Type IIA Orientifolds Research Articles

Yukawa couplings at infinite distance and swampland towers in chiral theories

We study limits of vanishing Yukawa couplings of 4d chiral matter fields in Quantum Gravity, using as a laboratory type IIA orientifolds with D6-branes. In these theories chiral fermions arise at brane intersections, where an infinite tower of charged particles dubbed gonions are localised. We show that in the limit Y → 0 some of these towers become asymptotically massless, while at the same time the kinetic term of some chiral fields becomes singular and at least two extra dimensions decompactify. For limits parametrised by a large complex structure saxion u, Yukawa couplings have a behaviour of the form Y ~ 1/ur, with r some positive rational number. Moreover, in this limit some of the gauge couplings associated to the Yukawa vanish. The lightest gonion scales are of order mgon ~ gsMP with s > 1, verifying the magnetic WGC with room to spare and with no need of its tower/sublattice versions. We also show how this behaviour can be understood in the context of the emergence of kinetic terms in Quantum Gravity. All these results may be very relevant for phenomenology, given the fact that some of the Yukawa couplings in the Standard Model are very small.

IR/UV mixing, towers of species and swampland conjectures

By applying the Covariant Entropy Bound (CEB) to an EFT in a box of size 1/ΛIR one obtains that the UV and IR cut-offs of the EFT are necessarily correlated. We argue that in a theory of Quantum Gravity (QG) one should identify the UV cutoff with the ‘species scale’, and give a general algorithm to calculate it in the case of multiple towers becoming light. One then obtains an upper bound on the characteristic mass scale of the tower in terms of the IR cut-off, given by Mtower ≲ {left({Lambda}_{mathrm{IR}}right)}^{2{alpha}_D} in Planck units, with αD = (D − 2 + p)/2p(D − 1), where p depends on the density of states. Identifying the IR cut-off with a (non-vanishing) curvature in AdS one reproduces the statement of the AdS Distance Conjecture (ADC), also giving an explicit lower bound for the α exponent. In particular, we find that the CEB implies α ≥ 1/2 in any dimension if there is a single KK tower, both in AdS and dS vacua. However values α < 1/2 are allowed if the particle tower is multiple or has a string component. We also consider the CKN constraint coming from avoiding gravitational collapse which further requires in general α ≥ 1/D for the lightest tower. We analyse the case of the DGKT-CFI class of Type IIA orientifold models and show it has both particle and string towers below the species scale, so that a careful analysis of how the ADC is defined is needed. We find that this class of models obey but do not saturate the CEB. The UV/IR constraints found apply to both AdS and dS vacua. We comment on possible applications of these ideas to the dS Swampland conjecture as well as to the observed dS phase of the universe.

Dynamical cobordism of a domain wall and its companion defect 7-brane

Starting from an already known solution in the literature, we study the dynamical cobordism induced by the backreaction of a non-supersymmetric, positive tension domain wall in string theory. This could e.g. be a non-BPS D8-brane of type I or a overline{D8} /O8 stack of a non-supersymmetric type IIA orientifold. The singularities which typically appear indicate either an inherent inconsistency of this background or the required presence of a suitable defect, as predicted by the cobordism conjecture. We provide evidence that this end-of-the-world 7-brane is explicitly described by a new kind of non-isotropic solution of the dilaton-gravity equations of motion. Intriguingly, on the formal level this solution turns out to be closely related to the initial solution for the non-supersymmetric domain wall.

The final model building for the supersymmetric Pati–Salam models from intersecting D6-branes

All the possible three-family {mathcal N}=1 supersymmetric Pati–Salam models constructed with intersecting D6-branes from Type IIA orientifolds on T^6/(mathbb {Z}_2times mathbb {Z}_2) are recently presented in arXiv:2112.09632. Taking models with largest wrapping number 5 and approximate gauge coupling unification at GUT scale as examples, we show string scale gauge coupling unification can be realized through two-loop renormalization group equation running by introducing seven pairs of vector-like particles from {mathcal N}=2 sector. The number of these introduced vector-like particles are fully determined by the brane intersection numbers while there are two D6-brane parallel to each other along one two-torus. We expect this will solve the gauge coupling unification problem in the generic intersecting brane worlds by introducing vector-like particles that naturally included in the {mathcal N}=2 sector.

