Supersymmetric SO Research Articles

UV finite GUT with SUSY breaking

We construct an example of a safe ultraviolet finite supersymmetric renormalizable SO(10) grand unified theory featuring a supersymmetric dynamical breaking mechanism. Our results constitute a step forward towards an ultraviolet safe extension of the Standard Model enjoying the benefits of grand unified theories. Published by the American Physical Society 2024

Testing realistic SO(10) SUSY GUTs with proton decay and gravitational waves

We present a comprehensive analysis of a supersymmetric SO(10) grand unified theory, which is broken to the Standard Model via the breaking of two intermediate symmetries. The spontaneous breaking of the first intermediate symmetry, B−L, leads to the generation of cosmic strings and right-handed neutrino masses and further to an observable cosmological background of gravitational waves and generation of light neutrino masses via type-I seesaw mechanism. Supersymmetry breaking manifests as sparticle masses below the B−L breaking but far above the electroweak scale due to proton decay limits. This naturally pushes the B−L breaking scale close to the grand unified theory scale, leading to the formation of metastable cosmic strings, which can provide a gravitational wave spectrum consistent with the recent pulsar timing arrays observation. We perform a detailed analysis of this model using two-loop renormalization group equations, including threshold corrections, to determine the symmetry-breaking scale consistent with the recent pulsar timing arrays signals such as NANOGrav 15-year data and testable by the next-generation limits on proton decay from Hyper-K and JUNO. Simultaneously, we find the regions of the model parameter space that can predict the measured quark and lepton masses and mixing, baryon asymmetry of our Universe, a viable dark matter candidate and can be tested by a combination of neutrinoless double beta decay searches and limits on the sum of neutrinos masses. Published by the American Physical Society 2024

Boundary confining dualities and Askey-Wilson type q-beta integrals

We propose confining dualities of mathcal{N} = (0, 2) half-BPS boundary conditions in 3d mathcal{N} = 2 supersymmetric SU(N), USp(2n) and SO(N) gauge theories. Some of these dualities have the novel feature that one (anti)fundamental chiral has Dirichlet boundary condition while the rest have Neumann boundary conditions. While some of the dualities can be extended to 3d bulk dualities, others should be understood intrinsically as 2d dualities as they seem to hold only at the boundary. The gauge theory Neumann half-indices are well-defined even for theories which contain monopole operators with non-positive scaling dimensions and they are given by Askey-Wilson type q-beta integrals. As a consequence of the confining dualities, new conjectural identities of such integrals are found.

Consistent Kaluza-Klein Truncations and Two-Dimensional Gauged Supergravity.

We consider generalized Scherk-Schwarz reductions of E_{9} exceptional field theory to D=2 space-time dimensions and, in particular, construct the resulting scalar potential of all gauged supergravities that can be obtained in this way. This provides the first general expression for a multitude of theories with an interesting structure of vacua, covering potentially many new AdS_{2} cases. As an application, we prove the consistency of the truncation of eleven-dimensional supergravity on S^{8}×S^{1} to SO(9) gauged maximal supergravity. Fluctuations around its supersymmetric SO(9)-invariant vacuum describe holographically the dynamics of interacting D0-branes.

Leptogenesis in SO(10) models with A4 modular symmetry

We study the prediction for leptogenesis in two renormalizable supersymmetric SO(10) × A4 modular models in which the neutrino mass is dominantly generated by the type I seesaw mechanism. The evolution of the lepton asymmetries are described in terms of the three-flavored density matrix equations for three heavy Majorana neutrinos, where both vanishing initial condition and thermal initial condition of the right-handed neutrinos are considered. We also present an analytical approximation based on the Boltzmann equations. We find regions of parameter space compatible with the measured fermion masses and mixing parameters as well as the baryon asymmetry of the Universe. The predictions for the light neutrino masses, the effective mass in neutrinoless double beta decay and the leptonic CP violation phases are discussed.

