Statistical mechanics of strings with Y-junctions

We investigate the Hagedorn transitions of string networks with Y-junctions as may occur, for example, with (p,q) cosmic superstrings. In a simplified model with three different types of string, the partition function reduces to three generalised coupled XY models. We calculate the phase diagram and show that, as the system is heated, the lightest strings first undergo the Hagedorn transition despite the junctions. There is then a second, higher, critical temperature above which infinite strings of all tensions, and junctions, exist. Conversely, on cooling to low temperatures, only the lightest strings remain, but they collapse into small loops

Finite temperature corrections and embedded strings in noncommutative geometry and the standard model with neutrino mixing

The recent extension of the standard model to include massive neutrinos in the framework of noncommutative geometry and the spectral action principle involves new scalar fields and their interactions with the usual complex scalar doublet. After ensuring that they bring no unphysical consequences, we address the question of how these fields affect the physics predicted in Weinberg-Salam theory, particularly in the context of the Electroweak phase transition. Applying the Dolan-Jackiw procedure, we calculate the finite temperature corrections, and find that the phase transition is first order. The new scalar interactions significantly improve the stability of the Electroweak Z string, through the ``bag'' phenomenon described by Watkins and Vachaspati. (Recently cosmic strings have climbed back into interest due to new evidence). Sourced by static embedded strings, an internal space analogy of Cartan's torsion is drawn, and a possible Higgs-force-like `gravitational' effect of this non-propagating torsion on the fermion masses is described. We also check that the field generating the Majorana mass for the $\nu_R$ is non-zero in the physical vacuum.Comment: 42 page

Power-law tails from multiplicative noise

We show that the well-known Langevin equation, modeling the Brownian motion and leading to a Gaussian stationary distribution of the corresponding Fokker-Planck equation, is changed by the smallest multiplicative noise. This leads to a power-law tail of the distribution at large enough momenta. At finite ratio of the correlation strength for the multiplicative and additive noise the stationary energy distribution becomes exactly the Tsallis distribution.Comment: 4 pages, LaTeX, revtex4 style, 2 figure

A renormalized large-n solution of the U(n) x U(n) linear sigma model in the broken symmetry phase

Dyson-Schwinger equations for the U(n) x U(n) symmetric matrix sigma model reformulated with two auxiliary fields in a background breaking the symmetry to U(n) are studied in the so-called bare vertex approximation. A large n solution is constructed under the supplementary assumption so that the scalar components are much heavier than the pseudoscalars. The renormalizability of the solution is investigated by explicit construction of the counterterms.Comment: RevTeX4, 14 pages, 2 figures. Version published in Phys. Rev.

Estimating the risk of adverse birth outcomes in pregnant women undergoing non-obstetric surgery using routinely collected NHS data: an observational study

Background: Previous research suggests that non-obstetric surgery is carried out in 1 – 2% of all pregnancies. However, there is limited evidence quantifying the associated risks. Furthermore, of the evidence available, none relates directly to outcomes in the UK, and there are no current NHS guidelines regarding non-obstetric surgery in pregnant women. Objectives: To estimate the risk of adverse birth outcomes of pregnancies in which non-obstetric surgery was or was not carried out. To further analyse common procedure groups. Data Source: Hospital Episode Statistics (HES) maternity data collected between 2002 – 3 and 2011 – 12. Main outcomes: Spontaneous abortion, preterm delivery, maternal death, caesarean delivery, long inpatient stay, stillbirth and low birthweight. Methods: We utilised HES, an administrative database that includes records of all patient admissions and day cases in all English NHS hospitals. We analysed HES maternity data collected between 2002 – 3 and 2011 – 12, and identified pregnancies in which non-obstetric surgery was carried out. We used logistic regression models to determine the adjusted relative risk and attributable risk of non-obstetric surgical procedures for adverse birth outcomes and the number needed to harm. Results: We identified 6,486,280 pregnancies, in 47,628 of which non-obstetric surgery was carried out. In comparison with pregnancies in which surgery was not carried out, we found that non-obstetric surgery was associated with a higher risk of adverse birth outcomes, although the attributable risk was generally low. We estimated that for every 287 pregnancies in which a surgical operation was carried out there was one additional stillbirth; for every 31 operations there was one additional preterm delivery; for every 25 operations there was one additional caesarean section; for every 50 operations there was one additional long inpatient stay; and for every 39 operations there was one additional low-birthweight baby. Limitations: We have no means of disentangling the effect of the surgery from the effect of the underlying condition itself. Many spontaneous abortions will not be associated with a hospital admission and, therefore, will not be included in our analysis. A spontaneous abortion may be more likely to be reported if it occurs during the same hospital admission as the procedure, and this could account for the associated increased risk with surgery during pregnancy. There are missing values of key data items to determine parity, gestational age, birthweight and stillbirth. Conclusions: This is the first study to report the risk of adverse birth outcomes following non-obstetric surgery during pregnancy across NHS hospitals in England. We have no means of disentangling the effect of the surgery from the effect of the underlying condition itself. Our observational study can never attribute a causal relationship between surgery and adverse birth outcomes, and we were unable to determine the risk of not undergoing surgery where surgery was clinically indicated. We have some reservations over associations of risk factors with spontaneous abortion because of potential ascertainment bias. However, we believe that our findings and, in particular, the numbers needed to harm improve on previous research, utilise a more recent and larger data set based on UK practices, and are useful reference points for any discussion of risk with prospective patients. The risk of adverse birth outcomes in pregnant women undergoing non-obstetric surgery is relatively low, confirming that surgical procedures during pregnancy are generally safe. Future work: Further evaluation of the association of non-obstetric surgery and spontaneous abortion. Evaluation of the impact of non-obstetric surgery on the newborn (e.g. neonatal intensive care unit admission, prolonged length of neonatal stay, neonatal death). Funding: The National Institute for Health Research Health Services and Delivery Research programme

Study of chiral symmetry restoration in linear and nonlinear O(N) models using the auxiliary field method

We consider the O(N) linear {\sigma} model and introduce an auxiliary field to eliminate the scalar self-interaction. Using a suitable limiting process this model can be continuously transformed into the nonlinear version of the O(N) model. We demonstrate that, up to two-loop order in the CJT formalism, the effective potential of the model with auxiliary field is identical to the one of the standard O(N) linear {\sigma} model, if the auxiliary field is eliminated using the stationary values for the corresponding one- and two-point functions. We numerically compute the chiral condensate and the {\sigma}- and {\pi}-meson masses at nonzero temperature in the one-loop approximation of the CJT formalism. The order of the chiral phase transition depends sensitively on the choice of the renormalization scheme. In the linear version of the model and for explicitly broken chiral symmetry, it turns from crossover to first order as the mass of the {\sigma} particle increases. In the nonlinear case, the order of the phase transition turns out to be of first order. In the region where the parameter space of the model allows for physical solutions, Goldstone's theorem is always fulfilled.Comment: 25 pages, 9 figures, 1 table, improved versio