A Metric for Gradient RG Flow of the Worldsheet Sigma Model Beyond First Order

Tseytlin has recently proposed that an action functional exists whose gradient generates to all orders in perturbation theory the Renormalization Group (RG) flow of the target space metric in the worldsheet sigma model. The gradient is defined with respect to a metric on the space of coupling constants which is explicitly known only to leading order in perturbation theory, but at that order is positive semi-definite, as follows from Perelman's work on the Ricci flow. This gives rise to a monotonicity formula for the flow which is expected to fail only if the beta function perturbation series fails to converge, which can happen if curvatures or their derivatives grow large. We test the validity of the monotonicity formula at next-to-leading order in perturbation theory by explicitly computing the second-order terms in the metric on the space of coupling constants. At this order, this metric is found not to be positive semi-definite. In situations where this might spoil monotonicity, derivatives of curvature become large enough for higher order perturbative corrections to be significant.Comment: 15 pages; Erroneous sentence in footnote 14 removed; this version therefore supersedes the published version (our thanks to Dezhong Chen for the correction

Generic metrics and the mass endomorphism on spin three-manifolds

Let $(M,g)$ be a closed Riemannian spin manifold. The constant term in the expansion of the Green function for the Dirac operator at a fixed point $p\in M$ is called the mass endomorphism in $p$ associated to the metric $g$ due to an analogy to the mass in the Yamabe problem. We show that the mass endomorphism of a generic metric on a three-dimensional spin manifold is nonzero. This implies a strict inequality which can be used to avoid bubbling-off phenomena in conformal spin geometry.Comment: 8 page

A characterization of Dirac morphisms

Relating the Dirac operators on the total space and on the base manifold of a horizontally conformal submersion, we characterize Dirac morphisms, i.e. maps which pull back (local) harmonic spinor fields onto (local) harmonic spinor fields.Comment: 18 pages; restricted to the even-dimensional cas

Surgery and the Spectrum of the Dirac Operator

We show that for generic Riemannian metrics on a simply-connected closed spin manifold of dimension at least 5 the dimension of the space of harmonic spinors is no larger than it must be by the index theorem. The same result holds for periodic fundamental groups of odd order. The proof is based on a surgery theorem for the Dirac spectrum which says that if one performs surgery of codimension at least 3 on a closed Riemannian spin manifold, then the Dirac spectrum changes arbitrarily little provided the metric on the manifold after surgery is chosen properly.Comment: 23 pages, 4 figures, to appear in J. Reine Angew. Mat

On the Protective Role of Identification with a Stigmatized Identity:Promoting Engagement and Discouraging Disengagement Coping Strategies

We examined the mechanisms by which identification with a stigmatized ingroup impacts well-being in stigmatized groups. The first three studies were conducted among gay men and lesbians in Europe and North America. Results support the idea that identification with homosexuals protects well-being by decreasing attempts at self-group distancing. Pursuit of self-group distancing was negatively related to well-being (studies 1 to 3a, N=1055). Other coping strategies were associated with identification but had no relationship with well-being. Identification was positively related to engagement coping strategies, namely, collective action, group affirmation and ingroup support, and negative related to disengagement strategies: ingroup blaming and avoidance of discrimination. A fourth study (study 3b) examined these mechanisms among Black North Americans (N=203). Again, identification was positively related to engagement strategies, and negatively related to disengagement; however, only collective action (positively) predicted well-being. Results are discussed in terms of how the effectiveness of different strategies for coping with stigma will differ depending on qualities of the identities in question and the specifics of the intergroup context

A Gradient Flow for Worldsheet Nonlinear Sigma Models

We discuss certain recent mathematical advances, mainly due to Perelman, in the theory of Ricci flows and their relevance for renormalization group (RG) flows. We consider nonlinear sigma models with closed target manifolds supporting a Riemannian metric, dilaton, and 2-form B-field. By generalizing recent mathematical results to incorporate the B-field and by decoupling the dilaton, we are able to describe the 1-loop beta-functions of the metric and B-field as the components of the gradient of a potential functional on the space of coupling constants. We emphasize a special choice of diffeomorphism gauge generated by the lowest eigenfunction of a certain Schrodinger operator whose potential and kinetic terms evolve along the flow. With this choice, the potential functional is the corresponding lowest eigenvalue, and gives the order alpha' correction to the Weyl anomaly at fixed points of (g(t),B(t)). Since the lowest eigenvalue is monotonic along the flow and reproduces the Weyl anomaly at fixed points, it accords with the c-theorem for flows that remain always in the first-order regime. We compute the Hessian of the lowest eigenvalue functional and use it to discuss the linear stability of points where the 1-loop beta-functions vanish, such as flat tori and K3 manifolds.Comment: Accepted version for publication. Citations added to Friedan and to Fateev, Onofri, and Zamolodchikov. Introduction modified slightly to discuss these citations. 25 pages, LaTe

The Dirac operator on generalized Taub-NUT spaces

We find sufficient conditions for the absence of harmonic $L^2$ spinors on spin manifolds constructed as cone bundles over a compact K\"ahler base. These conditions are fulfilled for certain perturbations of the Euclidean metric, and also for the generalized Taub-NUT metrics of Iwai-Katayama, thus proving a conjecture of Vi\csinescu and the second author.Comment: Final version, 16 page

Chemical and vibratory signals used in alarm communication in the termite Reticulitermes flavipes (Rhinotermitidae)

Termites have evolved diverse defence strategies to protect themselves against predators, including a complex alarm communication system based on vibroacoustic and/or chemical signals. In reaction to alarm signals, workers and other vulnerable castes flee away while soldiers, the specialized colony defenders, actively move toward the alarm source. In this study, we investigated the nature of alarm communication in the pest Reticulitermes flavipes. We found that workers and soldiers of R. flavipes respond to various danger stimuli using both vibroacoustic and chemical alarm signals. Among the danger stimuli, the blow of air triggered the strongest response, followed by crushed soldier head and light flash. The crushed soldier heads, which implied the alarm pheromone release, had the longest-lasting effect on the group behaviour, while the responses to other stimuli decreased quickly. We also found evidence of a positive feedback, as the release of alarm pheromones increased the vibratory communication among workers and soldiers. Our study demonstrates that alarm modalities are differentially expressed between castes, and that the response varies according to the nature of stimuli