Gepner Models Research Articles

Permutation orientifolds of Gepner models

In tensor products of a left-right symmetric CFT, one can define permutation orientifolds by combining orientation reversal with involutive permutation symmetries. We construct the corresponding crosscap states in general rational CFTs and their orbifolds, and study in detail those in products of affine U(1)2 models or N = 2 minimal models. The results are used to construct permutation orientifolds of Gepner models. We list the permutation orientifolds in a few simple Gepner models, and study some of their physical properties — supersymmetry, tension and RR charges. We also study the action of corresponding parity on D-branes, and determine the gauge group on a stack of parity-invariant D-branes. Tadpole cancellation condition and some of its solutions are also presented.

Crosscaps in Gepner models and the moduli space of $T^{2}$ orientifolds

Crosscaps in Gepner models and the moduli space of $T^{2}$ orientifolds

Generalised N=2 permutation branes

Generalised permutation branes in products of N=2 minimal models play an important role in accounting for all RR charges of Gepner models. In this paper an explicit conformal field theory construction of these generalised permutation branes for one simple class of examples is given. We also comment on how this may be generalised to the other cases.

D -brane charges in Gepner models

We construct Gepner models in terms of coset conformal field theories and compute their twisted equivariant K-theories. These classify the D-brane charges on the associated geometric backgrounds and therefore agree with the topological K-theories. We show this agreement for various cases, in particular, the Fermat quintic.

The topological cigar observables

We study the topologically twisted cigar, namely the SL(2,R)/U(1) superconformal field theory at arbitrary level, and find the BRST cohomology of the topologically twisted N=2 theory. We find a one to one correspondence between the spectrum of the twisted coset and singular vectors in the Wakimoto modules constructed over the SL(2,R) current algebra. The topological cigar cohomology is the crucial ingredient in calculating the closed string spectrum of topological strings on non-compact Gepner models.

On SUSY standard-like models from orbifolds ofD= 6 Gepner orientifolds

As a further elaboration of the proposal of Ref. [1] we address the construction of Standard-like models from configurations of stacks of orientifold planes and D-branes on an internal space with the structure ${(Gepner model)^{c=6} \times T^2}/Z_N$. As a first step, the construction of D=6 Type II B orientifolds on Gepner points, in the diagonal invariant case and for both, odd and even, affine levels is discussed. We build up the explicit expressions for B-type boundary states and crosscaps and obtain the amplitudes among them. From such amplitudes we read the corresponding spectra and the tadpole cancellation equations. Further compactification on a T^2 torus, by simultaneously orbifolding the Gepner and the torus internal sectors, is performed. The embedding of the orbifold action in the brane sector breaks the original gauge groups and leads to N=1 supersymmetric chiral spectra. Whenever even orbifold action on the torus is considered, new branes, with worldvolume transverse to torus coordinates, must be included. The detailed rules for obtaining the D=4 model spectra and tadpole equations are shown. As an illustration we present a 3 generations Left-Right symmetric model that can be further broken to a MSSM model.

A family of SCFTs hosting all ``very attractive'' relatives of the (2)4Gepner model

This work gives a manual for constructing superconformal field theories associated to a family of smooth K3 surfaces. A direct method is not known, but a combination of orbifold techniques with a non-classical duality turns out to yield such models. A four parameter family of superconformal field theories associated to certain quartic K3 surfaces in CP^3 is obtained, four of whose complex structure parameters give the parameters within superconformal field theory. Standard orbifold techniques are used to construct these models, so on the level of superconformal field theory they are already well understood. All "very attractive" K3 surfaces belong to the family of quartics underlying these theories, that is all quartic hypersurfaces in CP^3 with maximal Picard number whose defining polynomial is given by the sum of two polynomials in two variables. A particular member of the family is the (2)^4 Gepner model, such that these theories can be viewed as complex structure deformations of (2)^4 in its geometric interpretation on the Fermat quartic.

