Periods and Prepotential of N=2 SU(2) Supersymmetric Yang-Mills Theory with Massive Hypermultiplets

We derive a simple formula for the periods associated with the low energy effective action of $N=2$ supersymmetric $SU(2)$ Yang-Mills theory with massive $N_f\le 3$ hypermultiplets. This is given by evaluating explicitly the integral associated to the elliptic curve using various identities of hypergeometric functions. Following this formalism, we can calculate the prepotential with massive hypermultiplets both in the weak coupling region and in the strong coupling region. In particular, we show how the Higgs field and its dual field are expressed as generalized hypergeometric functions when the theory has a conformal point.Comment: 21 pages, LaTe

Social challenges of spatial planning for outdoor cat management in Amami Oshima Island, Japan

Outdoor cats pose substantial threats to native biodiversity, especially on islands. However, cats also provide benefits to people, such as companionship and the killing of pests. Thus, management of outdoor cats is controversial and can lead to conflicts among stakeholders. Although previous studies have examined stakeholders' preferences for outdoor cats and their management, little is known about the differences in their attitudes toward cat occurrences and management across habitats. Identifying these attitudinal differences would provide useful knowledge for policy makers about zoning management. We conducted structured interviews with residents in Amami Oshima Island, Japan, to evaluate the residents' attitudes to outdoor cats' occurrence and their management across habitats (Forest, Rural, and Town areas). Furthermore, we compared the attitudes of cat- owners and non-owners. The results show that the Forest was least preferred as an outdoor cat habitat. Lethal options as a management strategy were unacceptable to the residents, whereas adoption was acceptable in all areas. Cat-owners showed a significantly higher acceptance toward outdoor cats in Town and Rural areas than did non-owners; they also showed a lower acceptance of lethal options and a higher acceptance toward Trap, Neuter and Return (TNR) than non-owners. These findings imply that it is difficult to achieve consensus regarding outdoor cat management, especially in town and rural areas; however, outdoor cats from these areas move to the forests and pose a threat to the endangered species. Communication efforts with both cat-owners and non-owners should fill these attitudinal gaps among stakeholders and lead to effective management. (C) 2017 The Authors. Published by Elsevier B.V

Integral Equations of Fields on the Rotating Black Hole

It is known that the radial equation of the massless fields with spin around Kerr black holes cannot be solved by special functions. Recently, the analytic solution was obtained by use of the expansion in terms of the special functions and various astrophysical application have been discussed. It was pointed out that the coefficients of the expansion by the confluent hypergeometric functions are identical to those of the expansion by the hypergeometric functions. We explain the reason of this fact by using the integral equations of the radial equation. It is shown that the kernel of the equation can be written by the product of confluent hypergeometric functions. The integral equaton transforms the expansion in terms of the confluent hypergeometric functions to that of the hypergeometric functions and vice versa,which explains the reason why the expansion coefficients are universal.Comment: 14 pages, LaTeX, no figure

Prepotential of N=2N=2 Supersymmetric Yang-Mills Theories in the Weak Coupling Region

We show how to obtain the explicite form of the low energy quantum effective action for $N=2$ supersymmetric Yang-Mills theory in the weak coupling region from the underlying hyperelliptic Riemann surface. This is achieved by evaluating the integral representation of the fields explicitly. We calculate the leading instanton corrections for the group SU(\nc), SO(N) and $SP(2N)$ and find that the one-instanton contribution of the prepotentials for the these group coincide with the one obtained recently by using the direct instanton caluculation.Comment: 13 pages, LaTe

Prepotentials, Bi-linear Forms on Periods and Enhanced Gauge Symmetries in Type-II Strings

We construct a bi-linear form on the periods of Calabi-Yau spaces. These are used to obtain the prepotentials around conifold singularities in type-II strings compactified on Calabi-Yau space. The explicit construction of the bi-linear forms is achieved for the one-moduli models as well as two moduli models with K3-fibrations where the enhanced gauge symmetry is known to be observed at conifold locus. We also show how these bi-linear forms are related with the existence of flat coordinates. We list the resulting prepotentials in two moduli models around the conifold locus, which contains alpha' corrections of 4-D N=2 SUSY SU(2) Yang-Mills theory as the stringy effect.Comment: Latex file(34pp), a reference added, typos correcte

Ground-State Phase Diagram of the Two-Dimensional Extended Bose-Hubbard Model

We investigate the ground-state phase diagram of the soft-core Bose-Hubbard model with the nearest-neighbor repulsion on a square lattice by using an unbiased quantum Monte Carlo method. In contrast to the previous study[P. Sengupta {\it et. al.}, Phys. Rev. Lett. {\bf 94}, 207202 (2005)], we present the ground-state phase diagrams up to large hopping parameters. As a result, in addition to the known supersolid above half-filling, we find supersolid even below and at half-filling for large hopping parameters. Furthermore, for the strong nearest-neighbor repulsion, we show that the supersolid phase occupies a remarkably broad region in the phase diagram. The results are in qualitative agreement with that obtained by the Gutzwiller mean-field approximation[M. Iskin, Phys. Rev. A {\bf 83}, 051606(R) (2011) and T. Kimura, Phys. Rev. A {\bf 84}, 063630 (2011)]