The complete search for the supersymmetric Pati-Salam models from intersecting D6-branes

We construct a systematic method to build all the possible three-family mathcal{N} = 1 supersymmetric Pati-Salam models from Type IIA orientifolds on \U0001d54b6/(ℤ2× ℤ2) with intersecting D6-branes, in which the SU(4)C× SU(2)L× SU(2)R gauge symmetry can be broken down to the SU(3)C× SU(2)L× U(1)Y Standard Model gauge symmetry by the D-brane splitting and supersymmetry preserving Higgs mechanism. This is essentially achieved by solving all the common solutions for three generation conditions, RR tadpole cancellation conditions, and mathcal{N} = 1 supersymmetry conditions with deterministic algorithm. We find that there are 202752 possible supersymmetric Pati-Salam models in total, and show that there are only 33 independent models with different gauge coupling relations at GUTs scale after modding out equivalent relations, such as T-dualities, etc. In particular, there is one and only one independent model which has gauge coupling unification. Furthermore, one can construct other types of intersecting D-brane models utilizing such deterministic algorithm, and therefore we suggest a brand new method for D-brane model building.

Four-family supersymmetric Pati–Salam models from intersecting D6-branes

We investigate the construction of four-family supersymmetric Pati–Salam models from Type IIA orientifold with intersecting D6-branes. Utilizing the deterministic algorithm introduced in He W, Li T and Sun R (2021 arXiv: hep-th/2112.09632), we obtain 274 types of models with three rectangular tori and distinct gauge coupling relations at string scale, while 6 types of models with two rectangular tori and one tilted torus. In both cases, there exists a class of models with gauge coupling unification at string scale. In particular, for the models with two rectangular tori, one tilted torus and gauge coupling unification, the gaugino condensations are allowed, and thus supersymmetry breaking and moduli stabilization are possible for further phenomenological study.

The supersymmetry breaking soft terms, and fermion masses and mixings in the supersymmetric Pati-Salam model from intersecting D6-branes

A supersymmetric Pati-Salam model with wrapping number equal to 5 has been constructed in Type IIA orientifolds on T6/(ℤ2× ℤ2) with intersecting D6-branes recently. In particular, the string-scale gauge coupling unification can be achieved due to the intermediate-scale vector-like particles from mathcal{N} = 2 sector. We calculate the supersymmetry breaking soft terms, and study the Standard Model (SM) fermion masses and mixings. There are nine pairs of Higgs doublets from mathcal{N} = 2 sector. Interestingly, we can explain the SM quark masses and mixings, as well as the charged leptons masses from three point and four-point Yukawa interactions. Moreover, we calculate the supersymmetry breaking soft terms in a previous model with gauge coupling unification since we find a typo in the previous study.

Breeding Realistic D‐Brane Models

AbstractIntersecting branes provide a useful mechanism to construct particle physics models from string theory with a wide variety of desirable characteristics. The landscape of such models can be enormous, and navigating towards regions which are most phenomenologically interesting is potentially challenging. Machine learning techniques can be used to efficiently construct large numbers of consistent and phenomenologically desirable models. In this work we phrase the problem of finding consistent intersecting D‐brane models in terms of genetic algorithms, which mimic natural selection to evolve a population collectively towards optimal solutions. For a four‐dimensional supersymmetric type IIA orientifold with intersecting D6‐branes, we demonstrate that unique, fully consistent models can be easily constructed, and, by a judicious choice of search environment and hyper‐parameters, of the found models contain the desired Standard Model gauge group factor. Having a sizable sample allows us to draw some preliminary landscape statistics of intersecting brane models both with and without the restriction of having the Standard Model gauge factor.

Revisiting the supersymmetric Pati\u2013Salam models from intersecting D6-branes

Employing novel random and supervised scanning methods, we systematically revisit the construction of three-family N=1 supersymmetric Pati–Salam models in Type IIA orientifolds on mathbf{T}^6/({mathbb {Z}}_2times {mathbb {Z}}_2) with intersecting D6-branes. Arising from the stacks of D6-branes with U(n) gauge symmetries, the Pati–Salam gauge symmetries SU(4)_Ctimes SU(2)_L times SU(2)_R can be broken down to the Standard Model via D-brane splitting as well as D- and F-flatness preserving Higgs mechanism. Also, the hidden sector contains USp(n) branes, which are parallel with the orientifold planes or their {{mathbb {Z}}_2} images. We find that the Type II T-duality in the previous study is not an equivalent relation in Pati–Salam model building if the model is not invariant under SU(2)_L and SU(2)_R exchange, and provides a way to obtain new models. We systematically construct the new models with three families, which usually do not have gauge coupling unification at the string scale. We for the first time construct the Pati–Salam models with at least one wrapping number whose absolute value reaching 5. In particular, for one large wrapping number equal to 5, we find that one kind of model carries more refined gauge couplings, and thus with more possibilities to have approximate gauge coupling unification.

