Heterotic/heterotic duality in D = 6,4

Journal of High Energy Physics, 1997

We continue our study of heterotic/type-I duality in D < 10 dimensions. We consider the heterotic and type-I theories compactified on tori to lower dimensions. We calculate the special ("BPS-saturated") F 4 and R 4 terms in the effective one-loop heterotic action. These terms are expected to be non-perturbatively exact for D > 4.

Nuclear Physics B, 1996

We discuss the different discrete duality symmetries in six dimensions that act within and between (i) the 10-dimensional heterotic string compactified on T 4 , (ii) the 10dimensional Type IIA string compactified on K3 and (iii) the 10-dimensional Type IIB string compactified on K3. In particular we show that the underlying group-theoretical structure of these discrete duality symmetries is determined by the proper cubic group C/Z 2 . Our group theoretical interpretation leads to simple rules for constructing the explicit form of the different discrete Type II duality symmetries in an arbitrary background. The explicit duality rules we obtain are applied to construct dual versions of the 6-dimensional chiral null model.

Nuclear Physics B, 1999

Characters of E 8 ⊗E 8 and SO(32) heterotic strings involving the full internal symmetry Cartan subalgebra generators are defined after circle compactification so that they are T dual. The novel point, as compared with an earlier study of the type II case, is the appearence of Wilson lines. Using SO(17, 1) transformations between the weight lattices reveals the existence of an intermediate theory where T duality transformations are disentangled from the internal symmetry. This intermediate theory corresponds to a sort of twisted compactification of a novel type. Its modular invariance follows from an interesting interplay between three representations of the modular group.

Journal of High Energy Physics

A Double Field Theory (DFT) description of gauge symmetry enhancingbreaking in the heterotic string is presented. The construction, based on previous results for the bosonic string, relies on the extension of the tangent frame of DFT. The fluxes of a Scherk-Schwarz like generalized toroidal compactification are moduli dependent and become identified with the structure constants of the enhanced group at fixed "self-dual" points in moduli space. Slight displacements from such points provide the breaking of the symmetry, gauge bosons acquiring masses proportional to fluxes. The inclusion of fermions is also discussed.

We construct six stack D6-brane vacua (non-supersymmetric) that have at low energy exactly the standard model (with right handed neutrinos). The construction is based on D6-branes intersecting at angles in D = 4 type toroidal orientifolds of type-I strings. Three U(1)'s become massive through their couplings to RR fields and from the three surviving massless U(1)'s at low energies, one is the standard model hypercharge generator. The two extra massless U(1)'s get broken, as suggested recently (hep-th/0205147), by requiring some intersections to respect N = 1 supersymmetry thus supporting the appearance of massless charged singlets. Proton and lepton number are gauged symmetries and their anomalies are cancelled through a generalized Green-Schwarz mechanism that gives masses to the corresponding gauge bosons through couplings to RR fields. Thus proton is stable and neutrinos are of Dirac type with small masses as a result of a PQ like-symmetry. The models predict the existence of only two supersymmetric particles, superpartners of ν R 's.

Nuclear Physics B, 2001

A massive version of T-duality in six dimensions is given, that maps the K3 compactification of Romans' theory onto the K3 compactification of Type IIB theory. This is done by performing a (standard) Kaluza-Klein reduction on six-dimensional massive Type IIA and a Scherk-Schwarz reduction on Type IIB, mapping both theories onto the same fivedimensional theory. We also comment shortly on the difficulties arising if one intends to construct a massive generalisation of the six-dimensional string-string duality.

2010

We consider string vacua formed by compactifying Type II string theories on toroidal orbifolds and generalised Calabi-Yau manifolds and their transformations under a set of non-perturbative dualities. The dualities are the Type IIA-IIB exchanging T duality, the self-symmetry of Type IIB S duality, the non-trivial combination of the two, U duality, and the generalisation of T duality to include Calabi-Yaus, mirror symmetry. The requirement of the effective theory superpotential being invariant under these dualities is used to justify additional fluxes which do not descend via compactification from the ten dimensional action, which form an N = 2 theory. Their non-geometric structures, Bianchi constraints and tadpoles are determined and then classified in terms of modular S duality induced multiplets. The Z2 Z2 orientifold is used as an explicit example of the general methods, with N = 1 Type IIB non-geometric vacua which possess T and S duality invariance also constructed. These are t...

Physics Letters B, 1996

Heterotic strings on R 6 K3 generically appear to undergo some interesting new phase transition at that value of the string coupling for which the one of the six-dimensional gauge eld kinetic energies changes sign. An exception is the E 8 E 8 string with equal instanton numbers in the two E 8 's, which admits a heterotic/heterotic self-duality. In this paper, we generalize the dyonic string solution of the six-dimensional heterotic string to include non-trivial gauge eld congurations corresponding to self-dual Yang-Mills instantons in the four transverse dimensions. We nd that vacua which undergo a phase transition always admit a string solution exhibiting a naked singularity, whereas for vacua admitting a selfduality the solution is always regular. When there is a phase transition, there exists a choice of instanton numbers for which the dyonic string is tensionless and quasi-anti-self-dual at that critical value of the coupling. For other choices of instanton number, the string can be tensionless at dierent v alues of the coupling.

