Supersymmetry anomalies and the Wess–Zumino model in a supergravity background

We briefly recall the procedure for computing the Ward identities in the presence of a regulator which violates the symmetry being considered. We compute the first nontrivial correction to the supersymmetry Ward identity of the Wess–Zumino model in the presence of background supergravity using dimensional regularization. We find that the result can be removed using a finite local counter term and so there is no supersymmetry anomaly.

An Explicit Large Deviation Analysis of the Spatial Cycle Huang–Yang–Luttinger Model

We introduce a family of ‘spatial’ random cycle Huang–Yang–Luttinger (HYL)-type models in which the counter-term only affects cycles longer than some cut-off that diverges in the thermodynamic limit. Here, spatial refers to the Poisson reference process of random cycle weights. We derive large deviation principles and explicit pressure expressions for these models, and use the zeroes of the rate functions to study Bose–Einstein condensation. The main focus is a large deviation analysis for the diverging counter term where we identify three different regimes depending on the scale of divergence with respect to the main large deviation scale. Our analysis derives explicit bounds in critical regimes using the Poisson nature of the random cycle distributions.

A Monte Carlo approach to the worldline formalism in curved space

We present a numerical method to evaluate worldline (WL) path integrals defined on a curved Euclidean space, sampled with Monte Carlo (MC) techniques. In particular, we adopt an algorithm known as YLOOPS with a slight modification due to the introduction of a quadratic term which has the function of stabilizing and speeding up the convergence. Our method, as the perturbative counterparts, treats the non-trivial measure and deviation of the kinetic term from flat, as interaction terms. Moreover, the numerical discretization adopted in the present WLMC is realized with respect to the proper time of the associated bosonic point-particle, hence such procedure may be seen as an analogue of the time-slicing (TS) discretization already introduced to construct quantum path integrals in curved space. As a result, a TS counter-term is taken into account during the computation. The method is tested against existing analytic calculations of the heat kernel for a free bosonic point-particle in a D-dimensional maximally symmetric space.

Something new under the sun in secondary school: a case study

This paper reports on a case study carried out in an upper secondary school (grades 10-12), which for 17 years has established learning workshops, with interseriation and interdisciplinarity, as well as complementary distance learning. The establishment, located in the industrial City of Curitiba, Brazil, maintains agreements so that its students, electively, attend the technical education in the counter-term. The qualitative-quantitative methodology included documental analysis, observation, semi-structured interviews with principals, counselors, teachers and students and application of questionnaires to convenience samples of teachers and students. The results show that, according to social expectations, this school has become publicly different due to its methodologies and success in reconciling the preparation for higher studies and technical courses. Continuous assessment and parallel recovery reduce reprobation and abandonment to minimum levels. The predominant organizational image is that of the school as a company, with components of the bureaucratic model, to frame the innovations in the official molds, and the school’s image as culture. Implications of these organizational images are discussed.

Convergence in Quantum Field Theory without Use of Renormalization

In quantum field theory (QFT), it is well known that when Feynman diagrams containing loops are evaluated to account for self interactions, probability amplitude comes out to be infinite which is physically not admissible. So, to make the QFT convergent, various renormalization methods are conventionally followed in which an additional (infinite) counter term is postulated which neutralizes the original infinity generated by diagram. The resulting finite values of amplitudes have agreed with experiments with surprising accuracy. However, proponents of renormalization methods acknowledged that this ad-hoc procedure of subtraction of infinity from infinity to reach at a finite value is not at all satisfactory and there is no physical basis for bringing in the counter term. So, it is desirable to establish a method in QFT which does not generate any infinite term (thus not requiring renormalization), but which predicts same results as conventional methods do. In this paper, we describe such a technique taking self interaction quantum electrodynamics diagram representing electron or photon self energy. In our method, no problem of infinity arises and hence renormalization is not necessary. Still, the dependence of calculated probability amplitude on physical variables in our technique comes out to be same as conventional methods. Using similar procedure, we hope, the problem of non-renormalizability of quantum gravity may be solved in future.

Thermodynamics of rotating black branes in higher dimensional Einstein – nonlinear electrodynamics – dilaton gravity

In this paper, we propose a n-dimensional action in which gravity is coupled to exponential nonlinear electrodynamics and scalar dilaton field with Liouville-type potential. By varying the action, we obtain the field equations. Then, we construct a new class of charged, rotating black brane solutions, with k = [(n – 1)/2] rotation parameters, of this theory. Because of the presence of the Liouville-type dilaton potential, the asymptotic behavior of the obtained solutions is neither flat nor (anti)-de Sitter. We investigate the causal structure of the space–time in ample details. We find the suitable counter term that removes the divergences of the action in the presence of the dilaton field, and calculate the conserved and thermodynamic quantities of the space–time. Interestingly enough, we find that the conserved quantities crucially depend on the dilaton coupling constant, α, while they are independent of the nonlinear parameter, β. We also check the validity of the first law of thermodynamics on the black brane horizon. Finally, we study thermal stability of the solutions by computing the heat capacity in the canonical ensemble. We disclose the effects of rotation parameter, nonlinearity of electrodynamics, and dilaton field on the thermal stability conditions.

QUANTUM ANOMALIES AND SOME RECENT DEVELOPMENTS

Some of the developments related to quantum anomalies and path integrals during the past 10 years are briefly discussed. The covered subjects include the issues related to the local counter term in the context of 2-dimensional path integral bosonization and the treatment of chiral anomaly and index theorem on the lattice. We also briefly comment on a recent analysis of the connection between the two-dimensional chiral anomalies and the four-dimensional black hole radiation.

NEUTRINO PHYSICS AND NUCLEAR AXIAL TWO-BODY INTERACTIONS

We consider the counter-term describing isoscalar axial two-body currents in the nucleon–nucleon interaction, L1A, in the effective field theory approach. We determine this quantity using solar neutrino data. We investigate the variation of L1A when different sets of data are used.

ON THE DIFFERENTIAL EQUATIONS OF THE CHARACTERS FOR THE RENORMALIZATION GROUP

Owing to the analogy between the Connes–Kreimer theory of the renormalization and the integrable systems, we derive the differential equations of the unit mass for the renormalized character ϕ+ and the counter term ϕ-. We give another proof of the scattering type formula of ϕ-. The differential equation of ϕ- of the coordinate ε on ℙ1 is also given. The hierarchy of the renormalization groups is defined as the integrable systems.