Effective super-Higgs and Str M2 from four-dimensional strings

We introduce supersymmetry breaking terms into the superpotential of the supergravity theories recently derived as the point field limit of the four-dimensional N = 1 superstrings. The terms we discuss have the special feature of giving mass to the gravitino without inducing one-loop quadratic divergences in the effective theory. It is shown that this property of the effective theory is due to the special geometrical structure shared by the scalar Kähler manifolds of the four-dimensional superstring-induced models.     

Soft supersymmetry breaking in superstring-based low-energy supergravity

We study four-dimensional supergravity theories consistent with those symmetries of the underlying ten-dimensionl supergravity (or superstring) theory, which are preserved by string loop effects. On very general grounds, we derive constraints that the Kähler potential of these theories must satisfy, in order that soft supersymmetry breaking terms appear in the low-energy observable sector at tree level.     

One-Dimensional Structures Behind Twisted and Untwisted SuperYang–Mills Theory

We give a one-dimensional interpretation of the four-dimensional twisted N = 1 superYang–Mills theory on a Kähler manifold by performing an appropriate dimensional reduction. We prove the existence of a 6-generator superalgebra, which does not possess any invariant Lagrangian but contains two different subalgebras that determine the twisted and untwisted formulations of the N = 1 superYang–Mills theory.     

ASK/PSK-correspondence and the <Emphasis Type="Italic">r</Emphasis>-map

We formulate a correspondence between affine and projective special Kähler manifolds of the same dimension. As an application, we show that, under this correspondence, the affine special Kähler manifolds in the image of the rigid r-map are mapped to one-parameter deformations of projective special Kähler manifolds in the image of the supergravity r-map. The above one-parameter deformations are interpreted as perturbative \(\alpha '\)-corrections in heterotic and type II string compactifications with \(N=2\) supersymmetry. Also affine special Kähler manifolds with quadratic prepotential are mapped to one-parameter families of projective special Kähler manifolds with quadratic prepotential. We show that the completeness of the deformed supergravity r-map metric depends solely on the (well-understood) completeness of the undeformed metric and the sign of the deformation parameter.     

The gauge-invariant N=2 supersymmetric σ-model with general scalar potential

We construct the supersymmetric σ-model, in six dimensions, for an arbitrary hyper-Kähler manifold, and its minimal coupling to super-Yang-Mills theory. Non-trivial reduction to five or four dimensions yields the corresponding five- or four-dimensional N = 2 supersymmetric model with general scalar potential. We discuss briefly the coupling to supergravity in six dimensions and we give the on-shell supergravity torsion constraints.     

The effective interactions of chiral families in four-dimensional superstrings

The low-energy effective interactions in four-dimensional superstrings with N = 2 and N = 1 space-time supersymmetry and massless twisted (family) sector are obtained. Our results rely on some general symmetry properties of superstring particle states and on tensor-calculus techniques for supergravity couplings. The novel feature is that the N = 2 quaternionic manifold and N = 1 Kähler space of the scalar superpartners of family multiplets are non-symmetric spaces whose structure can be obtained by “integrating out” the massive superstring modes.     

Homogeneous Kähler manifolds and flat-potential N=1 supergravities

Given a homogeneous Kähler manifold, with trivial Kähler class, there is at least one (usually infinitely many) homogeneous Kähler metric and superpotential such that the scalar potential of the corresponding N=1 SUGRA vanishes identically. We give the explicit form of the function G for the general case.     

On the Renormalized Volume of Hyperbolic 3-Manifolds

The renormalized volume of hyperbolic manifolds is a quantity motivated by the AdS/CFT correspondence of string theory and computed via a certain regularization procedure. The main aim of the present paper is to elucidate its geometrical meaning. We use another regularization procedure based on surfaces equidistant to a given convex surface ?N. The renormalized volume computed via this procedure is equal to what we call the W-volume of the convex region N given by the usual volume of N minus the quarter of the integral of the mean curvature over ?N. The W-volume satisfies some remarkable properties. First, this quantity is self-dual in the sense explained in the paper. Second, it verifies some simple variational formulas analogous to the classical geometrical Schläfli identities. These variational formulas are invariant under a certain transformation that replaces the data at ?N by those at infinity of M. We use the variational formulas in terms of the data at infinity to give a simple geometrical proof of results of Takhtajan et al on the Kähler potential on various moduli spaces.     