The RR charges of the A-type Gepner models

It is shown that the RR charges of Gepner models are not all accounted for by the usual tensor product and permutation branes. In order to characterise the missing D-branes we study the matrix factorisation approach to the description of D-branes for Gepner models. For each of the A-type models we identify a set of matrix factorisations whose charges generate the full lattice of quantised charges. The additional factorisations that are required correspond to generalised permutation branes.

Permutation branes and linear matrix factorisations

All the known rational boundary states for Gepner models can be regarded as permutation branes. On general grounds, one expects that topological branes in Gepner models can be encoded as matrix factorisations of the corresponding Landau-Ginzburg potentials. In this paper we identify the matrix factorisations associated to arbitrary B-type permutation branes.

Free-field representation of permutation branes in Gepner models

We consider free-field realization of Gepner models basing on free-field realization of N=2 superconformal minimal models. Using this realization we analyse A/B-type boundary conditions starting from the ansatz when left-moving and right-moving free-fields degrees of freedom are glued at the boundary by an arbitrary constant matrix. It is shown that the only boundary conditions consistent with the singular vectors structure of unitary minimal models representations are given by permutation matrices and give thereby explicit free-field construction of permutation branes of Recknagel.

Free-field approach to D-branes in Gepner models

We represent free-field construction of boundary states in Gepner models basing on the free-field realization of N = 2 superconformal minimal models. Using this construction we consider the open string spectrum between the boundary states and propose as description in terms of Malikov, Schechtman, Vaintrob chiral de Rham complex of the Landau–Ginzburg orbifold. It allows to establish direct relation of the open string spectrum for boundary states in Gepner models to the open string spectrum for fractional branes in Landau–Ginzburg orbifolds. The example of 1 3 model considered in details.

A quantum McKay correspondence for fractional 2p-branes on LG orbifolds

We study fractional 2p-branes and their intersection numbers in non-compact orbifolds as well the continuation of these objects in Kahler moduli space to coherent sheaves in the corresponding smooth non-compact Calabi-Yau manifolds. We show that the restriction of these objects to compact Calabi-Yau hypersurfaces gives the new fractional branes in LG orbifolds constructed by Ashok et. al. in hep-th/0401135. We thus demonstrate the equivalence of the B-type branes corresponding to linear boundary conditions in LG orbifolds, originally constructed in hep-th/9907131, to a subset of those constructed in LG orbifolds using boundary fermions and matrix factorization of the world-sheet superpotential. The relationship between the coherent sheaves corresponding to the fractional two-branes leads to a generalization of the McKay correspondence that we call the quantum McKay correspondence due to a close parallel with the construction of branes on non-supersymmetric orbifolds. We also provide evidence that the boundary states associated to these branes in a conformal field theory description corresponds to a sub-class of the boundary states associated to the permutation branes in the Gepner model associated with the LG orbifold.

Matrix factorisations and permutation branes

The description of B-type D-branes on a tensor product of two N=2 minimal models in terms of matrix factorisations is related to the boundary state description in conformal field theory. As an application we show that the D0- and D2-brane for a number of Gepner models are described by permutation boundary states. In some cases (including the quintic) the images of the D2-brane under the Gepner monodromy generate the full charge lattice.

Recent progress in intersecting D‐brane models

AbstractThe aim of this article is to review some recent progress in the field of intersecting D‐brane models. This includes the construction of chiral, semi‐realistic flux compactifications, the systematic study of Gepner model orientifolds, the computation of various terms in the low energy effective action and the investigation of the statistics of solutions to the tadpole cancellation conditions.

