Massless radiation from Strings: quantum spectrum average statistics and cusp-kink configurations

We derive general formulae for computing the average spectrum for Bosonic or Fermionic massless emission from generic or particular sets of closed superstring quantum states, among the many occurring at a given large value of the number operator. In particular we look for states that can produce a Bosonic spectrum resembling the classical spectrum expected for peculiar cusp-like or kink-like classical configurations, and we perform a statistical counting of their average number. The results can be relevant in the framework of possible observations of the radiation emitted by cosmic strings.Comment: 13 pages, 4 figures, improved explanations, an appendix added on rotating folded strin

Handbook on string decay

We explain simple semi-classical rules to estimate the lifetime of any given highly-excited quantum state of the string spectrum in flat spacetime. We discuss both the decays by splitting into two massive states and by massless emission. As an application, we study a solution describing a rotating and pulsating ellipse which becomes folded at an instant of time -- the ``squashing ellipse''. This string interpolates between the folded string with maximum angular momentum and the pulsating circular string. We explicitly compute the quantum decay rate for the corresponding quantum state, and verify the basic rules that we propose. Finally, we give a more general (4-parameter) family of closed string solutions representing rotating and pulsating elliptical strings.Comment: 18 pages, 9 figures. Final version appeared in JHE

Search for the most stable massive state in superstring theory

In ten dimensional type II superstring, all perturbative massive states are unstable, typically with a short lifetime compared to the string scale. We find that the lifetime of the average string state of mass M has the asymptotic form T < const.1/(g^2 M). The most stable string state seems to be a certain state with high angular momentum which can be classically viewed as a circular string rotating in several planes ("the rotating ring"), predominantly decaying by radiating soft massless NS-NS particles, with a lifetime T = c_0 M^5/g^2. Remarkably, the dominant channel is the decay into a similar rotating ring state of smaller mass. The total lifetime to shrink to zero size is ~ M^7. In the presence of D branes, decay channels involving open strings in the final state are exponentially suppressed, so the lifetime is still proportional to M^5, except for a D brane at a special angle or flux. For large mass, the spectrum for massless emission exhibits qualitative features typical of a thermal spectrum, such as a maximum and an exponential tail. We also discuss the decay properties of rotating rings in the case of compact dimensions.Comment: 24 pages, 1 figure. Correction on lifetime of average stat

Electromagnetic corrections in the anomaly sector

Chiral perturbation theory in the anomaly sector for $N_f=2$ is extended to include dynamical photons, thereby allowing a complete treatment of isospin breaking. A minimal set of independent chiral lagrangian terms is determined and the divergence structure is worked out. There are contributions from irreducible and also from reducible one-loop graphs, a feature of ChPT at order larger than four. The generating functional is non-anomalous at order $e^2p^4$, but not necessarily at higher order in $e^2$. Practical applications to $\gamma\pi\to\pi\pi$ and to the $\pi^0\to2\gamma$ amplitudes are considered. In the latter case, a complete discussion of the corrections beyond current algebra is presented including quark mass as well as electromagnetic effects.Comment: 26 pages, 3 figure

Decoupling of Degenerate Positive-norm States in Witten's String Field Theory

We show that the degenerate positive-norm physical propagating fields of the open bosonic string can be gauged to the higher rank fields at the same mass level. As a result, their scattering amplitudes can be determined from those of the higher spin fields. This phenomenon arises from the existence of two types of zero-norm states with the same Young representations as those of the degenerate positive-norm states in the old covariant first quantized (OCFQ) spectrum. This is demonstrated by using the lowest order gauge transformation of Witten's string field theory (WSFT) up to the fourth massive level (spin-five), and is found to be consistent with conformal field theory calculation based on the first quantized generalized sigma-model approach. In particular, on-shell conditions of zero-norm states in OCFQ stringy gauge transformation are found to correspond, in a one-to-one manner, to the background ghost fields in off-shell gauge transformation of WSFT. The implication of decoupling of scalar modes on Sen's conjectures was also briefly discussed.Comment: 18 pages, use Latex with revtex