Tracking down the route to the SM with inflation and gravitational waves

We explore supersymmetric SO(10) models predicting observable proton decay and various topological defects which produce different shapes and strengths of gravitational wave backgrounds depending on the scales of intermediate symmetry breaking and inflation as well. We compare these to their non-supersymmetric counterparts. By identifying the scales at which gravitational wave signals appear, we would be able to track down a particular breaking chain and discern if it has a supersymmetric origin or not. It would also be useful to observe gravitational waves from more than one source among all possible topological defects and first order phase transitions for a realistic breaking chain. For these purposes, we work out specific examples in which the grand unification and relevant intermediate scales are calculable explicitly. It turns out that examples with gravitational waves from different sources are quite difficult to obtain, and the predicted gravitational wave profiles from domain walls and first order phase transitions obtained in some examples will require detectors in the kHz to MHz region.

Inflationary Universe with a Coleman-Weinberg potential meets non-thermal leptogenesis

Baryon asymmetry via non-thermal leptogenesis is explained in the framework of the standard Coleman-Weinberg inflationary model. The CP-violation asymmetry factor arises from the out-of-equilibrium decays of heavy right-handed neutrinos in supersymmetric SO(10) GUT models. All quantities of interest are computed in terms of the two parameters of the inflationary potential, namely the vacuum expectation value of the inflaton, M, and the amplitude A. For successful baryogenesis we obtain analytical expressions relating A to M, and also the reheating temperature after inflation as well as the mass of the inflaton to M. Assuming typical values of CP-violation asymmetry obtained in concrete supersymmetric SO(10) unified models, we show graphically all three quantities of interest versus M. Interestingly enough, we obtain for (A,M) numerical values comparable to the ones previously obtained in the slow-roll approximation of inflationary dynamics upon comparison with CMB data, such as amplitude of scalar perturbations and spectral index. Proton decay is also briefly discussed. Our results may be of interest to model builders.

Comparatively light extra Higgs states as signature of SUSY SO(10) GUTs with 3rd family Yukawa unification

We study 3rd family Yukawa unification in the context of supersymmetric (SUSY) SO (10) GUTs and SO(10)-motivated boundary conditions for the SUSY-breaking soft terms. We consider μ < 0 such that the SUSY loop-threshold effects enable a good fit to all third family masses of the charged Standard Model (SM) fermions. We find that fitting the third family masses together with the mass of the SM-like Higgs particle, the scenario predicts the masses of the superpartner particles and of the extra Higgs states of the MSSM: while the sparticles are predicted to be comparatively heavy (above the present LHC bound but within reach of future colliders), the spectrum has the characteristic feature that the lightest new particles are the extra MSSM Higgses. We show that this effect is rather robust with respect to many deformations of the GUT boundary conditions, but turns out to be sensitive to the exactness of top-bottom Yukawa unification. Nevertheless, with moderate deviations of a few percent from exact top-bottom Yukawa unification (stemming e.g. from GUT-threshold corrections or higher-dimensional operators), the scenario still predicts extra MSSM Higgs particles with masses not much above 1.5 TeV, which could be tested e.g. by future LHC searches for ditau decays H0/A0→ ττ . Finding the extra MSSM Higges before the other new MSSM particles could thus be a smoking gun for a Yukawa unified SO(10) GUT.

New ultraviolet operators in supersymmetric SO(10) GUT and consistent cosmology

We consider the minimal supersymmetric grand unified model (MSGUT) based on the group $\mathrm{SO}(10)$, and study conditions leading to possible domain wall (DW) formation. It has been shown earlier that the supersymmetry preserving vacuum expectation values (vev's) get mapped to distinct but degenerate set of vev's under action of $D$ parity, leading to formation of domain walls as topological pseudo-defects. The metastability of such walls can make them relatively long lived and contradict standard cosmology. Thus we are led to consider adding a nonrenormalisable Planck scale suppressed operator, that breaks $\mathrm{SO}(10)$ symmetry but preserves Standard Model symmetry. For a large range of right handed breaking scales $M_R$, this is shown to give rise to the required pressure difference to remove the domain walls without conflicting with consistent big bang nucleosynthesis (BBN) while avoiding gravitino overproduction. However, if the walls persist till the onset of weak (thermal) inflation, then a low $\sim 10 - 100$ TeV $M_R$ becomes problematic.

