On the universality of goldstino action

We find the Goldstino action descending from the N=1 Goldstone-Maxwell superfield action associated with the spontaneous partial supersymmetry breaking, N=2 to N=1, in superspace. The new Goldstino action has higher (second-order) spacetime derivatives, while it can be most compactly described as a solution to the simple recursive relation. Our action seems to be related to the standard (having only the first-order derivatives) Akulov-Volkov action for Goldstino via a field redefinition.Comment: 11 pages, LaTeX; a few misprints corrected, a footnote and a sentence adde

From N=2 strings to F&M theory

Taking the N=2 strings as the starting point, we discuss the equivalent self-dual field theories and analyse their symmetry structure in 2+2 dimensions. Restoring the full `Lorentz' invariance in the target space necessarily leads to an extension of the N=2 string theory to a theory of 2+2 dimensional supermembranes propagating in 2+10 dimensional target space. The supermembrane requires maximal conformal supersymmetry in 2+2 dimensions, in the way advocated by Siegel. The corresponding self-dual N=4 Yang-Mills theory and the self-dual N=8 (gauged) supergravity in 2+2 dimensions thus appear to be naturally associated to the membrane theory, not a string. Since the same theory of membranes seems to represent the M-theory which is apparently underlying the all known N=1 string theories, the N=2 strings now appear on equal footing with the other string models as particular limits of the unique fundamental theory. Unlike the standard 10-dimensional superstrings, the N=2 strings seem to be much closer to a membrane description of F&M theory.Comment: 9 pages, LaTeX, talk given at the International Workshop `Integrable Models and Strings', Garbsen, Germany, June 24--25, 199

Cosmological constant in F(R) supergravity

A cosmological constant in the regime of low space-time curvature is calculated in the recently proposed version of F(R) supergravity with a generic cubic function F. The F(R) supergravity is the N=1 supersymmetric extension of f(R) gravity. The cubic model is known to successfully describe a chaotic (slow-roll) inflation in the regime of high space-time curvature. We find that a simple extension of the same model allows a positive cosmological constant in the regime of low space-time curvature. The inflaton superfield in F(R) supergravity (like inflaton in f(R) gravity) violates the Strong Energy Condition and thus breaks the restriction of the standard supergravity (with usual matter) that can only have either a negative or vanishing cosmological constant.Comment: 10 pages, LaTeX, no figures; Introduction and Conclusion expanded, references adde

Dark Energy in Modified Supergravity

We propose a supersymmetric extension of the dynamical dark energy function and the corresponding scalar (super)potential in F(R) supergravity. Our model is viable in the Einstein approximation, and also has an analytic (regular) Wess-Zumino-type scalar superpotential. The hidden sector responsible for spontaneous supersymmetry breaking is given.Comment: LaTeX, 9 pages, 1 figure; secs. 2 and 3 extended, references updated, title and abstract revise

One-loop finiteness of the four-dimensional Donaldson-Nair-Schiff non-linear sigma-model

The most general four-dimensional non-linear sigma-model, having the second-order derivatives only and interacting with a background metric and an antisymmetric tensor field, is constructed. Despite its apparent non-renormalizability, just imposing the one-loop UV-finiteness conditions determines the unique model, which may be finite to all orders of the quantum perturbation theory. This model is known as the four-dimensional Donaldson-Nair-Schiff theory, which is a four-dimensional analogue of the standard two-dimensional Wess-Zumino-Novikov-Witten model, and whose unique finiteness properties and an infinite-dimensional current algebra have long been suspected.Comment: 11 pages, LaTeX, macros included; revised versio

F(R) supergravity

We review the F(R) supergravity recently proposed in Phys. Lett. B674 (2009) 59 and Class. Quantum Grav. 26 (2009) 135006. Our construction supersymmetrizes popular f(R) theories of modified gravity in four spacetime dimensions. We use curved superspace of N=1 Poincar'e supergravity in its minimal (2nd order) formulation so that our F(R) supergravity action is manifestly invariant under local N=1 supersymmetry. We prove that the F(R) supergravity is classically equivalent to the standard N=1 Poincar'e supergravity (minimally) coupled to a dynamical chiral superfield, via a Legendre-Weyl transform in superspace. A K"ahler potential, a superpotential and a scalar potential of the chiral superfield are governed by a single holomorphic function. We find the conditions of vanishing cosmological constant without fine-tuning, which define a no-scale F(R) supergravity.Comment: 10 pages; to appear in the Proceedings of International Conference `Invisible Universe', Paris, Palais de l'UNESCO, June 29 -July 3, 200