Physics Letters B, 1996

In this note we compare the moduli spaces of the heterotic string compactified on a two-torus and F-Theory compactified on an elliptic K3 surface for the case of an unbroken E 8 ×E 8 gauge group. The explicit map relating the deformation parameters α and β of the F-Theory K3 surface to the moduli T and U of the heterotic torus is found using the close relationship between the K3 discriminant and the discriminant of the Calabi-Yau-threefold X 1,1,2,8,12 (24) in the limit of a large base P 1 .

Physical Review D, 2015

We study F-theory duals of singular heterotic K3 models that correspond to abelian toroidal orbifolds T 4 / N. While our focus is on the standard embedding, we also comment on models with Wilson lines and more general gauge embeddings. In the process of constructing the duals, we work out a Weierstrass description of the heterotic toroidal orbifold models, which exhibit singularities of Kodaira type I * 0 , IV * , III * , and II *. This construction unveils properties like the instanton number per fixed point and a correlation between the orbifold order and the multiplicities in the Dynkin diagram. The results from the Weierstrass description are then used to restrict the complex structure of the F-theory Calabi-Yau threefold such that the gauge group and the matter spectrum of the heterotic theories are reproduced. We also comment on previous approaches that have been employed to construct the duality and point out the differences to our case. Our results show explicitly how the various orbifold models are connected and described in F-theory.

Journal of High Energy Physics

Non-invertible symmetries have recently been understood to provide interesting constraints on RG flows of QFTs. In this work, we show how non-invertible symmetries can also be used to generate entirely new RG flows, by means of so-called non-invertible twisted compactification. We illustrate the idea in the example of twisted compactifications of 4d $$ \mathcal{N} $$ N = 4 super-Yang-Mills (SYM) to three dimensions. After giving a catalogue of non-invertible symmetries descending from Montonen-Olive duality transformations of 4d $$ \mathcal{N} $$ N = 4 SYM, we show that twisted compactification by non-invertible symmetries can be used to obtain 3d $$ \mathcal{N} $$ N = 6 theories which appear otherwise unreachable if one restricts to twists by invertible symmetries.

We discuss the construction of four dimensional non-supersymmetric models obtained from configurations of D6-branes intersecting at angles. We present the first examples of string GUT models which break exactly to the Standard Model (SM) at low energy. Even though the models are non supersymmetric (SUSY), the demand that some open string sectors preserve N=1 SUSY creates gauge singlet scalars that break the extra anomaly free U(1)'s generically present in the models, predicting s˜νs˜ν R 's and necessarily creating Majorana mass terms for right handed neutrinos.

Physics Letters B, 1999

We show that the geometry of K3 surfaces with singularities of type A-D-E contains enough information to reconstruct a copy of the Lie algebra associated to the given Dynkin diagram. We apply this construction to explain the enhancement of symmetry in F and IIA theories compactified on singular K3's.

Physical Review Letters, 1985

Compactification to four dimensions of a low-energy approximation to ten-dimensional O(32) string theory leads only to grand unified theories with trivial replication of families. The E(8) S E(8) string is more promising and leads in four dimensions to SU(8) with six families. If compactification breaks the symmetry to lower-rank groups, e.g. , SU( ) or E(6), there may be any number of families. In the SU(8) and SU(7) models there is nontrivial family symmetry.

Nuclear Physics B, 2006

We discuss the construction of chiral four dimensional T 6 /(Z 3 × Z 3) orientifold compactifications of IIA theory, using D6-branes intersecting at angles and not aligned with the orientifold O6 planes. Cancellation of mixed U(1) anomalies requires the presence of a generalized Green-Schwarz mechanism mediated by RR partners of closed string untwisted moduli. In this respect we describe the appearance of three quark and lepton family SU(3) C × SU(2) L × U(1) Y non-supersymmetric orientifold models with only the massless spectrum of the SM at low energy that can have either no exotics present and three families of ν R 's (A ′-model class) or the massless fermion spectrum of the N=1 SM with a small number of massive non-chiral colour exotics and in one case with extra families of ν R 's (B ′-model class). Moreover we discuss the construction of SU(5), flipped SU(5) and Pati-Salam SU(4) c × SU(2) L × SU(2) R GUTS-the latter also derived from adjoint breaking-with only the SM at low energy. Some phenomenological features of these models are also briefly discussed. All models are constructed with the Weinberg angle to be 3/8 at the string scale.