Radiative Symmetry Breaking on D-branes at Non-supersymmetric Singularities (original) (raw)
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D-Branes at Singularities:A Bottom-Up Approach to the String Embedding of the Standard Model
Journal of High Energy Physics, 2000
We propose a bottom-up approach to the building of particle physics models from string theory. Our building blocks are Type II D-branes which we combine appropriately to reproduce desirable features of a particle theory model: 1) Chirality ; 2) Standard Model group ; 3) N = 1 or N = 0 supersymmetry ; 4) Three quark-lepton generations. We start such a program by studying configurations of D = 10, Type IIB D3-branes located at singularities. We study in detail the case of Z Z N N = 1, 0 orbifold singularities leading to the SM group or some left-right symmetric extension. In general, tadpole cancellation conditions require the presence of additional branes, e.g. D7-branes. For the N = 1 supersymmetric case the unique twist leading to three quark-lepton generations is Z Z 3 , predicting sin 2 θ W = 3/14 = 0.21. The models obtained are the simplest semirealistic string models ever built. In the non-supersymmetric case there is a three-generation model for each Z Z N , N > 4, but the Weinberg angle is in general too small. One can obtain a large class of D = 4 compact models by considering the above structure embedded into a Calabi Yau compactification. We explicitly construct examples of such compact models using Z Z 3 toroidal orbifolds and orientifolds, and discuss their properties. In these examples, global cancellation of RR charge may be achieved by adding anti-branes stuck at the fixed points, leading to models with hidden sector gravity-induced supersymmetry breaking. More general frameworks, like F-theory compactifications, allow completely N = 1 supersymmetric embeddings of our local structures, as we show in an explicit example. .
In quest of "just" the Standard Model on D-branes at a singularity
Journal of High Energy Physics, 2002
In this note we explore the possibility of obtaining gauge bosons and fermionic spectrum as close as possible to the Standard Model content, by placing D3branes at a Z N orbifold-like singularity in the presence of D7-branes. Indeed, we find that this is plausible provided a sufficiently high N is allowed for and the singular point is also fixed by an orientifold action. If extra charged matter is not permitted then the singularity should necessarily be non-supersymmetric. Correct hypercharge assignments require a dependence on some Abelian gauge D7-groups. In achieving such a construction we follow a recent observation made in Ref.
Spontaneous Gauge Symmetry Breaking in a Non-Supersymmetric D-brane Model
We investigate a D-brane system in which spontaneous gauge symmetry breaking occurs. The system consists of four D3-branes and three anti-D7-branes at C^3/Z_3 singularity. The singularity is blown up by vacuum expectation values of the states of twisted closed string, whose effects appear as Fayet-Iliopoulos terms in low-energy effective field theory. We derive an effective potential for scalar fields in four-dimensional effective field theory using the technique of superstring world-sheet theory. Since there is no supersymmetry in this system, one-loop masses for some scalar fields are considered. We find some stationary and stable vacua in which the original U(2) x U(1)_1 x U(1)_2 x U(3) gauge symmetry is spontaneously broken to U(1) x U(1)' x U(3) gauge symmetry. Both Fayet-Iliopoulos terms and one-loop masses are necessary for the existence of such vacua. We carefully investigate a geometrical aspect of the gauge symmetry breaking. We show that the gauge symmetry breaking is understood as the separation of D3-branes. Some implications to the possibility of low-scale string models are also discussed.
Radiative symmetry breaking in brane models
Nuclear Physics B, 2000
We propose a way to generate the electroweak symmetry breaking radiatively in nonsupersymmetric type I models with string scale in the TeV region. By identifying the Higgs field with a tree-level massless open string state, we find that a negative squared mass term can be generated at one loop. It is finite, computable and typically a loop factor smaller than the string scale, that acts as an ultraviolet cutoff in the effective field theory. When the Higgs open string has both ends confined on our world brane, its mass is predicted to be around 120 GeV, i.e. that of the lightest Higgs in the minimal supersymmetric model for large tan β and m A . Moreover, the string scale turns out to be one to two orders of magnitude higher than the weak scale. We also discuss possible effects of higher order string threshold corrections that might increase the string scale and the Higgs mass.
