The effective action of D‐branes in Calabi‐Yau orientifold compactifications

In this review article we study type IIB superstring compactifications in the presence of space‐time filling D‐branes while preserving 𝒩=1 supersymmetry in the effective four‐dimensional theory. This amount of unbroken supersymmetry and the requirement to fulfill the consistency conditions imposed by the space‐time filling D‐branes lead to Calabi‐Yau orientifold compactifications. For a generic Calabi‐Yau orientifold theory with space‐time filling D3‐ or D7‐branes we derive the low‐energy spectrum. In a second step we compute the effective 𝒩=1 supergravity action which describes in the low‐energy regime the massless open and closed string modes of the underlying type IIB Calabi‐Yau orientifold string theory. These 𝒩=1 supergravity theories are analyzed and in particular spontaneous supersymmetry breaking induced by non‐trivial background fluxes is studied. For D3‐brane scenarios we compute soft‐supersymmetry breaking terms resulting from bulk background fluxes whereas for D7‐brane systems we investigate the structure of D‐ and F‐terms originating from worldvolume D7‐brane background fluxes. Finally we relate the geometric structure of D7‐brane Calabi‐Yau orientifold compactifications to 𝒩=1 special geometry.     

Tensor constructions of open string theories II: Vector bundles, D-branes and orientifold groups

A generalized Chan-Paton construction is presented which is analogous to the tensor product of vector bundles. To this end open string theories are considered where the space of states decomposes into sectors whose product is described by a semigroup. The cyclicity properties of the open string theory are used to prove that the relevant semigroups are direct unions of Brandt semigroups. The known classification of Brandt semigroups then implies that all such theories have the structure of a theory with Dirichlet-branes. We also describe the structure of an arbitrary orientifold group, and show that the truncation to the invariant subspace defines a consistent open string theory. Finally, we analyze the possible orientifold projections of a theory with several kinds of branes.     

Gauge sector statistics of intersecting D‐brane models

In this paper, which is based on the first part of the author's PhD thesis, we review the statistics of the open string sector in T⁶/(ℤ₂ × ℤ₂) orientifold compactifications of type IIA. After an introduction to the orientifold setup we discuss the two different techniques that have been developed, using either a saddle point approximation or a direct computer based method. We explain the two approaches by means of eight‐ and six‐dimensional toy models and present the results for the four‐dimensional models in detail. Special emphasis is placed on models containing phenomenologically interesting gauge groups, in particular those containing a standard model, Pati‐Salam or SU(5) part.     

Induced effective action in 6D hypermultiplet theory on a vector/tensor background

We consider the six dimensional hypermultiplet, vector and tensor multiplet models in (1,0) harmonic superspace and discuss the corresponding superfield actions. Manifestly a (1,0) supersymmetric procedure of computing the effective action is developed in the framework of the superfield proper-time technique. The leading low-energy contributions to the effective action is calculated.     

Semi-simple unification on T/Z12 orientifold in the type IIB supergravity

The semi-simple unification model based on SU(5)_GUT×U(3)_H gauge group is an interesting extension of the minimal SU(5)_GUT grand unification theory (GUT), since it solves the two serious problems in the standard GUT: the triplet–doublet splitting problem and the presence of dangerous dimension five operators for proton decay. Here, the extra U(3)_H gauge interaction plays a crucial role on the GUT breaking. In this Letter, we show that the full multiplet structure of the U(3)_H sector required for the desired GUT breaking is reproduced naturally on T⁶/Z₁₂ orientifold in the type IIB supergravity with a D3–D7 system. The SU(5)_GUT vector multiplet lives on D7-branes and the U(3)_H sector resides on D3-branes. We also show that various interesting features in the original SU(5)_GUT×U(3)_H model are explained in the present brane-world scenario. A possible extension to the type IIB string theory is also discussed.     

Massive N = 2a supergravity in ten dimensions

A new version of the non-chiral N = 2a supergravity in ten dimensions is obtained, in which the two-index tensor field of the theory “eats” the single vector field and acquires a mass in a Higgs-type mechanism. The new theory, although it contains no fundamental vectors, bears many formal resemblances to gauged supergravities (in particular, the recently constructed F(4) theory in six dimensions). The scalar potential has no extrema, but nevertheless the classical equations of motion admit a wide variety of spontaneous compactifications, many to four dimensions.     