Systematics of type IIA moduli stabilisation

We analyse the flux-induced scalar potential for type IIA orientifolds in the presence of p-form, geometric and non-geometric fluxes. Just like in the Calabi-Yau case, the potential presents a bilinear structure, with a factorised dependence on axions and saxions. This feature allows one to perform a systematic search for vacua, which we implement for the case of geometric backgrounds. Guided by stability criteria, we consider configurations with a particular on-shell F-term pattern, and show that no de Sitter extrema are allowed for them. We classify branches of supersymmetric and non-supersymmetric vacua, and argue that the latter are perturbatively stable for a large subset of them. Our solutions reproduce and generalise previous results in the literature, obtained either from the 4d or 10d viewpoint.

M-theory and orientifolds

We construct the M-Theory lifts of type IIA orientifolds based on K3-fibred Calabi-Yau threefolds with compatible involutions. Such orientifolds are shown to lift to M-Theory on twisted connected sum G2 manifolds. Beautifully, the two building blocks forming the G2 manifold correspond to the open and closed string sectors. As an application, we show how to use such lifts to explicitly study open string moduli. Finally, we use our analysis to construct examples of G2 manifolds with different inequivalent TCS realizations.

Model building on the non‐factorisable type IIA orientifold

We construct global semi‐realistic supersymmetric models with intersecting D6‐branes on the non‐factorisable orientifold . The non‐factorisable structure gives rise to differences compared to the factorisable case: additional conditions for the three‐cycles to be Lagrangian and extra constraints on the wrapping numbers for building fractional cycles.

Deforming D‐brane models on orbifolds

We review the stabilisation of complex structure moduli in Type IIA orientifolds, especially on with discrete torsion, via deformations of orbifold singularities. While D6‐branes in SO(2N) and USp(2N) models always preserve supersymmetry and thus give rise to flat directions, in an exemplary Pati‐Salam model with only U(N) gauge groups ten out of the 15 deformation moduli can be stabilised at the orbifold point.

The importance of being rigid: D6-brane model building on [formula omitted] with discrete torsion

Model building with rigid D6-branes on the Type IIA orientifold on T6/Z2×Z6′ with discrete torsion is considered. The systematic search for models of particle physics is significantly reduced by proving new symmetries among different lattice orientations. Suitable rigid D6-branes without matter in adjoint and symmetric representations are classified, and SO(2N) and USp(2N) gauge factors on orientifold invariant D6-branes are distinguished in terms of their discrete Wilson line and displacement parameters. Constraints on the non-existence of exotic matter prohibit global completions of local MSSM and left–right symmetric models, while globally defined supersymmetric Pati–Salam models are found. For the latter, only one particle generation possesses perturbative Yukawa couplings. Masses for the mild amount of exotic matter and the role of Abelian symmetries are briefly discussed.Last but not least, it is shown that for all three two-torus volumes of about the same order of magnitude, gauge coupling unification at one loop can be achieved, while for highly unisotropic choices a low string scale in the TeV range is compatible with the observed strengths of gauge and gravitational couplings.

Discrete gauge symmetries in D-brane models

In particle physics model building discrete symmetries are often invoked to forbid unwanted or dangerous couplings. A classical example is the R-parity of the MSSM, which guarantees the absence of dimension four baryon- and lepton-number violating operators. Although phenomenologically useful, these discrete symmetries are, in the context of field theory, poorly motivated at a more fundamental level. Moreover, discrete {\em global} symmetries are expected to be violated in consistent couplings to quantum gravity, while their {\em gauged} versions are expected to actually exist. In this paper we study discrete gauge symmetries in brane models in string theory, and argue that they are fairly generic in this framework. In particular we study the appearance of discrete gauge symmetries in (MS)SM brane constructions in string theory, and show that a few discrete ${Z_N}$ gauge symmetries, including R-parity and {\it baryon triality}, appear naturally as remnants of continuous U(1) gauge symmetries with St\"uckelberg $N(B\wedge F)$ couplings. Interestingly, they correspond to the simplest anomaly-free discrete symmetries of the MSSM as classified in the early 90's. We provide a number of examples based on type IIA intersecting brane constructions with a (MS)SM spectrum. We also study the appearance of discrete generalizations of R-parity in unified SU(5) type IIA orientifolds and local F-theory SU(5) GUTs.