Anomalies and tadpoles in open/closed string duality
Classical and Quantum Gravity, 2004
We discuss the role played by the divergences appearing in the interaction between a fractional D3 brane dressed with an SU (N) gauge field and a stack of N fractional D3 branes on the orbifolds C 2 /Z 2 and C 3 /(Z 2 × Z 2). In particular we show that the logarithmic divergences in the closed string channel, interpreted as due to twisted massless tadpoles, are mapped, under open/closed string duality, in the logarithmic ones in the open string channel, due to the massless states circulating in the annulus diagram and corresponding to the one-loop divergences that one finds in the gauge theory living in the world volume of the brane. This result provides a quantitative evidence of why the chiral and scale anomalies of the supersymmetric and non conformal gauge theories supported by the world volume of the branes can be inferred from supergravity calculations.
Radiative brane-mass terms in D>5 orbifold gauge theories
Physics Letters B, 2003
A gauge theory with gauge group G defined in D > 4 space-time dimensions can be broken to a subgroup H on four dimensional fixed point branes, when compactified on an orbifold. Mass terms for extra dimensional components of gauge fields A i (brane scalars) might acquire (when allowed by the brane symmetries) quadratically divergent radiative masses and thus jeopardize the stability of the four-dimensional theory. We have analyzed Z 2 compactifications and identified the brane symmetries remnants of the higher dimensional gauge invariance. No mass term is allowed for D = 5 while for D > 5 a tadpole ∝ F α ij can appear when there are U α (1) factors in H. A detailed calculation is done for the D = 6 case and it is established that the tadpole is related, although does not coincide, with the U α (1) anomaly induced on the brane by the bulk fermions. In particular, no tadpole is generated from gauge bosons or fermions in real representations.
Continuous gauge and supersymmetry breaking for open strings on D-branes
Journal of High Energy Physics, 2000
We consider freely acting orbifold compactifications, which interpolate in two possible decompactification limits between the supersymmetric type II string and the nonsupersymmetric type 0 string. In particular we discuss how D-branes are incorporated into these orbifold models. Investigating the open string spectrum on D3-branes, we will show that one can interpolate in this way between N = 4 supersymmetric U (N ) respectively U (2N ) Yang-Mills theories and non-supersymmetric U (N ) × U (N ) gauge theories with adjoint massless scalar fields plus bifundamental massless fermions in a smooth way.
We show how to construct chiral tachyon-free perturbative orientifold models, where supersymmetry is broken at the string scale on a collection of branes while, to lowest order, the bulk and the other branes are supersymmetric. In higher orders, supersymmetry breaking is mediated to the remaining sectors, but is suppressed by the size of the transverse space or by the distance from the brane where supersymmetry breaking primarily occurred. This setting is of interest for orbifold models with discrete torsion, and is of direct relevance for low-scale string models. It can guarantee the stability of the gauge hierarchy against gravitational radiative corrections, allowing an almost exact supergravity a millimeter away from a non-supersymmetric world.
Tadpole and Anomaly Cancellation Conditions in D-Brane Orbifold Models
International Journal of Modern Physics A, 2003
We derive and generalize the RR twisted tadpole cancellation conditions necessary to obtain consistent D=4, ZN orbifold compactifications of Type IIB string theory. At least two different types of branes (or antibranes with opposite RR charges) are introduced into the construction. The matter spectra and their contribution to the non-Abelian gauge anomalies are computed. Their relation with the tadpole cancellation conditions is also reviewed. The presence of tachyons is a common feature for some of the nonsupersymmetric systems of branes.
Towards realistic string vacua from branes at singularities
Journal of High Energy Physics, 2009
We report on progress towards constructing string models incorporating both realistic D-brane matter content and moduli stabilisation with dynamical low-scale supersymmetry breaking. The general framework is that of local D-brane models embedded into the LARGE volume approach to moduli stabilisation. We review quiver theories on del Pezzo n (dP n ) singularities including both D3 and D7 branes. We provide supersymmetric examples with three quark/lepton families and the gauge symmetries of the Standard, Left-Right Symmetric, Pati-Salam and Trinification models, without unwanted chiral exotics. We describe how the singularity structure leads to family symmetries governing the Yukawa couplings which may give mass hierarchies among the different generations. We outline how these models can be embedded into compact Calabi-Yau compactifications with LARGE volume moduli stabilisation, and state the minimal conditions for this to be possible. We study the general structure of soft supersymmetry breaking. At the singularity all leading order contributions to the soft terms (both gravity-and anomaly-mediation) vanish. We enumerate subleading contributions and estimate their magnitude. We also describe model-independent physical implications of this scenario. These include the masses of anomalous and non-anomalous U (1)'s and the generic existence of a new hyperweak force under which leptons and/or quarks could be charged. We propose that such a gauge boson could be responsible for the ghost muon anomaly recently found at the Tevatron's CDF detector.