Properties of hyperkahler manifolds and their twistor spaces

We describe the relation between supersymmetric sigma-models on hyperkahler manifolds, projective superspace, and twistor space. We review the essential aspects and present a coherent picture with a number of new results.Comment: 26 pages. v2: Sign mistakes corrected; Kahler potential explicitly calculated in example; references added. v3: Published version--several small clarifications per referee's reques

Fish swimming in schools save energy regardless of their spatial position

For animals, being a member of a group provides various advantages, such as reduced vulnerability to predators, increased foraging opportunities and reduced energetic costs of locomotion. In moving groups such as fish schools, there are benefits of group membership for trailing individuals, who can reduce the cost of movement by exploiting the flow patterns generated by the individuals swimming ahead of them. However, whether positions relative to the closest neighbours (e.g. ahead, sided by side or behind) modulate the individual energetic cost of swimming is still unknown. Here, we addressed these questions in grey mullet Liza aurata by measuring tail-beat frequency and amplitude of 15 focal fish, swimming in separate schools, while swimming in isolation and in various positions relative to their closest neighbours, at three speeds. Our results demonstrate that, in a fish school, individuals in any position have reduced costs of swimming, compared to when they swim at the same speed but alone. Although fish swimming behind their neighbours save the most energy, even fish swimming ahead of their nearest neighbour were able to gain a net energetic benefit over swimming in isolation, including those swimming at the front of a school. Interestingly, this energetic saving was greatest at the lowest swimming speed measured in our study. Because any member of a school gains an energetic benefit compared to swimming alone, we suggest that the benefits of membership in moving groups may be more strongly linked to reducing the costs of locomotion than previously appreciated

Lifshitz fermionic theories with z=2 anisotropic scaling

We construct fermionic Lagrangians with anisotropic scaling z=2, the natural counterpart of the usual z=2 Lifshitz field theories for scalar fields. We analyze the issue of chiral symmetry, construct the Noether axial currents and discuss the chiral anomaly giving explicit results for two-dimensional case. We also exploit the connection between detailed balance and the dynamics of Lifshitz theories to find different z=2 fermionic Lagrangians and construct their supersymmetric extensions.Comment: Typos corrected, comment adde

First-order supersymmetric sigma models and target space geometry

We study the conditions under which N=(1,1) generalized sigma models support an extension to N=(2,2). The enhanced supersymmetry is related to the target space complex geometry. Concentrating on a simple situation, related to Poisson sigma models, we develop a language that may help us analyze more complicated models in the future. In particular, we uncover a geometrical framework which contains generalized complex geometry as a special case.Comment: 1+19 pages, JHEP style, published versio

Relating harmonic and projective descriptions of N=2 nonlinear sigma models

Recent papers have established the relationship between projective superspace and a complexified version of harmonic superspace. We extend this construction to the case of general nonlinear sigma models in both frameworks. Using an analogy with Hamiltonian mechanics, we demonstrate how the Hamiltonian structure of the harmonic action and the symplectic structure of the projective action naturally arise from a single unifying action on a complexified version of harmonic superspace. This links the harmonic and projective descriptions of hyperkahler target spaces. For the two examples of Taub-NUT and Eguchi-Hanson, we show how to derive the projective superspace solutions from the harmonic superspace solutions.Comment: 25 pages; v3: typo fixed in eq (1.36

Covariant path integral for chiral p-forms

The covariant path integral for chiral bosons obtained by McClain, Wu and Yu is generalized to chiral p-forms. In order to handle the reducibility of the gauge transformations associated with the chiral p-forms and with the new variables (in infinite number) that must be added to eliminate the second class constraints, the field-antifield formalism is used.Comment: revtex, 9 pages, submitted to Physical Review