Random walks and the Hagedorn transition

We study details of the approach to the Hagedorn temperature in string theory in various static spacetime backgrounds. We show that the partition function for a {\it single} string at finite temperature is the torus amplitude restricted to unit winding around Euclidean time. We use the worldsheet path integral to derive the statement that the the sum over random walks of the thermal scalar near the Hagedorn transition is precisely the image under a modular transformation of the sum over spatial configurations of a single highly excited string. We compute the radius of gyration of thermally excited strings in $AdS_D\times S^n$. We show that the winding mode indicates an instability despite the AdS curvature at large radius, and that the negative mass squared decreases with decreasing AdS radius, much like the type 0 tachyon. We add further arguments to statements by Barbon and Rabinovici, and by Adams {\it et. al.}, that the Euclidean AdS black hole can thought of as a condensate of the thermal scalar. We use this to provide circumstantial evidence that the condensation of the thermal scalar decouples closed string modes.Comment: 34 pages (7 of references), 5 figures. v2: Reference added, grant acknowledgement added, typos correcte

High prevalence of PRPH2 in autosomal dominant retinitis pigmentosa in france and characterization of biochemical and clinical features.

PURPOSE: To assess the prevalence of PRPH2 in autosomal dominant retinitis pigmentosa (adRP), to report 6 novel mutations, to characterize the biochemical features of a recurrent novel mutation, and to study the clinical features of adRP patients. DESIGN: Retrospective clinical and molecular genetic study. METHODS: Clinical investigations included visual field testing, fundus examination, high-resolution spectral-domain optical coherence tomography (OCT), fundus autofluorescence imaging, and electroretinogram (ERG) recording. PRPH2 was screened by Sanger sequencing in a cohort of 310 French families with adRP. Peripherin-2 protein was produced in yeast and analyzed by Western blot. RESULTS: We identified 15 mutations, including 6 novel and 9 previously reported changes in 32 families, accounting for a prevalence of 10.3% in this adRP population. We showed that a new recurrent p.Leu254Gln mutation leads to protein aggregation, suggesting abnormal folding. The clinical severity of the disease in examined patients was moderate with 78% of the eyes having 1-0.5 of visual acuity and 52% of the eyes retaining more than 50% of the visual field. Some patients characteristically showed vitelliform deposits or macular involvement. In some families, pericentral RP or macular dystrophy were found in family members while widespread RP was present in other members of the same families. CONCLUSIONS: The mutations in PRPH2 account for 10.3% of adRP in the French population, which is higher than previously reported (0%-8%) This makes PRPH2 the second most frequent adRP gene after RHO in our series. PRPH2 mutations cause highly variable phenotypes and moderate forms of adRP, including mild cases, which could be underdiagnosed

ANOMALIES IN QUANTUM FIELD THEORY AND DIFFERENTIAL GEOMETRY

Anomalies in field theory appeared first in perturbative computations involving Feynman diagrams. It is only recently that differential geometric techniques have been used to obtain the form of gauge and gravitational anomalies in a direct and simple way. This is possible because of the topological nature of the anomaly. In the first chapter of this thesis the gauged Wess-Zumino action is constructed by differential geometry methods. After reviewing the relevant techniques, an expression for the action valid in any (even) number of space-time dimensions is obtained. This expression is compared with Witten's result in four dimensions. The link between topology and the anomaly is provided by the appropriate index theorem. The index density is a supersymmetric invariant polynomial from which the anomaly and other related objects can be obtained through the use of the ''descent equations.'' A new proof of the Atiyah-Singer index theorem for the Dirac operator is presented. This proof is based on the use of a WKB approximation to evaluate the supertrace of the kernel for a supersymmetric hamiltonian. The necessary WKB techniques are developed and mechanical systems with bosonic and fermionic degrees of freedom are discussed