Comments on Open-String Orbifolds with a Non-Vanishing B_{ab}

We study the effect of a non-vanishing flux for the NS-NS antisymmetric tensor in open-string orbifolds. As in toroidal models, the total dimension of the Chan-Paton gauge group is reduced proportionally to the rank of $B_{ab}$, both on D9 and on D5-branes, while the Moebius amplitude involves some signs that, in the $Z_2$ case, allow one to connect continuously ${\rm U} (n)$ groups to $Sp(n) \otimes Sp(n)$ groups on each set of D-branes. In this case, non-universal couplings between twisted scalars and gauge vectors arise, as demanded by the generalised Green-Schwarz mechanism. We also comment on the role of the NS-NS antisymmetric tensor in a recently proposed type scenario, where supersymmetry is broken on the D-branes, while it is preserved in the bulk.Comment: 28 pages, harvmac. Misprints corrected. References added. Version to appear on Nucl. Phys.

Aspects of Type I Compactifications and Type I-Heterotic Duality

We review the construction of open descendants of the type IIB superstring on the Z-orbifold. It results in a chiral four-dimensional model with gauge group $SO(8) \otimes U(12)$ and three generations of matter in the $(8,12^*)\oplus (1,66)$ representations. As a test of type I - heterotic duality, that reduces to a weak/weak duality in D=4, a heterotic model on the same orbifold is also presented. The massless spectrum reproduces exactly the one found in the type I case apart from additional twisted matter charged with respect to the SO(8) gauge group. The puzzle is solved by noting that at generic points in the moduli space these states get masses.Comment: Talk delivered at the V Korean-Italian Meeting on Relativistic Astrophysics, 8 pages, Late

Non-Supersymmetric Open String Vacua

We review the construction of non-supersymmetric open string vacua in various dimensions. They can be obtained either projecting the (compactified) non-supersymmetric 0B theory, or applying the Scherk-Schwarz mechanism to open strings. Generically, these vacua generate a non-vanishing cosmological constant. However, one can construct particular kinds of Scherk-Schwarz compactifications with vanishing cosmological constant, at least for low orders, based on asymmetric orbifolds. A generic feature of these models is that supersymmetry remains unbroken on the branes at all mass level, while it is broken in the bulk in a way that preserves Fermi-Bose degeneracy at each mass level in the perturbative string spectrum.Comment: 8 pages, Latex + JHEP.cls. Contribution to the Proceedings of the Trieste Meeting of the TMR Network on Physics beyond the S

Open Strings and Supersymmetry Breaking

We review several mechanisms for supersymmetry breaking in orientifold models. In particular, we focus on non-supersymmetric open-string realisations that correspond to consistent flat-space solutions of the classical equations of motion. In these models, the one-loop vacuum energy can typically fixed by the size of the compact extra dimensions, and can thus be tuned to extremely small values if enough extra dimensions are large.Comment: Contribution to the proceedings of the XVI SIGRAV conference. V2 refs added, V3 one ref adde

Non-tachyonic open descendants of the 0B string theory

We use the crosscap constraint to construct open descendants of the 0B string compactified on $T^6 /Z_3$ and on $T^4/Z_2$ free of tachyons both in the closed and in the open unoriented sectors. In four dimensions the construction results in a Chan-Paton gauge group $U(8)\otimes U(12)\otimes U(12)$ with three generations of chiral fermions in the representations $(\overline{8},1,\overline{12}) +(8,12,1)+(1,\overline{66},1)+(1,1,66)$.Comment: 13 pages, Latex. Minor corrections. Final version to appear on Phys.Lett.

Discrete Deformations in Type I Vacua

We study supersymmetric orientifolds where the world-sheet parity transformation is combined with a conjugation of some compact complex coordinates. We investigate their T-duality relation to standard orientifolds and discuss the origin of continuous and discrete moduli. In contrast to standard orientifolds, the antisymmetric tensor describes a continuous deformation, while the off-diagonal part of the metric is frozen to quantized values and is responsible for the rank reduction of the gauge group. We also give a geometrical interpretation of some recently constructed six-dimensional permutational orientifolds.Comment: 12 pages, TeX, harvmac, 4 figures, eq.(3.15) change

Rankin-Selberg methods for closed strings on orbifolds

In recent work we have developed a new unfolding method for computing one-loop modular integrals in string theory involving the Narain partition function and, possibly, a weak almost holomorphic elliptic genus. Unlike the traditional approach, the Narain lattice does not play any role in the unfolding procedure, T-duality is kept manifest at all steps, a choice of Weyl chamber is not required and the analytic structure of the amplitude is transparent. In the present paper, we generalise this procedure to the case of Abelian Z_N orbifolds, where the integrand decomposes into a sum of orbifold blocks that can be organised into orbits of the Hecke congruence subgroup {\Gamma}_0(N). As a result, the original modular integral reduces to an integral over the fundamental domain of {\Gamma}_0(N), which we then evaluate by extending our previous techniques. Our method is applicable, for instance, to the evaluation of one-loop corrections to BPS-saturated couplings in the low energy effective action of closed string models, of quantum corrections to the K\"ahler metric and, in principle, of the free-energy of superstring vacua.Comment: 47 pages, 1 figur

Universality of Gauge Thresholds in Non-Supersymmetric Heterotic Vacua

We compute one-loop threshold corrections to non-abelian gauge couplings in four-dimensional heterotic vacua with spontaneously broken $\cal N = 2 \to \cal N = 0$ supersymmetry, obtained as Scherk-Schwarz reductions of six-dimensional K3 compactifications. As expected, the gauge thresholds are no-longer BPS protected, and receive contributions also from the excitations of the RNS sector. Remarkably, the difference of thresholds for non-abelian gauge couplings is BPS saturated and exhibits a universal behaviour independently of the orbifold realisation of K3. Moreover, the thresholds and their difference develop infra-red logarithmic singularities whenever charged BPS-like states, originating from the twisted RNS sector, become massless at special loci in the classical moduli space.Comment: 12 pages, corrected eqs. 3.19, 3.20 and 3.23 and an overall factor of 2 in all threshold

Unusual gauged supergravities from type IIA and type IIB orientifolds

We analyse different N=4 supergravities coupled to six vector multiplets corresponding to low-energy descriptions of the bulk sector of T6/Z2 orientifolds with p-brane in IIB (p odd) and in IIA (p even) superstrings. When fluxes are turned on, a gauging emerges corresponding to some non-semisimple Lie algebra related to nilpotent algebras N_p inside so(6,6), with dimension 15 + (p-3)(9-p). The non-metric axions have Stueckelberg couplings that induce a spontaneous breaking of gauge symmetries. In four cases the gauge algebra is non-abelian with a non-commutative structure of the compactification torus, due to fluxes of NS-NS and R-R forms.Comment: 13 pages, LaTe