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We reconsider the toy-model of topological inflation, based on the R*4-modified gravity. By using its equivalence to the certain scalar-tensor gravity model in four space-time dimensions, we compute the inflaton scalar potential and investigate a possibility of inflation. We confirm the existence of the slow-roll inflation with an exit. However, the model suffers from the eta-problem that gives rise to the unacceptable value of the spectral index n_s of scalar perturbations., Comment: 12 pages, 3 figures, LaTeX, misprints corrected and references updated

We revisit the old (fourth-order or quadratically generated) gravity model of Starobinsky in four space-time dimensions, and derive the (inflaton) scalar potential in the equivalent scalar-tensor gravity model via a Legendre-Weyl transform. The inflaton scalar potential is used to compute the (CMB) observables of inflation associated with curvature perturbations (namely, the scalar and tensor spectral indices, and the tensor-to-scalar ratio), including the new next-to-leading-order terms with respect to the inverse number of e-foldings. The results are compared to the recent (WMAP5) experimental bounds. We confirm both mathematical and physical equivalence between f(R) gravity theories and the corresponding scalar-tensor gravity theories., Comment: 10 pages, 1 figure, 1 table, LaTeX; few comments added, style improved, references added and updated

We consider the purely gravitational fourth-order (in the spacetime curvature) quantum corrections to the Einstein-Hilbert gravity action, coming from superstrings in the leading order with respect to the Regge slope parameter, and study their impact on the evolution of the Hubble scale in the context of the FRW cosmology, in four spacetime dimensions. We propose the generalized Friedmann equations, and rule out the most naive (Bel-Robinson tensor squared) gravity. Our new cosmological equations have exact inflationary solutions without a spacetime singularity., Comment: 8 pages, LaTeX, contribution to the Proceedings of Osaka Workshop `Progress of String Theory and Quantum Field Theory', December 7-10, 2007, at Osaka City University, Japan

A four-dimensional supergravity toy model in an arbitrary self-dual gravi-photon background is constructed in Euclidean space, by freezing out the gravi-photon field strength in the standard N=(1,1) extended supergravity with two non-chiral gravitini. Our model has local N=(1/2,0) supersymmetry. Consistency of the model requires the background gravi-photon field strength to be equal to the self-dual (bilinear) anti-chiral gravitino condensate., Comment: 8 pages, LaTeX, no figures; small additions, few references added

The well known relation between extended supersymmetry and complex geometry in the non-linear sigma-models is reviewed, and some recent developments related to the introduction of the non-anti-commutativity, in the context of the supersymmetric non-linear sigma-models formulated in extended superspace, are discussed. This contribution is suitable for both physicists and mathematicians interesting in the interplay between geometry, supersymmetry and noncommutativity., Comment: contribution to the International Workshop on Noncommutative Geometry and Physics, November 1-4, 2005, Sendai, Japan; 17 pages, LaTeX

The component structure of a generic N=1/2 supersymmetric Non-Linear Sigma-Model (NLSM) defined in the four-dimensional (Euclidean) Non-Anti-Commutative (NAC) superspace is investigated in detail.The most general NLSM is described in terms of arbitrary K"ahler potential,and chiral and anti-chiral superpotentials. The case of a single chiral superfield gives rise to splitting of the NLSM potentials, whereas the case of several chiral superfields results in smearing (or fuzziness) of the NLSM potentials, while both effects are controlled by the auxiliary fields. We eliminate the auxiliary fields by solving their algebraic equations of motion, and demonstrate that the results are dependent upon whether the auxiliary integrations responsible for the fuzziness are performed before or after elimination of the auxiliary fields. There is no ambiguity in the case of splitting, i.e. for a single chiral superfield. Fully explicit results are derived in the case of the N=1/2 supersymmetric NAC-deformed CP(n) NLSM in four dimensions. Here we find another surprise that our results differ from the N=1/2 supersymmetric CP(n) NLSM derived by the quotient construction from the N=1/2 supersymmetric NAC-deformed gauge theory. We conclude that an N=1/2 supersymmetric deformation of a generic NLSM from the NAC superspace is not unique., Comment: 16 pages, LaTeX, no figures

