dictionary describes the correspondence between Γ-invariant tensors on M and tensors on M /Γ.

Spinorial structures, discrete symmetries and some consequences

In this paper, we discuss fundamental aspects related to the helicity and dynamics of the spin-1/2 fermions encompassed within the very well-known Lounesto’s classification. More specifically, we investigate how the bi-spinorial structures behave under discrete symmetries, as well as analyze some consequences on the spinors dynamics. In addition, we find an interesting relation between the spinor helicity and the Lounesto spinor classification.

Discrete and higher-form symmetries in SCFTs from wrapped M5-branes

We analyze topological mass terms of BF type arising in supersymmetric M-theory compactifications to AdS5. These describe spontaneously broken higher-form gauge symmetries in the bulk. Different choices of boundary conditions for the BF terms yield dual field theories with distinct global discrete symmetries. We discuss in detail these symmetries and their ’t Hooft anomalies for 4d $$ \mathcal{N} $$ N = 1 SCFTs arising from M5-branes wrapped on a Riemann surface without punctures, including theories from M5-branes at a ℤ2 orbifold singularity. The anomaly polynomial is computed via inflow and contains background fields for discrete global 0-, 1-, and 2-form symmetries and continuous 0-form symmetries, as well as axionic background fields. The latter are properly interpreted in the context of anomalies in the space of coupling constants.