Kähler metrics and gauge kinetic functions for intersecting D6‐branes on toroidal orbifolds – The complete perturbative story

We systematically derive the perturbatively exact holomorphic gauge kinetic function, the open string Kähler metrics and closed string Kähler potential on intersecting D6‐branes by matching open string one‐loop computations of gauge thresholds with field theoretical gauge couplings in 𝒩 = 1 supergravity. We consider all cases of bulk, fractional and rigid D6‐branes on T⁶/Ω ℛ and the orbifolds T⁶/(ℤ_N × Ω ℛ) and T⁶/(ℤ₂ × ℤ_2M × Ω ℛ) without and with discrete torsion, which differ in the number of bulk complex structures and in the bulk Kähler potential. Our analysis includes all supersymmetric configurations of vanishing and non‐vanishing angles among D6‐branes and O6‐planes, and all possible Wilson line and displacement moduli are taken into account. The shape of the Kähler moduli turns out to be orbifold independent but angle dependent, whereas the holomorphic gauge kinetic functions obtain three different kinds of one‐loop corrections: a Kähler moduli dependent one for some vanishing angle independently of the orbifold background, another one depending on complex structure moduli only for fractional and rigid D6‐branes, and finally a constant term from intersections with O6‐planes. These results are of essential importance for the construction of the related effective field theory of phenomenologically appealing D‐brane models. As first examples, we compute the complete perturbative gauge kinetic functions and Kähler metrics for some T⁶/ℤ₂ × ℤ₂ examples with rigid D‐branes of [1]. As a second class of examples, the Kähler metrics and gauge kinetic functions for the fractional QCD and leptonic D6‐brane stacks of the Standard Model on T⁶/ℤ₆^′T⁶/ℤ₆^′ from [2] are given.     

A string calculation of the Kähler potentials for moduli of ZN orbifolds

We present a method for calculating the Kähler potentials of the moduli of Z_N orbifolds directly from string theory. The explicit Kähler potentials associated with b_(1,1) and b_(1,2) moduli are given for any (2,0) symmetric Z_N orbifold. These results are exact at the string tree level.     

Dimensional reduction of superstring models

Compactification of ten-dimensional supergravity on Calabi-Yau manifolds (as recently proposed by Candelas, Horowitz, Strominger, and the author) gives n=1 supergravity theories in four dimensions. This paper is devoted to working out the Kähler potential and superpotential which arise.     

One-loop string corrections to the effective field theory

We calculate the parity-conserving one-loop string corrections to the bosonic part of the 10-dimensional effective field theory for the heterotic string. There is no renormalization of the Chamseddine-Chapline-Manton supergravity action, but terms of fourth order in the curvature tensors are generated. Most of these are of the same forms as those found at the tree level of the string topological expansion, such as (TrR²)², (TrR²)(TrF²) and (TrF²)². However, we also find a non-zero Tr(F⁴) coupling which was not present at the tree level. We comment on the phenomenological implications of these results, which include absences of renormalization of the Kähler metric and of the gauge kinetic function of the effective field theory in four dimensions after compactification, and a modification of the classical equations to be obeyed by the manifold of compactification.     

Euclidean SYM theories by time reduction and special holonomy manifolds

Euclidean supersymmetric theories are obtained from Minkowskian theories by performing a reduction in the time direction. This procedure elucidates certain mysterious features of Zumino's N = 2 model in four dimensions, provides manifestly hermitian Euclidean counterparts of all non-mimimal SYM theories, and is also applicable to supergravity theories. We reanalyse the twists of the 4d N = 2 and N = 4 models from this point of view. Other applications include SYM theories on special holonomy manifolds. In particular, we construct a twisted SYM theory on Kähler 3-folds and clarify the structure of SYM theory on hyper-Kähler 4-folds.     

