Elliptic genera of ALE and ALF manifolds from gauged linear sigma models

We compute the equivariant elliptic genera of several classes of ALE and ALF manifolds using localization in gauged linear sigma models. In the sigma model computation the equivariant action corresponds to chemical potentials for U(1) currents and the elliptic genera exhibit interesting pole structure as a function of the chemical potentials. We use this to decompose the answers into polar terms that exhibit wall crossing and universal terms. We compare our results to previous results on the large radius limit of the Taub-NUT elliptic genus and also discuss applications of our results to counting of BPS world-sheet spectrum of monopole strings in the 5d N=2 super Yang-Mills theory and self-dual strings in the 6d N=(2,0) theories.Comment: 1+60 page

Intervention Types and Frequency in Animal Prosthetics and Orthotics

Orthotic and prosthetic interventions in veterinary medicine have been performed on a wide range of animal species, aiding in rehabilitation and healing for various pathologies. Contrary to popular belief, veterinary orthotics and prosthetics are not a recent development but have a long history. This study aimed to assess the frequency, cause, and nature of veterinary interventions that could have benefited from orthotic and prosthetic interventions across different species. Data were collected through a survey administered to veterinarians and veterinary orthotic and prosthetic professionals. The outcomes of the investigation contribute to enhancing the knowledge surrounding veterinary amputations, arthrodesis, and the use of orthotic and prosthetic interventions. The survey findings reveal valuable insights into the world of veterinary orthotics and prosthetics, highlighting the growing recognition of their potential benefits among veterinarians. The diverse range of interventions reported and the inclusion of various species underscore the versatility and applicability of orthotics and prosthetics in veterinary medicine. By addressing the recommendations from this study, future research can further advance the field of veterinary orthotics and prosthetics, expanding our understanding of their applications, improving treatment options, and ultimately enhancing the quality of life and mobility of animals in need

Three-Charge Black Holes and Quarter BPS States in Little String Theory

We show that the system of $k$ NS5-branes wrapping $\mathbb{T}^4\times S^1$ has non-trivial vacuum structure. Different vacua have different spectra of 1/4 BPS states that carry momentum and winding around the $S^1$. In one vacuum, such states are described by black holes; in another, they can be thought of as perturbative BPS states in Double Scaled Little String Theory. In general, both kinds of states are present. We compute the degeneracy of perturbative BPS states exactly, and show that it differs from that of the corresponding black holes. We comment on the implication of our results to the black hole microstate program, UV/IR mixing in Little String Theory, string thermodynamics, the string/black hole transition, and other issues.Comment: 53 pages, 3 figure