Scalar potential for the gauged Heisenberg algebra and a non-polynomial antisymmetric tensor theory

We study some issues related to the effective theory of Calabi–Yau compactifications with fluxes in type II theories. At first the scalar potential for a generic electric Abelian gauging of the Heisenberg algebra, underlying all possible gaugings of R–R isometries, is presented and shown to exhibit, in some circumstances, a “dual” no-scale structure under the interchange of hypermultiplets and vector multiplets. Subsequently a new setting of such theories, when all R–R scalars are dualized into antisymmetric tensors, is discussed. This formulation falls in the class of non-polynomial tensor theories considered long ago by Freedman and Townsend and it may be relevant for the introduction of both electric and magnetic charges.     

The improved tensor multiplet in N = 2 supergravity

We construct a scale-invariant action for the N = 2 tensor multiplet which can be coupled to conformal supergravity. In spite of its non-polynomial form the action describes a free massless hypermultiplet. When used as a compensating multiplet it leads to a new minimal formulation of N = 2 Poincaré or de Sitter supergravity. We discuss its consequences and present a comparison with previous off-shell formulations.     

Nonperturbative yukawa couplings from string instantons

Nonperturbative D-brane instantons can generate perturbatively absent though phenomenologically relevant couplings for type II orientifold compactifications with D-branes. We discuss the generation of the perturbatively vanishing SU(5) GUT Yukawa coupling of type <10 10 5(H)>. Moreover, for a simple globally consistent intersecting D6-brane model, we discuss the generation of mass terms for matter fields. This can serve as a mechanism for decoupling exotic matter.     

No‐go result for supersymmetric gauge theories in the causal approach

We consider the massless supersymmetric vector multiplet in a purely quantum framework and propose a power counting formula. Then we prove that the interaction Lagrangian for a massless supersymmetric non‐Abelian gauge theory (SUSY‐QCD) is uniquely determined by some natural assumptions, as in the case of Yang‐Mills models. The result can be easily generalized to the case when massive multiplets are present, but one finds out that the massive and the massless Bosons must be decoupled, in contradiction with the standard model. Going to the second order of perturbation theory produces an anomaly which cannot be eliminated. We make a thorough analysis of the model working only with the component fields.     

Extended string field theory for massless higher-spin fields

We propose a new gauge field theory which is an extension of ordinary string field theory by assembling multiple state spaces of the bosonic string. The theory includes higher-spin fields in its massless spectrum together with the infinite tower of massive fields. From the theory, we can easily extract the minimal gauge-invariant quadratic action for tensor fields with any symmetry. As examples, we explicitly derive the gauge-invariant actions for some simple mixed symmetric tensor fields. We also construct covariantly gauge-fixed action by extending the method developed for string field theory.     

Stabilization of the compactification volume by quantum corrections

We discuss prospects for stabilizing the volume modulus of N = 1 supersymmetric type IIB orientifold compactifications using only perturbative corrections to the K?hler potential. Concretely, we consider the known string loop corrections and tree-level alpha' corrections. They break the no-scale structure of the potential, which otherwise prohibits stabilizing the volume modulus. We argue that when combined, these corrections provide enough flexibility to stabilize the volume of the internal space without nonperturbative effects, although we are not able to present a completely explicit example within the limited set of currently available models. Furthermore, a certain amount of fine-tuning is needed to obtain a minimum at large volume.     

Massive supersymmetric quantum gauge theory

We continue the study of the supersymmetric vector multiplet in a purely quantum framework. We obtain some new results which make the connection with the standard literature. First we construct the one‐particle physical Hilbert space taking into account the (quantum) gauge structure of the model. Then we impose the condition of positivity for the scalar product only on the physical Hilbert space. Finally we obtain a full supersymmetric coupling which is gauge invariant in the supersymmetric sense in the first order of perturbation theory. By integrating out the Grassmann variables we get an interacting Lagrangian for a massive Yang‐Mills theory related to ordinary gauge theory; however the number of ghost fields is doubled so we do not obtain the same ghost couplings as in the standard model Lagrangian.     