We offer a simple non-perturbative formula for the component action of a generic N=1/2 supersymmetric chiral model in terms of an arbitrary number of chiral superfields in four dimensions, which is obtained by the Non-Anti-Commutative (NAC) deformation of a generic four-dimensional N=1 supersymmetric non-linear sigma-model described by arbitrary Kaehler superpotential and scalar superpotential. The auxiliary integrations responsible for fuzziness are eliminated in the case of a single chiral superfield. The scalar potential in components is derived by eliminating the auxiliary fields. The NAC-deformation of the CP(1) Kaehler non-linear sigma-model with an arbitrary scalar superpotential is calculated as an example., Comment: 9 pages, LaTeX, no figures; section 5 and references added

We studied a nilpotent Non-Anti-Commutative (NAC) deformation of the effective superpotentials in supersymmetric gauge theories, caused by a constant self-dual graviphoton background. We derived the simple non-perturbative formula applicable to any NAC (star) deformed chiral superpotential. It is remarkable that the deformed superpotential is always `Lorentz'-invariant. As an application, we considered the NAC deformation of the pure super-Yang-Mills theory whose IR physics is known to be described by the Veneziano-Yankielowicz superpotential (in the undeformed case). The unbroken gauge invariance of the deformed effective action gives rise to severe restrictions on its form. We found a non-vanishing gluino condensate in vacuum but no further dynamical supersymmetry breaking in the deformed theory., Comment: 20 pages, LaTeX; small changes, additions and references added

We calculate the charged hypermultiplet low-energy effective action in the Coulomb branch of the 4D, N=2 gauge theory, by using the harmonic superspace approach. We find that the unique leading contribution is given by the harmonic-analytic Lagrangian of the fourth order in the hypermultiplet superfields, with the induced coupling constant being proportional to central charges of N=2 SUSY algebra. The central charges are identified with Cartan generators of the internal symmetry, and they give BPS masses to the hypermultiplets. The induced hyper-K"ahler metrics appear to be the Taub-NUT metric or its higher-dimensional generalizations. Simultaneously, non-trivial scalar potentials are produced. Within the harmonic superspace method, we show an equivalence between the two known approaches to the 4D central charges. In the first one, the central charges are obtained via the Scherk-Schwarz dimensional reduction from six dimensions, whereas in the second one they are generated by a covariantly-constant background gauge superfield. Our analysis is extended to a more general situation with the non-vanishing Fayet-Iliopoulos (FI) terms. The perturbatively-induced Taub-NUT self-coupling in the Coulomb branch is found to be stable against adding the FI term, whereas the non-perturbatively generated (Eguchi-Hanson type) hypermultiplet self-interaction is proposed for the Higgs branch., Comment: 30 pages, LaTeX, macros included; minor revisions in sects. 5 and 6, as well as in the references

Based on our previous studies of the BRST cohomology of the critical N=2 strings, we construct the loop measure and make explicit the role of the spectral flow at arbitrary genus and Chern class, in a holomorphic field basis. The spectral flow operator attributes to the existence of the hidden `small' N=4 superconformal symmetry which is non-linearly realized. We also discuss the symmetry properties of N=2 string amplitudes on locally-flat backgrounds., Comment: 7 pages, Talk given at the International Workshop on Strings, Gravity and Related Topics, 29--30 June 1995, ICTP, Trieste, Italy

We investigate in detail the critical $N{=}2$ fermionic string with and without a global ${\bf Z}_2$ twist. An analysis of BRST cohomology shows that twisted sectors contain massless `spacetime' fermions which are {\it non-local\/} with respect to the standard massless boson. However, two distinct GSO projections exist, one (untwisted) retaining merely the usual boson and its spectral-flow partner, the other (twisted) yielding two fermions and one boson, on the massless level. The corresponding chiral BRST-invariant vertex operators are constructed in certain pictures, and their fusion and picture-changing are investigated, including the construction of inverse picture-changing operators. The $N{=}2$ `spacetime supersymmetry' generators are {\it null\/} operators, since the twisted massless states fail to interact. The untwisted three- and four-point functions are recalculated at tree-level., Comment: 42 pages, LaTeX, no figures, 115 kb, ITP-UH-05/94, DESY 94-104 (extensive revision and expansion of earlier version)

