Symmetries are not only fascinating, but they can also be exploited when designing numerical algorithms and data structures for scientific engineering problems in symmetrical domains. Geometrical symmetries are studied, particularly in the context of so called equivariant operators, which are relevant to a wide range of numerical applications. In these cases, it is possible to exploit the symme...

Compact Type IIB D = 4, N = 1 orientifolds have certain U(1) σ-model symmetries at the level of the effective Lagrangian. These symmetries are generically anomalous. We study the particular case of ZN orientifolds and find that these anomalies may be cancelled by a generalized Green-Schwarz mechanism. This mechanism works by the exchange of twisted RR-fields associated to the orbifold singulari...

Using the concept of variational tricomplex endowed with a presymplectic structure, we formulate the general notion of symmetry. We show that each generalized symmetry of a gauge system gives rise to a sequence of conservation laws that are represented by onshell closed forms of various degrees. This extends the usual Noether’s correspondence between global symmetries and conservation laws to t...

Autosimilar melodies put together the interplay of several melodies within a monody, the augmentations of a given melody, and the notion of autosimilarity which is well known in fractal objects. From a mathematical study of their properties, arising from experimentations by their inventor, composer Tom Johnson, we have generalized the notion towards the dual aspects of the group of symmetries o...

We study the symmetries of the two dimensional Heterotic string theory by following the approach of Kinnersley et al for the study of stationary axially-symmetric Einstein-Maxwell equations. We identify the finite dimensional symmetries which are the analogues of the groups G and H ′ for the Einstein-Maxwell equations. We also give the constructions for the infinite number of conserved currents...

We show that symmetries and gauge symmetries of a large class of 2-dimensional σ-models are described by a new type of a current algebra. The currents are labeled by pairs of a vector field and a 1-form on the target space of the σ-model. We compute the current-current commutator and analyse the anomaly cancellation condition, which can be interpreted geometrically in terms of Dirac structures,...

Considering the existence of nonconformal stochastic fluctuations in the metric tensor a generalized uncertainty principle and a deformed dispersion relation (associated to the propagation of photons) are deduced. Matching our model with the so called quantum κ–Poincaré group will allow us to deduce that the fluctuation–dissipation theorem could be fulfilled without needing a restoring mechanis...

We study pure exchange economies with symmetries on preferences up to taste intensity transformations. In a 2-person, 2-good endowment economy, we show that bilateral symmetry on each utility functional precludes a rectangle in the Edgeworth box as the location of Pareto optimal allocations. Under strictly quasi-concave preferences, a larger set can be ruled out. The inadmissible region is stil...

The notion of a weak chimeras provides a tractable definition for chimera states in networks of finitely many phase oscillators. Here, we generalize the definition of a weak chimera to a more general class of equivariant dynamical systems by characterizing solutions in terms of the isotropy of their angular frequency vector-for coupled phase oscillators the angular frequency vector is given by ...

Adding symmetry breaking constraints is one of the oldest ways of breaking variable symmetries for CSPs. For instance, it is well known that all the symmetries for the pigeon hole problem can be removed by ordering the variables. We have generalized this result to all CSPs where the variables are subject to an all different constraint. In such case it is possible to remove all variable symmetri...