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We present the explicit formulas relating Hopf maps with Wigner's little groups. They, particularly, explain simple action of group on a fiber for the first and second Hopf fibrations, and present most simplified form for the third one. Corresponding invariant Lagrangians are presented, and their possible reductions are discussed. [ABSTRACT FROM AUTHOR]

We review on a recent construction of the on-shell supersymmetric brane action for the codimension-two branes with nonzero tension in the flux compactification of a 6D chiral gauged supergravity. On dimensionally reducing on 4D gauged supergravity for a new supersymmetric unwarped background with conical branes, we consider the modulus stabilization for determining the soft masses of the scalars localized on the branes and show that the bulk U(1)R provides a new mechanism for mediating the SUSY breaking. [ABSTRACT FROM AUTHOR]

Even though the chaotic inflation is one of the most popular inflation models for its simple dynamics and compelling resolutions to the initial condition problems, its realization in supergravity has been considered a challenging task. We discuss how the chaotic inflation dominated by the D-term can be induced in supergravity, which would give a new perspective on the inflation model building in supergravity. [ABSTRACT FROM AUTHOR]

We have applied the method of dualization to construct the coset realization of the bosonic sector of the $\mathcal{N}=2$, D = 6 supergravity which is coupled to a tensor multiplet. The bosonic field equations are regained through the Cartan–Maurer equation which the Cartan form satisfies. The first-order formulation of the theory is also obtained as a twisted self-duality condition within the nonlinear coset construction. [ABSTRACT FROM AUTHOR]

We review some aspects of the spinorial geometry approach to the classification of supersymmetric solutions of supergravity theories. In particular, we explain how spinorial geometry can be used to express the Killing spinor equations in terms of a linear system for the fluxes and the geometry of spacetime. The solutions of this linear system express some of the fluxes in terms of the spacetime geometry and determine the conditions on the spacetime geometry imposed by supersymmetry. We also present some of the recent applications like the classification of maximally supersymmetric G-backgrounds in IIB, this includes the most general pp-wave solution preserving 1/2 supersymmetry, and the classification of N = 31 backgrounds in ten and eleven dimensions. [ABSTRACT FROM AUTHOR]

In the light-cone gauge choice for Abelian and non-Abelian gauge fields, the vector boson propagator carries in it an additional "spurious" or "unphysical" pole intrinsic to the choice requiring a careful mathematical treatment. Research in this field over the years has shown us that mathematical consistency only is not enough to guarantee physically meaningful results. Whatever the prescription invoked to handle such an object, it has to preserve causality in the process. On the other hand, the covariantization technique is a well-suited one to tackle gauge-dependent poles in the Feynman integrals, dispensing the use of ad hoc prescriptions. In this work we show that the covariantization technique in the light-cone gauge is a direct consequence of the canonical quantization of the theory. [ABSTRACT FROM AUTHOR]

We consider a particular solution to Slavnov–Taylor identity in four-dimensional supergravity. The consideration is performed for pure supergravity, no matter superfields are included. The solution is obtained by inserting dressing functions into ghost part of the classical action for supergravity. As a consequence, physical part of the effective action is local invariant with respect to diffeomorphism and structure groups of transformation for dressed effective superfields of vielbein and spin connection. [ABSTRACT FROM AUTHOR]

Entropy production by a dilaton decay is studied in the model where the dilaton acquires potential via gaugino condensation in the hidden gauge group. Its effect on the Affleck-Dine baryogenesis is investigated. It is shown that the baryon asymmetry produced by this mechanism with the higher-dimensional terms is diluted by the dilaton decay and can be regulated to the observed value. [ABSTRACT FROM AUTHOR]

Using the right representation in the evaluation of the creation probability of the universe, one can show that the external dimension of the Freund–Rubin model is min(s,n-s), where s is the rank of the antisymmetric field strength in the model. [ABSTRACT FROM AUTHOR]

Recent developments in string theory suggest that there might exist extra spatial dimensions, which are not small nor compact. The framework of most brane cosmological models is that the matter fields are confined on a brane-world embedded in five dimensions (the bulk). Motivated by this we re-examine the classification of the second-order symmetric tensors in 5-D, and prove two theorems which collect together some basic results on the algebraic structure of these tensors in five-dimensional spacetimes. We also briefly indicate how one can obtain, by induction, the classification of symmetric two-tensors (and the corresponding canonical forms) on n-dimensional (n>4) spaces from the classification on four-dimensional spaces. This is important in the context of 11-D supergravity and 10-D superstrings. [ABSTRACT FROM AUTHOR]

We study the ir dynamics of the type IIB supergravity solution describing N D3-branes and M fractional D3-branes on the resolved conifold. The baryon mass and the tension of domain wall in the dual gauge theory are evaluated and compared with those for the deformed conifold. The ir behavior of the solution for the general conifold is also discussed. We show that the area law behavior of the Wilson loop is attributed to the existence of the locus in the ir where the D3-brane charge vanishes. [ABSTRACT FROM AUTHOR]