The [formula omitted] effective actions of D-branes in Type IIA and IIB orientifolds

We discuss the four-dimensional N = 1 effective actions of single space–time filling D p -branes in general Type IIA and Type IIB Calabi–Yau orientifold compactifications. The effective actions depend on an infinite number of normal deformations and gauge connection modes. For D6-branes the N = 1 Kähler potential, the gauge-coupling function, the superpotential and the D-terms are determined as functions of these fields. They can be expressed as integrals over chains which end on the D-brane cycle and a reference cycle. The infinite deformation space will reduce to a finite dimensional moduli space of special Lagrangian submanifolds upon imposing F- and D-term supersymmetry conditions. We show that the Type IIA moduli space geometry is captured by three real functionals encoding the deformations of special Lagrangian submanifolds, holomorphic three-forms and Kähler two-forms of Calabi–Yau manifolds. These elegantly combine in the N = 1 Kähler potential, which reduces after applying mirror symmetry to the results previously determined for space–time filling D3-, D5- and D7-branes. We also propose general chain integral expressions for the Kähler potentials of Type IIB D-branes.

RR photons

Type II string compactifications to 4d generically contain massless Ramond-Ramond U(1) gauge symmetries. However there is no massless matter charged under these U(1)’s, which makes a priori difficult to measure any physical consequences of their existence. There is however a window of opportunity if these RR U(1)’s mix with the hypercharge U(1) Y (hence with the photon). In this paper we study in detail different avenues by which U(1) RR bosons may mix with D-brane U(1)’s. We concentrate on Type IIA orientifolds and their M-theory lift, and provide geometric criteria for the existence of such mixing, which may occur either via standard kinetic mixing or via the mass terms induced by Stückelberg couplings. The latter case is particularly interesting, and appears whenever D-branes wrap torsional p-cycles in the compactification manifold. We also show that in the presence of torsional cycles discrete gauge symmetries and Aharanov-Bohm strings and particles appear in the 4d effective action, and that type IIA Stückelberg couplings can be understood in terms of torsional (co)homology in M-theory. We provide examples of Type IIA Calabi-Yau orientifolds in which the required torsional cycles exist and kinetic mixing induced by mass mixing is present. We discuss some phenomenological consequences of our findings. In particular, we find that mass mixing may induce corrections relevant for hypercharge gauge coupling unification in F-theory SU(5) GUT’s.

FLUX PARAMETER SPACES IN TYPE II VACUA

We study the flux parameter spaces for semirealistic supersymmetric Pati–Salam models in the AdS vacua on Type IIA orientifold and realistic supersymmetric Pati–Salam models in the Minkowski vacua on Type IIB orientifold. Because the fluxes can be very large, we show explicitly that there indeed exists a huge number of semirealistic Type IIA and realistic Type IIB flux models. In the Type IIA flux models, in the very large flux limit, the theory can become weakly coupled and the AdS vacua can approach to the Minkowski vacua. In a series of realistic Type IIB flux models, at the string scale, the gauge symmetry can be broken down to the Standard Model gauge symmetry, the gauge coupling unification can be achieved naturally, all the extra chiral exotic particles can be decoupled, and the observed Standard Model fermion masses and mixings can be obtained as well. In particular, the real parts of the dilaton, Kähler moduli, and the unified gauge coupling are independent of the very large fluxes. The very large fluxes only affect the real and/or imaginary parts of the complex structure moduli, and/or the imaginary parts of the dilaton and Kähler moduli. However, these semirealistic Type IIA and realistic Type IIB flux models cannot be populated in the string landscape.

Semi-flatland

We study perturbative compactifications of Type II string theory that rely on a fibration structure of the extra dimensions a la SYZ. Non-geometric spaces are obtained by using T-dualities as monodromies. These vacua generically preserve N=1 supersymmetry in four dimensions, and are U-dual to M-theory on G2 manifolds. Several examples are discussed, some of which admit an asymmetric orbifold description. The massless spectrum is matched to that of the dual M-theory compactification on a Joyce manifold when a comparison is possible. We explore the possibility of twisted reductions where left-moving spacetime fermion number Wilson lines are turned on in the fiber. We also give an explanation from this semiflat viewpoint for the Hanany-Witten brane-creation effect and for the equivalence of the Type IIA orientifold on T5/Z2 and Type IIB on S1 x K3.

Comments on orientifolds without vector structure

We revisit type I compactifications with a Spin(32)/Z2 gauge bundle that admits no vector structure. We elucidate the relation of this Z2 obstruction to discrete B- field flux and to 't Hooft flux and clarify some subtleties in the T-duality transformation to type IIA intersecting D-brane models. We reexamine the earliest 3-generation GUT model on magnetized D-branes and show its consistency when a discrete B-flux is switched on. We further generalize partially known results for toroidal models to type I compactifications without vector structure and their mirror dual type IIA orientifolds on genuine Calabi-Yau manifolds. We illustrate this by working out the example of the quintic in some detail.