The most general homogeneous monodromy conditions in $N{=}2$ string theory are classified in terms of the conjugacy classes of the global symmetry group $U(1,1)\otimes{\bf Z}_2$. For classes which generate a discrete subgroup $\G$, the corresponding target space backgrounds ${\bf C}^{1,1}/\G$ include half spaces, complex orbifolds and tori. We propose a generalization of the intercept formula to matrix-valued twists, but find massless physical states only for $\Gamma{=}{\bf 1}$ (untwisted) and $\Gamma{=}{\bf Z}_2$ (\`a la Mathur and Mukhi), as well as for $\Gamma$ being a parabolic element of $U(1,1)$. In particular, the sixteen ${\bf Z}_2$-twisted sectors of the $N{=}2$ string are investigated, and the corresponding ground states are identified via bosonization and BRST cohomology. We find enough room for an extended multiplet of `spacetime' supersymmetry, with the number of supersymmetries being dependent on global `spacetime' topology. However, world-sheet locality for the chiral vertex operators does not permit interactions among all massless `spacetime' fermions., Comment: 42 pages, LaTeX, no figures, 120 kb, ITP-UH-24/93, DESY 93-191 (abstract and introduction clarified, minor corrections added)

The $N=2$ fermionic string theory is revisited in light of its recently proposed equivalence to the non-compact $N=4$ fermionic string model. The issues of space-time Lorentz covariance and supersymmetry for the BRST quantized $N=2$ strings living in uncompactified $2 + 2$ dimensions are discussed. The equivalent local quantum supersymmetric field theory appears to be the most transparent way to represent the space-time symmetries of the extended fermionic strings and their interactions. Our considerations support the Siegel's ideas about the presence of $SO(2,2)$ Lorentz symmetry as well as at least one self-dual space-time supersymmetry in the theory of the $N=2(4)$ fermionic strings, though we do not have a compelling reason to argue about the necessity of the {\it maximal} space-time supersymmetry. The world-sheet arguments about the absence of all string massive modes in the physical spectrum, and the vanishing of all string-loop amplitudes in the Polyakov approach, are given on the basis of general consistency of the theory., Comment: 29 pages, LaTeX, ITP-UH-1/93

The $N=2$ supersymmetric {\it self-dual} Yang-Mills theory and the $N=4$ and $N=2$ {\it self-dual} supergravities in $2+2$ space-time dimensions are formulated for the first time. These formulations utilize solutions of the Bianchi identities subject to the super-Yang-Mills or supergravity constraints in the relevant $N$-extended superspace with the space-time signature $(2,2)$., Comment: 11 pages

We present the Green-Schwarz $\s\-$model coupled to the $N=1$ {\it {supersymmetric}} Yang-Mills and supergravity in a four-dimensional space-time with the indefinite signature $(+,+,-,-)$. We first confirm the $\k\-$invariance of the Green-Schwarz action, and show that all the $\b\-$functions for the backgrounds vanish consistently after the use of their superfield equations. Subsequently, we inspect the supersymmetric {\it self-duality} conditions, that have been developed in our previous paper on the Yang-Mills and supergravity backgrounds. Remarkably, the Majorana-Weyl spinor dictating the {\it supersymmetric self-duality} conditions is consistent with the couplings of Green-Schwarz superstring. Such Green-Schwarz superstring is supposed to be the underlying theory of the {\it supersymmetric self-dual} Yang-Mills theory, which is conjectured to generate {\it all} exactly soluble supersymmetric systems in lower dimensions., Comment: 11 pages

The properties of Dirac gamma matrices in a four-dimensional space-time with the $(2,2)$ signature are studied. The basic spinors are classified, and the existence of Majorana-Weyl spinors is noted. Supersymmetry in $2 + 2$ dimensions is discussed, and the existence of the {\it real chiral} scalar supermultiplet is discovered. Supersymmetric {\it self-dual} Yang-Mills theories and {\it self-dual} supergravity model in $2 + 2$ dimensions, that are apparently relevant to integrable systems, are formulated for the first time., Comment: 15 pages

The internal space-time symmetry and simple supersymmetry of relativistic particles are briefly discussed in terms of the little group of the Poincare group. The little group generators in a finite-dimensional matrix representation of the N = 1 super-Poincare algebra are explicitly constructed. The supergeometry of a massive case continuously becomes that of a massless case in the infinite-momentum limit. The origin of the gage transformations associated with the massless supermultiplets becomes transparent in that limit.