B − L violating interactions in supersymmetric SO(10) models

An analysis is given of B − L violating interactions in SO(10) arising from the integration of of SU(5) of heavy Higgs. The analysis is done within the well defined missing partner model where the doublet-triplet splitting arises naturally. The Higgs representations of the model consist of two 10-plets, one 120, one 210 plet and a representations of SO(10). The SO(10) symmetry is spontaneously broken by the singlet in the and 210. In this work we focus on the B−L interactions arising from the elimination of plets of SU(5). We compute five field and six field B−L violating operators. The analysis extends previous analyses where B−L violating interactions arising from the elimination of and were computed. Specifically we compute dimension 6, 7 and 9 operators. These interactions can generate GUT scale baryogengesis, proton decay, and oscillations.

Grand unified parity solution to the strong CP problem

A beyond the standard model theory that respects parity symmetry at short distances is known to provide a solution to the strong CP problem without the need for an axion, while keeping the CKM phase unconstrained. In this paper we present a supersymmetric SO(10) grand unified embedding of this idea with Yukawa couplings generated by {\bf 10}, ${\bf \overline{126}}$ and {\bf 120} Higgs fields. This model is known to provide a unified description of masses and mixings of quarks and leptons. When CP symmetry is imposed on this model, the discrete gauge subgroup C of SO(10) combines with it to generate an effective parity symmetry, leading to hermitian quark mass matrices. Imposing an additional discrete symmetry, $G$, we show that there are no other tree level sources of $\theta$ in the model; $G$ also guarantees that the one- and two-loop contributions to $\theta$ vanish. We then show that the leading three-loop effects and the effect of higher-dimensional operators invariant under $G$ give rise to $\theta$ near the current experimental bound, making the model testable in the current searches for neutron electric dipole moment.

Confronting SUSY SO(10) with updated Lattice and Neutrino data

We present an updated fit of supersymmetric SO(10) models to quark and lepton masses and mixing parameters. Including latest results from lattice QCD determinations of quark masses and neutrino oscillation data, we show that fits neglecting supersymmetric threshold corrections are strongly disfavoured in our setup. Only when we include these corrections we find good fit points. We present χ2-profiles for the threshold parameters, which show that in our setup the thresholds related to the third generation of fermions exhibit two rather narrow minima.

New minimal supersymmetric GUT emergence and sub-Planckian renormalization group flow

Consistency of trans-unification renormalization group (RG) evolution is used to discuss the domain of definition of the New Minimal Supersymmetric SO(10)GUT (NMSGUT). We define the 1-loop RGE $\ensuremath{\beta}$ functions, simplifying generic formulae using constraints of gauge invariance and superpotential structure. We also calculate the 2 loop contributions to the gauge coupling and gaugino mass and indicate how to get full 2 loop results for all couplings. Our method overcomes combinatorial barriers that frustrate computer algebra based attempts to calculate SO(10) $\ensuremath{\beta}$ functions involving large irreps. Use of the RGEs identifies a perturbative domain $Q&lt;{M}_{E}$, where ${M}_{E}&lt;{M}_{\text{Planck}}$ is the scale of emergence where the NMSGUT, with GUT compatible soft supersymmetry breaking terms emerges from the strong UV dynamics associated with the Landau poles in gauge and Yukawa couplings. Due to the strength of the RG flows the Landau poles for gauge and Yukawa couplings lie near a cutoff scale ${\mathrm{\ensuremath{\Lambda}}}_{E}$ for the perturbative dynamics of the NMSGUT which just above ${M}_{E}$. SO(10) RG flows into the IR are shown to facilitate small gaugino masses and generation of negative Non Universal Higgs masses squared needed by realistic NMSGUT fits of low energy data. Running the simple canonical theory emergent at ${M}_{E}$ through ${M}_{X}$ down to the electroweak scale enables tests of candidate scenarios such as supergravity based NMSGUT with canonical kinetic terms and NMSGUT based dynamical Yukawa unification.