Massive vector multiplets in supergravity

Starting from a vector multiplet we construct general lagrangians using the tensor calculus. After a Weyl rescaling and other field redefinitions we find lagrangians for the massive spin $\text{(1,}\text{1}\text{2}\text{,}\text{1}\text{2}\text{, 0)}$ model coupled to supergravity. Among the class of lagrangians which we consider we find no supersymmetry breaking.     

Couplings of N=1 chiral spinor multiplets

We derive the action for n_L≥1 chiral spinor multiplets coupled to vector and scalar multiplets. We give the component form of the action, which contains gauge invariant mass terms for the antisymmetric tensors in the spinor superfield and additional Green–Schwarz couplings to vector fields. We observe that supersymmetry provides mass terms for the scalars in the spinor multiplet that do not arise from eliminating an auxiliary field. We construct the dual action by explicitly performing the duality transformations in superspace and give its component form.     

On 3D non-linear vector-vector duality

We consider the duality between topologically massive and self-dual nonabelian vector fields in three dimensions. In Fock-Schwinger gauge we obtain an explicit, albeit nonlocal, self-dual action equivalent to the topologically massive action. The inverse construction is performed for a restricted class of modified self-dual actions and leads to a topologically massive theory with two interacting gauge fields.     

Remarks on Wilson lines,modular invariance and possible string relics in Calabi-Yau compactifications

When one mods out a (2,2) conformal field theory by the action of a discrete group, it is possible to include Wilson lines to break the gauge symmetry. We simplify and generalize an earlier analysis by Witten of the constraints that modular invariance places on the allowed symmetry breaking patterns. The analysis does not depend on the details of the original conformal field theory. We then consider the fractionally charged states in such theories, first discussed by Wen and Witten. We note that these are rather generic, and consider the possibilities for their detection. We also note that, while in general they are expected to be massive (∼M_Planck), in models based on free fields, such as orbifold compactifications, there are likely to be massless (very light) fractionally charged states.     

WZW Orientifolds and Finite Group Cohomology

The simplest orientifolds of the WZW models are obtained by gauging a symmetry group generated by a combined involution of the target Lie group G and of the worldsheet. The action of the involution on the target is by a twisted inversion , where ζ is an element of the center of G. It reverses the sign of the Kalb-Ramond torsion field H given by a bi-invariant closed 3-form on G. The action on the worldsheet reverses its orientation. An unambiguous definition of Feynman amplitudes of the orientifold theory requires a choice of a gerbe with curvature H on the target group G, together with a so-called Jandl structure introduced in [31]. More generally, one may gauge orientifold symmetry groups that combine the -action described above with the target symmetry induced by a subgroup Z of the center of G. To define the orientifold theory in such a situation, one needs a gerbe on G with a Z-equivariant Jandl structure. We reduce the study of the existence of such structures and of their inequivalent choices to a problem in group-Γ cohomology that we solve for all simple simply connected compact Lie groups G and all orientifold groups . Membre du C.N.R.S.     

Gauged supergravities in various spacetime dimensions

In this review article we study the gaugings of extended supergravity theories in various space‐time dimensions. These theories describe the low‐energy limit of non‐trivial string compactifications. For each theory under consideration we review all possible gaugings that are compatible with supersymmetry. They are parameterized by the so‐called embedding tensor which is a group theoretical object that has to satisfy certain representation constraints. This embedding tensor determines all couplings in the gauged theory that are necessary to preserve gauge invariance and supersymmetry. The concept of the embedding tensor and the general structure of the gauged supergravities are explained in detail. The methods are then applied to the half‐maximal (N = 4) supergravities in d = 4 and d = 5 and to the maximal supergravities in d = 2 and d = 7. Examples of particular gaugings are given. Whenever possible, the higher‐dimensional origin of these theories is identified and it is shown how the compactification parameters like fluxes and torsion are contained in the embedding tensor.