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

Determinants of outcome following surgery for oral squamous cell carcinoma

The recent changes in incidence and prevalence of oral squamous cell carcinoma in relation to gender and age mirror the changing patterns of exposure to tobacco and alcohol, the main etiological agents. Most cases of oral cancer are managed by surgery, often combined with radiotherapy. Histopathological assessment of the resection specimen provides information vital for postoperative management and prognosis. This review considers the full range of histological determinants of outcome in relation to the primary oral tumor and any metastatic involvement of the cervical lymphatic system, together with an outline of more general patient factors that may also impact on morbidity and mortality rates. </jats:p

The Positivity of Energy for Asymptotically Anti-de Sitter Spacetimes

We use the formulation of asymptotically anti-de Sitter boundary conditions given by Ashtekar and Magnon to obtain a coordinate expression for the general asymptotically AdeS metric in a neighbourhood of infinity. From this, we are able to compute the time delay of null curves propagating near infinity. If the gravitational mass is negative, so will be the time delay (relative to null geodesics at infinity) for certain null geodesics in the spacetime. Following closely an argument given by Penrose, Sorkin, and Woolgar, who treated the asymptotically flat case, we are then able to argue that a negative time delay is inconsistent with non-negative matter-energies in spacetimes having good causal properties. We thereby obtain a new positive mass theorem for these spacetimes. The theorem may be applied even when the matter flux near the boundary-at-infinity falls off so slowly that the mass changes, provided the theorem is applied in a time-averaged sense. The theorem also applies in certain spacetimes having local matter-energy that is sometimes negative, as can be the case in semi-classical gravity.Comment: (Plain TeX - figures not included

The Cosmic Censor Forbids Naked Topology

For any asymptotically flat spacetime with a suitable causal structure obeying (a weak form of) Penrose's cosmic censorship conjecture and satisfying conditions guaranteeing focusing of complete null geodesics, we prove that active topological censorship holds. We do not assume global hyperbolicity, and therefore make no use of Cauchy surfaces and their topology. Instead, we replace this with two underlying assumptions concerning the causal structure: that no compact set can signal to arbitrarily small neighbourhoods of spatial infinity (``$i^0$-avoidance''), and that no future incomplete null geodesic is visible from future null infinity. We show that these and the focusing condition together imply that the domain of outer communications is simply connected. Furthermore, we prove lemmas which have as a consequence that if a future incomplete null geodesic were visible from infinity, then given our $i^0$-avoidance assumption, it would also be visible from points of spacetime that can communicate with infinity, and so would signify a true naked singularity.Comment: To appear in CQG, this improved version contains minor revisions to incorporate referee's suggestions. Two revised references. Plain TeX, 12 page

Late disruption of central visual field disrupts peripheral perception of form and color.

Evidence from neuroimaging and brain stimulation studies suggest that visual information about objects in the periphery is fed back to foveal retinotopic cortex in a separate representation that is essential for peripheral perception. The characteristics of this phenomenon have important theoretical implications for the role fovea-specific feedback might play in perception. In this work, we employed a recently developed behavioral paradigm to explore whether late disruption to central visual space impaired perception of color. In the first experiment, participants performed a shape discrimination task on colored novel objects in the periphery while fixating centrally. Consistent with the results from previous work, a visual distractor presented at fixation ~100ms after presentation of the peripheral stimuli impaired sensitivity to differences in peripheral shapes more than a visual distractor presented at other stimulus onset asynchronies. In a second experiment, participants performed a color discrimination task on the same colored objects. In a third experiment, we further tested for this foveal distractor effect with stimuli restricted to a low-level feature by using homogenous color patches. These two latter experiments resulted in a similar pattern of behavior: a central distractor presented at the critical stimulus onset asynchrony impaired sensitivity to peripheral color differences, but, importantly, the magnitude of the effect was stronger when peripheral objects contained complex shape information. These results show a behavioral effect consistent with disrupting feedback to the fovea, in line with the foveal feedback suggested by previous neuroimaging studies

A uniqueness theorem for the adS soliton

The stability of physical systems depends on the existence of a state of least energy. In gravity, this is guaranteed by the positive energy theorem. For topological reasons this fails for nonsupersymmetric Kaluza-Klein compactifications, which can decay to arbitrarily negative energy. For related reasons, this also fails for the AdS soliton, a globally static, asymptotically toroidal $\Lambda<0$ spacetime with negative mass. Nonetheless, arguing from the AdS/CFT correspondence, Horowitz and Myers (hep-th/9808079) proposed a new positive energy conjecture, which asserts that the AdS soliton is the unique state of least energy in its asymptotic class. We give a new structure theorem for static $\Lambda<0$ spacetimes and use it to prove uniqueness of the AdS soliton. Our results offer significant support for the new positive energy conjecture and add to the body of rigorous results inspired by the AdS/CFT correspondence.Comment: Revtex, 4 pages; Matches published version. More detail in Abstract and one equation corrected. For details of proofs and further results, see hep-th/020408

Theorems on gravitational time delay and related issues

Two theorems related to gravitational time delay are proven. Both theorems apply to spacetimes satisfying the null energy condition and the null generic condition. The first theorem states that if the spacetime is null geodesically complete, then given any compact set $K$, there exists another compact set $K'$ such that for any $p,q \not\in K'$, if there exists a ``fastest null geodesic'', $\gamma$, between $p$ and $q$, then $\gamma$ cannot enter $K$. As an application of this theorem, we show that if, in addition, the spacetime is globally hyperbolic with a compact Cauchy surface, then any observer at sufficiently late times cannot have a particle horizon. The second theorem states that if a timelike conformal boundary can be attached to the spacetime such that the spacetime with boundary satisfies strong causality as well as a compactness condition, then any ``fastest null geodesic'' connecting two points on the boundary must lie entirely within the boundary. It follows from this theorem that generic perturbations of anti-de Sitter spacetime always produce a time delay relative to anti-de Sitter spacetime itself.Comment: 15 pages, 1 figure. Example of gauge perturbation changed/corrected. Two footnotes added and one footnote remove