Standard-like Models from Intersecting D5-branes

We construct intersecting D5-brane orbifold models that yield the (non-supersymmetric) standard model up to vector-like matter and charged-singlet scalars. The models are constrained by the requirement that twisted tadpoles cancel, and that the gauge boson coupled to the weak hypercharge U(1)Y does not get a string-scale mass via a generalised Green-Schwarz mechanism. Gauge coupling constant ratios close to those measured are easily obtained for reasonable values of the parameters, consistently with having the string scale close to the electroweak scale, as required to avoid the hierarchy problem. [email protected] [email protected], [email protected] The D-brane world offers an attractive, bottom-up route to getting standardlike models from Type II string theory [1]. Open strings that begin and end on a stack of M D-branes generate the gauge bosons of the group U(M) living in the world volume of the D-branes. So the standard approach is to start with one stack of 3 D-branes, another of 2, and n other stacks each having just 1 D-brane, thereby generating the gauge group U(3) × U(2) × U(1). Fermions in bi-fundamental representations of the corresponding gauge groups can arise at the intersections of such stacks [2], but to get D = 4 chiral fermions the intersecting branes should sit at a singular point in the space transverse to the branes, an orbifold fixed point, for example. In general, such configurations yield a non-supersymmetric spectrum, so to avoid the hierarchy problem the string scale associated with such models must be no more than a few TeV. Gravitational interactions occur in the bulk ten-dimensional space, and to ensure that the Planck energy has its observed large value, it is necessary that there are large dimensions transverse to the branes [3]. The D-branes with which we are concerned wrap the 3-space we inhabit and closed 1-, 2or 3cycles of a toroidally compactified T , T 2 × T 2 or T 2 × T 2 × T 2 space. Thus getting the correct Planck scale effectively means that only D4and D5-brane models are viable, since for D6-branes there is no dimension transverse to all of the intersecting branes. In a non-supersymmetric theory the cancellation of the closed-string (twisted) Ramond-Ramond (RR) tadpoles does not ensure the cancellation of the Neveu-Schwarz-Neveu-Schwarz (NSNS) tadpoles. There is a resulting instability in the complex structure moduli [4]. One way to stabilise some of the (complex structure) moduli is to use an orbifold, rather than a torus, for the space wrapped by the D-branes. If the embedding is supersymmetric, then the instabilities are removed. This has been studied [5], using D6-branes, but it has so far proved difficult to get realistic phenomenology consistent with experimental data from such models. Unlike D4-brane models on T 2 × T /ZZN , D5-brane models on T 4 × T /ZZN are necessarily non-supersymmetric in the closed string sector [6] and contain closed-string tachyons in the twisted sector. These tachyons may be a source of instability of the background [7, 8]. We have nothing to add to current understanding of this point. During the past year orientifold models with intersecting D6and D5-branes have been constructed that yield precisely the fermionic spectrum of the standard model (plus three generations of right-chiral neutrinos) [8, 9]. (Other recent work on intersecting brane models, both supersymmetric and non-supersymmetric, and their phenomenological implications may be found in [10].) The spectrum includes open-string SU(2)L doublet scalar tachyons that may be regarded as the Higgs doublets that break the electroweak symmetry group, but also, unavoidably, open string colour-triplet and charged singlet tachyons either of which is potentially fatal for the phenomenology. The wrapping numbers of the various stacks are constrained by the requirement of RR tadpole cancellation, and this ensures the absence of nonabelian anomalies in the emergent low-energy quantum field theory. A generalised Green-Schwarz mechanism ensures that that the gauge bosons associated with all anomalous U(1)s acquire string-scale masses [11], but the gauge bosons of some nonanomalous U(1)s can also acquire string-scale masses [9]; in all such cases the U(1)