Some Pathways in non-Linear Supersymmetry: Special Geometry Born-Infeld's, Cosmology and dualities

This review is devoted to some aspects of non-linear Supersymmetry in four dimensions that can be efficiently described via nilpotent superfields, in both rigid and curved Superspace. Our focus is mainly on the partial breaking of rigid $N=2$ Supersymmetry and on a class of generalized Born-Infeld systems that originate from Special Geometry and on some prototype cosmological models, starting from the Supergravity embedding of Starobinsky inflation. However, as an aside we also review briefly some interesting two-field extensions of the Born-Infeld Lagrangian whose field equations enjoy extended duality symmetries.Comment: Contribution to the Proceedings of "Group Theory, Probability, and the Structure of Spacetime", A Conference on the Occasion of Professor V.S. Varadarajan's Retirement, UCLA Mathematics Department, November 7-9, 2014. To appear in a special issue of "p-Adic Numbers, Ultrametric Analysis and Applications". 35 pages LaTeX, 1 eps figure. Typos corrected, reference adde

Massive Born--Infeld and Other Dual Pairs

We consider massive dual pairs of p-forms and (D-p-1)-forms described by non-linear Lagrangians, where non-linear curvature terms in one theory translate into non-linear mass-like terms in the dual theory. In particular, for D=2p and p even the two non-linear structures coincide when the non-linear massless theory is self-dual. This state of affairs finds a natural realization in the four-dimensional massive N=1 supersymmetric Born-Infeld action, which describes either a massive vector multiplet or a massive linear (tensor) multiplet with a Born-Infeld mass-like term. These systems should play a role for the massive gravitino multiplet obtained from a partial super-Higgs in N=2 Supergravity.Comment: 17 pages, LaTeX. Misprints corrected. Final version to appear in JHE

Doubly Self-Dual Actions in Various Dimensions

The self-duality of the N=1 supersymmetric Born--Infeld action implies a double self-duality of the tensor multiplet square-root action when the scalar and the antisymmetric tensor are interchanged via Poincare' duality. We show how this phenomenon extends to D space-time dimensions for non-linear actions involving pairs of forms of rank p and D-p-2. As a byproduct, we construct a new two-field generalization of the Born-Infeld action whose equations of motion are invariant under a U(1) duality. In these systems, the introduction of Green-Schwarz terms results in explicit non-linear mass-like terms for dual massive pairs.Comment: 17 pages, LaTeX. References added, duality group of eq. (4.16) changed to SU(2). Final version to appear in JHE

Cosmology and Supergravity

Abdus Salam was a true master of 20th Century Theoretical Physics. Not only was he a pioneer of the Standard Model (for which he shared the Nobel Prize with S. Glashow and S.Weinberg), but he also (co)authored many other outstanding contributions to the field of Fundamental Interactions and their unification. In particular, he was a major contributor to the development of supersymmetric theories, where he also coined the word "Supersymmetry" (replacing the earlier "Supergauges" drawn from String Theory). He also introduced the basic concept of "Superspace" and the notion of "Goldstone Fermion"(Goldstino). These concepts proved instrumental for the exploration of the ultraviolet properties and for the study of spontaneously broken phases of super Yang-Mills theories and Supergravity. They continue to play a key role in current developments in Early-Universe Cosmology. In this contribution we review models of inflation based on Supergravity with spontaneously broken local supersymmetry, with emphasis on the role of nilpotent superfields to describe a de Sitter phase of our Universe.Comment: 20 pages, Latex. Contribution to the Proceedings of the "Memorial Meeting for Nobel Laureate Prof. Abdus Salam's 90th Birthday", Nanyang Technological University, Singapore, 25-28 January 2016. arXiv admin note: text overlap with arXiv:1509.0150

Scale invariant Volkov-Akulov Supergravity

A scale invariant Goldstino theory coupled to Supergravity is obtained as a standard supergravity dual of a rigidly scale invariant higher--curvature Supergravity with a nilpotent chiral scalar curvature. The bosonic part of this theory describes a massless scalaron and a massive axion in a de Sitter Universe.Comment: CERN-PH-TH-2015-193. Misprints corrected. Final version to appear in Phys. Lett.

Two-Field Born-Infeld with Diverse Dualities

We elaborate on how to build, in a systematic fashion, two-field Abelian extensions of the Born-Infeld Lagrangian. These models realize the non-trivial duality groups that are allowed in this case, namely U(2), SU(2) and U(1)xU(1). For each class, we also construct an explicit example. They all involve an overall square root and reduce to the Born-Infeld model if the two fields are identified, but differ in quartic and higher interactions. The U(1)xU(1) and SU(2) examples recover some recent results obtained with different techniques, and we show that the U(1)xU(1) model admits an N=1 supersymmetric completion. The U(2) example includes some unusual terms that are not analytic at the origin of field space.Comment: 30 pages. Final version with reference added, typo corrected and comment added in the Conclusions. To appear in a special Nucl. Phys. B issue dedicated to the memory of Raymond Stor

Comments on the classification of orientifolds

The simple current construction of orientifolds based on rational conformal field theories is reviewed. When applied to SO(16) level 1, one can describe all ten-dimensional orientifolds in a unified framework.Comment: 9 pages, Contribution to proceedings of RTN-workshop in Leuven, Belgium, September 200

Generalized Born--Infeld Actions and Projective Cubic Curves

We investigate $U(1)^{\,n}$ supersymmetric Born-Infeld Lagrangians with a second non-linearly realized supersymmetry. The resulting non-linear structure is more complex than the square root present in the standard Born-Infeld action, and nonetheless the quadratic constraints determining these models can be solved exactly in all cases containing three vector multiplets. The corresponding models are classified by cubic holomorphic prepotentials. Their symmetry structures are associated to projective cubic varieties.Comment: 17 pages, LaTeX, 1 eps figure. Comments added and misprints corrected. Final version to appear in Fortschritte der Physik - Progress of Physic

Mass scales, supersymmetry breaking and open strings

We review physical motivations and possible realizations of string vacua with large internal volume and/or low string scale and discuss the issue of supersymmetry breaking. In particular, we describe the key features of Scherk-Schwarz deformations in type I models and conclude by reviewing the phenomenon of ``brane supersymmetry breaking'': the tadpole conditions of some type-I models require that supersymmetry be {\it broken at the string scale} on a collection of branes, while being exact, to lowest order, in the bulk and on other branes.Comment: Based on talks presented by the authors at STRINGS '99. Submitted to Classical and Quantum Gravity. misprints correcte

Degeneracy Between the Regge Slope of Mesons and Baryons from Supersymmetry

We consider the degeneracy between the Regge slope of mesons and baryons in QCD. We argue that within the "orientifold large-N approximation" asymptotically massive mesons and baryons become supersymmetric partners and hence degenerate. To this end, we generalize QCD by a SU(N) theory with a quark in the two-index antisymmetric representation. We show that in this framework the meson is represented by an oriented bosonic QCD-string and the baryon is represented by an un-oriented fermionic QCD-string. At large-N, due to an equivalence with super Yang-Mills, the tensions of the bosonic and the fermionic strings coincide. Our description of mesons and baryons as oriented and un-oriented bosonic and fermionic QCD-strings is in full agreement with the spectra of open strings in the dual type 0' string theory.Comment: v2: extended version. Appendices and references adde