The Quantized O(1,2)/O(2)×Z2O(1,2)/O(2)\times Z_2 Sigma Model Has No Continuum Limit in Four Dimensions. I. Theoretical Framework

The nonlinear sigma model for which the field takes its values in the coset space $O(1,2)/O(2)\times Z_2$ is similar to quantum gravity in being perturbatively nonrenormalizable and having a noncompact curved configuration space. It is therefore a good model for testing nonperturbative methods that may be useful in quantum gravity, especially methods based on lattice field theory. In this paper we develop the theoretical framework necessary for recognizing and studying a consistent nonperturbative quantum field theory of the $O(1,2)/O(2)\times Z_2$ model. We describe the action, the geometry of the configuration space, the conserved Noether currents, and the current algebra, and we construct a version of the Ward-Slavnov identity that makes it easy to switch from a given field to a nonlinearly related one. Renormalization of the model is defined via the effective action and via current algebra. The two definitions are shown to be equivalent. In a companion paper we develop a lattice formulation of the theory that is particularly well suited to the sigma model, and we report the results of Monte Carlo simulations of this lattice model. These simulations indicate that as the lattice cutoff is removed the theory becomes that of a pair of massless free fields. Because the geometry and symmetries of these fields differ from those of the original model we conclude that a continuum limit of the $O(1,2)/O(2)\times Z_2$ model which preserves these properties does not exist.Comment: 25 pages, no figure

Student politics, teaching politics, black politics: an interview with Ansel Wong

Ansel Wong is the quiet man of British black politics, rarely in the limelight and never seeking political office. And yet his ‘career’ here – from Black Power firebrand to managing a multimillion budget as head of the Greater London Council’s Ethnic Minority Unit in the 1980s – spells out some of the most important developments in black educational and cultural projects. In this interview, he discusses his identification with Pan-Africanism, his involvement in student politics, his role in the establishment of youth projects and supplementary schools in the late 1960s and 1970s, and his involvement in black radical politics in London in the same period, all of which took place against the background of revolutionary ferment in the Third World and the world of ideas, and were not without their own internal class and ethnic conflicts

The Quantized O(1,2)/O(2)×Z2O(1,2)/O(2)\times Z_2 Sigma Model Has No Continuum Limit in Four Dimensions. II. Lattice Simulation

A lattice formulation of the $O(1,2)/O(2)\times Z_2$ sigma model is developed, based on the continuum theory presented in the preceding paper. Special attention is given to choosing a lattice action (the ``geodesic'' action) that is appropriate for fields having noncompact curved configuration spaces. A consistent continuum limit of the model exists only if the renormalized scale constant $\beta_R$ vanishes for some value of the bare scale constant~$\beta$. The geodesic action has a special form that allows direct access to the small-$\beta$ limit. In this limit half of the degrees of freedom can be integrated out exactly. The remaining degrees of freedom are those of a compact model having a $\beta$-independent action which is noteworthy in being unbounded from below yet yielding integrable averages. Both the exact action and the $\beta$-independent action are used to obtain $\beta_R$ from Monte Carlo computations of field-field averages (2-point functions) and current-current averages. Many consistency cross-checks are performed. It is found that there is no value of $\beta$ for which $\beta_R$ vanishes. This means that as the lattice cutoff is removed the theory becomes that of a pair of massless free fields. Because these fields have neither the geometry nor the symmetries of the original model we conclude that the $O(1,2)/O(2)\times Z_2$ model has no continuum limit.Comment: 32 pages, 7 postscript figures, UTREL 92-0

Breast Cancer Polygenic Risk Score and Contralateral Breast Cancer Risk.

Previous research has shown that polygenic risk scores (PRSs) can be used to stratify women according to their risk of developing primary invasive breast cancer. This study aimed to evaluate the association between a recently validated PRS of 313 germline variants (PRS313) and contralateral breast cancer (CBC) risk. We included 56,068 women of European ancestry diagnosed with first invasive breast cancer from 1990 onward with follow-up from the Breast Cancer Association Consortium. Metachronous CBC risk (N = 1,027) according to the distribution of PRS313 was quantified using Cox regression analyses. We assessed PRS313 interaction with age at first diagnosis, family history, morphology, ER status, PR status, and HER2 status, and (neo)adjuvant therapy. In studies of Asian women, with limited follow-up, CBC risk associated with PRS313 was assessed using logistic regression for 340 women with CBC compared with 12,133 women with unilateral breast cancer. Higher PRS313 was associated with increased CBC risk: hazard ratio per standard deviation (SD) = 1.25 (95%CI = 1.18-1.33) for Europeans, and an OR per SD = 1.15 (95%CI = 1.02-1.29) for Asians. The absolute lifetime risks of CBC, accounting for death as competing risk, were 12.4% for European women at the 10th percentile and 20.5% at the 90th percentile of PRS313. We found no evidence of confounding by or interaction with individual characteristics, characteristics of the primary tumor, or treatment. The C-index for the PRS313 alone was 0.563 (95%CI = 0.547-0.586). In conclusion, PRS313 is an independent factor associated with CBC risk and can be incorporated into CBC risk prediction models to help improve stratification and optimize surveillance and treatment strategies