Duality transformation and non-Kähler couplings and potentials in anN=1 supergravity theory

A condition for the breakdown of the duality transformation to transform a theory with complex linear superfields to the one with chiral scalar superfields is obtained, when coupled to theN-1 old minimal supergravity multiplet. The recently constructedN=1 supergravity theory, with multiple compensators coupled to a chiral scalar matter supper-field, which has non-Kähler couplings and potential, satisfies this condition. We also indicate other ways of satisfying this condition.     

Completeness in Supergravity Constructions

We prove that the supergravity r- and c-maps preserve completeness. As a consequence, any component \({\mathcal{H}}\) of a hypersurface {h = 1} defined by a homogeneous cubic polynomial h such that \({-\partial^2h}\) is a complete Riemannian metric on \({\mathcal{H}}\) defines a complete projective special Kähler manifold and any complete projective special Kähler manifold defines a complete quaternionic Kähler manifold of negative scalar curvature. We classify all complete quaternionic Kähler manifolds of dimension less or equal to 12 which are obtained in this way and describe some complete examples in 16 dimensions.     

On Certain Kähler Quotients of Quaternionic Kähler Manifolds

We prove that, given a certain isometric action of a two-dimensional Abelian group A on a quaternionic Kähler manifold M which preserves a submanifold N ? M, the quotient M′ = N/A has a natural Kähler structure. We verify that the assumptions on the group action and on the submanifold N ? M are satisfied for a large class of examples obtained from the supergravity c-map. In particular, we find that all quaternionic Kähler manifolds M in the image of the c-map admit an integrable complex structure compatible with the quaternionic structure, such that N ? M is a complex submanifold. Finally, we discuss how the existence of the Kähler structure on M′ is required by the consistency of spontaneous ${\mathcal{N} = 2}$ to ${\mathcal{N} = 1}$ supersymmetry breaking.     

Hybrid inflation in supergravity with (SU(1,1)/U(1))m Kähler manifolds

In the presence of fields without superpotential but with large vevs through D-terms the mass-squared of the inflaton in the context of supergravity hybrid inflation receives positive contributions which could cancel the possibly negative Kähler potential ones. The mechanism is demonstrated using Kähler potentials associated with products of SU(1,1)/U(1) Kähler manifolds. In a particularly simple model of this type all supergravity corrections to the F-term potential turn out to be proportional to the inflaton mass allowing even for an essentially completely flat inflationary potential. The model also allows for a detectable gravitational wave contribution to the microwave background anisotropy. Its initial conditions are quite natural largely due to a built in mechanism for a first stage of “chaotic” D-term inflation.     

New compactifications of Chiral N = 2, d = 10 supergravity

We present a number of new compactifying solutions of chiral N = 2 ten-dimensional supergravity to five dimensions. Several are of the standard Freund-Rubin type; we give a complete classification of such compactifications for which the internal space M⁵ is a coset manifold. In another type of solution M⁵ is a non-Einstein U(1) bundle over a four-dimensional Kähler space, and the complex three-index field strength is nonvanishing in the internal directions. The latter construction gives a solution with SU(3) symmetry when M⁵ is taken to be a stretched five-sphere.     

The conformal factor and DiffS1/S1

Two-dimensional gravity coupled with an open string is considered to geometrically construct a string field theory following Bowick and Rajeev. The phase space of this system can be thought of as an extended loop space, and is in fact a Kähler manifold. Each loop carries a conformal factor. Bowick and Rajeev's proposal is modified so that the ghost fields stand on the same footing as the x^μ-fields. The closed string field is modified to be the Kähler potential of the extended loop space. The canonical line bundle is not needed for the equation of motion for a closed string field. A covariant (free) open string field theory is constructed as a by-product in this approach.     

Unification of families based on a coset space E7/SU(5) × SU(3) × U(1)

We show that the usual three families of quarks and leptons are identifiable with quasi Nambu-Goldstone fermions in a supersymmetric non-linear realization of E₇ corresponding to the Kähler manifold E₇/SU(5) × SU(3) × U(1). So the triplication of families suggests the underlying preon theory realizing the global E₇ linearly. Possible connections with N = 8 supergravity are also discussed.