Chiral supersymmetric Standard Model spectra from orientifolds of Gepner models

We construct d=4, N=1 orientifolds of Gepner models with just the chiral spectrum of the Standard Model. We consider all simple current modular invariants of c=9 tensor products of N=2 minimal models. For some very specific tensor combinations, and very specific modular invariants and orientifold projections, we find a large number of such spectra. We allow for Standard Model singlet (dark) matter and non-chiral exotics. The Chan–Paton gauge group is either U(3)×Sp(2)×U(1)×U(1) or U(3)×U(2)×U(1)×U(1). In many cases the Standard Model hypercharge U(1) has no coupling to RR 2-forms and hence remains massless; in some of those models the B–L gauge boson does acquire a mass.

Supersymmetric standard model spectra from RCFT orientifolds

We present supersymmetric, tadpole-free d = 4 , N = 1 orientifold vacua with a three family chiral fermion spectrum that is identical to that of the standard model. Starting with all simple current orientifolds of all Gepner models we perform a systematic search for such spectra. We consider several variations of the standard four-stack intersecting brane realization of the standard model, with all quarks and leptons realized as bifundamentals and perturbatively exact baryon and lepton number symmetries, and with a U ( 1 ) Y vector boson that does not acquire a mass from Green–Schwarz terms. The number of supersymmetric Higgs pairs H 1 + H 2 is left free. In order to cancel all tadpoles, we allow a “hidden” gauge group, which must be chirally decoupled from the standard model. We also allow for non-chiral mirror-pairs of quarks and leptons, non-chiral exotics and (possibly chiral) hidden, standard model singlet matter, as well as a massless B–L vector boson. All of these less desirable features are absent in some cases, although not simultaneously. In particular, we found cases with massless Chan–Paton gauge bosons generating nothing more than SU ( 3 ) × SU ( 2 ) × U ( 1 ) . We obtain almost 180 000 rationally distinct solutions (not counting hidden sector degrees of freedom), and present distributions of various quantities. We analyse the tree level gauge couplings, and find a large range of values, remarkably centered around the unification point.

Particle models from orientifolds at Gepner-orbifold points

We consider configurations of stacks of orientifold planes and D-branes wrapped on a non trivial internal space of the structure {(Gepner model)^{c=3n} x T^{2(3-n)}}/Z_N, for n=1,2,3. By performing simple moddings by discrete symmetries of Gepner models at orienti fold points, consistent with a Z_N orbifold action, we show that projection on D-brane configurations can be achieved, generically leading to chiral gauge theories. Either supersymmetric or non-supersymmetric (tachyon free) models can be obtained. We illustrate the procedure through some explicit examples.

A note on partition functions of Gepner model orientifolds

In this note we generalize the description of simple current extended Gepner model orientifolds as presented in hep-th/0401148 on the case of even levels and non-trivial dressings of the parity transformation. We provide a comprehensive list of all the important ingredients for the construction of such orientifolds. Namely we present explicit expressions for the Klein-bottle, annulus and Möbius strip amplitudes and derive the general tadpole cancellation conditions. As an example we construct a supersymmetric Pati–Salam like model.

Chiral Supersymmetric Gepner Model Orientifolds

We explicitly construct A-type orientifolds of supersymmetric Gepner models. In order to reduce the tadpole cancellation conditions to a treatable number we explicitly work out the generic form of the one-loop Klein bottle, annulus and Moebius strip amplitudes for simple current extensions of Gepner models. Equipped with these formulas, we discuss two examples in detail to provide evidence that in this setting certain features of the MSSM like unitary gauge groups with large enough rank, chirality and family replication can be achieved.

Crosscaps in Gepner Models and Type IIA Orientifolds

As a first step to a detailed study of orientifolds of Gepner models associated with Calabi-Yau manifolds, we construct crosscap states associated with anti-holomorphic involutions (with fixed points) of Calabi-Yau manifolds. We argue that these orientifolds are dual to M-theory compactifications on (singular) seven-manifolds with $G_2$ holonomy. Using the spacetime picture as well as the M-theory dual, we discuss aspects of the orientifold that should be obtained in the Gepner model. This is illustrated for the case of the quintic.