Michele Trapletti

A Z2xZ2 standard model

We present a Z_2 x Z_2 orbifold compactification of the E_8 x E_8 heterotic string which gives rise to the exact chiral MSSM spectrum. The GUT breaking SU(5) to SU(3)_C x SU(2)_L x U(1)_Y is realized by modding out a freely acting symmetry. This ensures precision gauge coupling unification. Further, it allows us to break the GUT group without switching on flux in hypercharge direction, such that the standard model gauge bosons can remain massless when the orbifold singularities are blown up. The model has vacuum configurations with matter parity, a large top Yukawa coupling and other phenomenologically appealing features.

Gauge unification in highly anisotropic string compactifications

Abstract It is well known that heterotic string compactifications have, in spite of their conceptual simplicity and aesthetic appeal, a serious problem with precision gauge coupling unification in the perturbative regime of string theory. Using both a duality-based and a field-theoretic definition of the boundary of the perturbative regime, we reevaluate the situation in a quantitative manner. We conclude that the simplest and most promising situations are those where some of the compactification radii are exceptionally large, corresponding to highly anisotropic orbifold models. Thus, one is led to consider constructions which are known to the effective field-theorist as higher-dimensional or orbifold grand unified theories (orbifold GUTs). In particular, if the discrete symmetry used to break the GUT group acts freely, a non-local breaking in the larger compact dimensions can be realized, leading to a precise gauge coupling unification as expected on the basis of the MSSM particle spectrum. Furthermore, a somewhat more model dependent but nevertheless very promising scenario arises if the GUT breaking is restricted to certain singular points within the manifold spanned by the larger compactification radii.

Resolutions of ℂn/ℤn orbifolds, their U(1) bundles, and applications to string model building

We describe blowups of n/n orbifolds as complex line bundles over n−1 . We construct some gauge bundles on these resolutions. Apart from the standard embedding, we describe U(1) bundles and an SU(n−1) bundle. Both blowups and their gauge bundles are given explicitly. We investigate ten dimensional SO(32) super Yang-Mills theory coupled to supergravity on these backgrounds. The integrated Bianchi identity implies that there are only a finite number of U(1) bundle models. We describe how the orbifold gauge shift vector can be read off from the gauge background. In this way we can assert that in the blow down limit these models correspond to heterotic 2/2 and 3/3 orbifold models. (Only the 3 model with unbroken gauge group SO(32) cannot be reconstructed in blowup without torsion.) This is confirmed by computing the charged chiral spectra on the resolutions. The construction of these blowup models implies that the mismatch between type-I and heterotic models on T6/3 does not signal a complication of S-duality, but rather a problem of type-I model building itself: The standard type-I orbifold model building only allows for a single model on this orbifold, while the blowup models give five different models in blow down.

Merging Heterotic Orbifolds and K3 Compactifications with Line Bundles

We clarify the relation between six-dimensional Abelian orbifold compactifications of the heterotic string and smooth heterotic K3 compactifications with line bundles for both SO(32) and E8 × E8 gauge groups. The T 4 /ZN cases for N = 2,3,4 are treated exhaustively, and for N = 6 some examples are given. While all T 4 /Z2 and nearly all T 4 /Z3 models have a simple smooth match involving one line bundle only, this is only true for some T 4 /Z4 and T 4 /Z6 cases. We comment on possible matchings with more than one line bundle for the remaining cases. The matching is provided by comparisons of the massless spectra and their anomalies as well as a field theoretic analysis of the blow-ups.

SUSY breaking mediation by throat fields

Abstract We investigate, in the general framework of KKLT, the mediation of supersymmetry breaking by fields propagating in the strongly warped region of the compactification manifold (‘throat fields’). Such fields can couple both to the supersymmetry breaking sector at the IR end of the throat and to the visible sector at the UV end. We model the supersymmetry breaking sector by a chiral superfield which develops an F term vacuum expectation value (also responsible for the uplift). It turns out that the mediation effect of vector multiplets propagating in the throat can compete with modulus-anomaly mediation. Moreover, such vector fields are naturally present as the gauge fields arising from isometries of the throat (most notably the SO ( 4 ) isometry of the Klebanov–Strassler solution). Their mediation effect is important in spite of their large 4d mass. The latter is due to the breaking of the throat isometry by the compact manifold at the UV end of the throat. The contribution from heavy chiral superfields is found to be subdominant.

Heterotic SO(32) model building in four dimensions

Four dimensional heterotic SO(32) orbifold models are classified systematically with model building applications in mind. We obtain all 3, 7 and 2N models based on vectorial gauge shifts. The resulting gauge groups are reminiscent of those of type-I model building, as they always take the form SO(2n0) ? U(n1) ? ... ? U(nN?1) ? SO(2nN). The complete twisted spectrum is determined simultaneously for all orbifold models in a parametric way depending on n0,...,nN, rather than on a model by model basis. This reveals interesting patterns in the twisted states: They are always built out of vectors and anti-symmetric tensors of the U(n) groups, and either vectors or spinors of the SO(2n) groups. Our results may shed additional light on the S-duality between heterotic and type-I strings in four dimensions. As a spin-off we obtain an SO(10) GUT model with four generations from the 4 orbifold.

Multiple anomalous U(1)s in heterotic blow-ups

Abstract The existence of multiple anomalous U(1)s is demonstrated explicitly in a blow-up version of a heterotic Z 3 orbifold. Another blow-up of the same orbifold supports further evidence for the type I/heterotic duality in four dimensions. It has a single anomalous U(1) which does not factorize universally. As multiple anomalous U(1)s as well as non-universal factorization have never been established on heterotic orbifolds explicitly, these findings might appear contradictory at first sight. Possible inconsistencies are avoided by reinterpreting a charged twisted state as a second non-universal localized axion. The mismatch between the charges of the orbifold and blow-up spectra is resolved by suitable field redefinitions. The anomaly of the field redefinitions corresponds to the difference of blow-up and heterotic orbifold anomalies.

A Note on T-duality in Heterotic String Theory

Abstract We revisit the T-duality transformation rules in heterotic string theory, pointing out that the chiral structure of the world-sheet leads to a modification of the standard Buschers transformation rules. The simplest instance of such modifications arises for toroidal compactifications, which are rederived by analyzing a bosonized version of the heterotic world-sheet Lagrangian. Our study indicates that the usual heterotic toroidal T-duality rules naively extended to the curved case cannot be correct, leading in particular to an incorrect Bianchi identity for the field strength H of the Kalb–Ramond field B. We explicitly show this problem and provide a specific example of dual models where we are able to get new T-duality rules which, contrary to the standard ones, lead to a correct T-dual Bianchi identity for H to all orders in α ′ .

Vector mediation in the KKLT model

We face the issue of SUSY breaking and mediation in the KKLT scenario. We model the compact CY space, in the vicinity of a throat, as a 5d warped space, thus neglecting the compact dimensions transverse to the throat. We adopt an effective field theory approach, and build a model with a warped extra dimension bounded by a UV brane, where the visible sector is located, and an IR brane, where the SUSY breaking sector is located. From the string perspective the latter is the bottom of the throat, the first the “rest” of the CY space, to which the throat is glued. We study the mediation of SUSY breaking between the branes, and show that there is an effect due to extra massive bulk vector fields, which are expected in the KKLT model. Such an effect competes with the so‐called “modulus‐anomaly” mediation.