Resurrecting minimal Yukawa sector of SUSY SO(10)

Supersymmetric SO(10) models with Yukawa coupling matrices involving only a 10H and a {overline{126}}_H of Higgs fields can lead to a predictive and consistent scenario for fermion masses and mixings, including the neutrino sector. However, when coupled minimally to a symmetry breaking sector that includes a 210H and a 126H, these models lead either to an unacceptably small neutrino mass scale, or to non-perturbative values of the gauge couplings. Here we show that with the addition of a 54H to the symmetry breaking sector, the successful predictions of these models for fermion masses and mixings can be maintained. The 54H enables a reduction of the B − L symmetry breaking scale to an intermediate value of order 1012 GeV, consistent with the observed neutrino mass spectrum, while preserving perturbative gauge coupling unification. We obtain an excellent fit to all fermion masses and mixings in this framework. We analyze carefully the prediction of the model for CP violation in neutrino oscillations. Consistency with proton lifetime, however, requires a mini-split SUSY spectrum with the squarks and sleptons having masses of order 100 TeV, accompanied by TeV scale gauginos and Higgsinos. Such a spectrum may arise from pure gravity mediation, which would predict the partial lifetime for the decay pto overline{nu}{K}^{+} to be an order of magnitude above the current experimental limit.

New weak-scale physics from SO(10) with high-scale supersymmetry

Gauge coupling unification and the stability of the Higgs vacuum are among two of the cherished features of low-energy supersymmetric models. Putting aside questions of naturalness, supersymmetry might only be realised in nature at very high energy scales. If this is the case, the preservation of gauge coupling unification and the stability of the Higgs vacuum would certainly require new physics, but it need not necessarily be at weak scale energies. New physics near the unification scale could in principle ensure Grand Unification, while new physics below $\mu \sim 10^{10}$ GeV could ensure the stability of the Higgs vacuum. Surprisingly however, we find that in the context of a supersymmetric SO(10) Grand Unified Theory, gauge coupling unification and the Higgs vacuum stability, when taken in conjunction with existing phenomenological constraints, require the presence of $\mathcal{O}$(TeV)-scale physics. This weak-scale physics takes the form of a complex scalar SU(2)$_L$ triplet with zero hypercharge, originating from the $\mathbf{210}$ of SO(10).

Leptonic CP violation and proton decay in SUSY SO(10)

We study the correlation between proton lifetime and leptonic CP violation in a class of renormalizable supersymmetric SO(10) grand unified theories (GUTs) with 10, 126 and 120 Higgs fields, which provides a unified description of all fermion masses and a possible resolution for the strong CP problem. This specific model is unique in that it can so far be compatible with current proton lifetime limits for a supersymmetry (SUSY) breaking scale as low as 5 TeV due to the presence of a specific Yukawa texture. Our investigation reveals that a discovery of leptonic CP violation in neutrino oscillations would lead to substantial reduction of the parameter space of the model and the potential ruling out of type-II dominance in the neutrino mass seesaw. Furthermore, the previously predicted proton partial lifetimes are sufficiently long for only certain values of the leptonic CP phase.

Extended MSSM in supersymmetric SO(10) grand unification

We apply the perturbative grand unification due to renormalization to distinguish TeV-scale relics of supersymmetric $\rm{SO}(10)$ scenarios. With rational theoretical constraints taken into account, we find that for the breaking pattern of either $\rm{SU}(5)$ or Pati-Salam only extra matter $\mathbf{16}$ supermultiplet of $SO(10)$ can appear at TeV scale, apart from MSSM spectrum.

Light pseudo-Goldstone Higgs boson from SO(10) GUT with realistic phenomenology

Within the supersymmetric SO(10) grand unified theory (GUT), a new mechanism, giving the light Higgs doublet as a pseudo-Goldstone mode, is suggested. Realizing this mechanism, we present an explicit model with fully realistic phenomenology. In particular, desirable symmetry breaking and natural all-order hierarchy are achieved. The constructed model allows one to have a realistic fermion pattern, nucleon stability, and successful gauge coupling unification. The suggested mechanism opens prospects in the field for a novel $SO(10)$ GUT model building and for further investigations.

Couplings in renormalizable supersymmetric SO(10) models

We study the most general renormalizable couplings containing Higgs [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] in the supersymmetric SO(10) models. The Clebsch–Gordan coefficients are calculated using the maximal subgroup [Formula: see text].

M2-brane dynamics in the classical limit of the BMN matrix model

We investigate the large-N limit of the BMN matrix model by analyzing the dynamics of ellipsoidal M2-branes that spin in the 11-dimensional maximally supersymmetric SO(3)×SO(6) plane-wave background. We identify finite-energy solutions by specifying the local minima of the corresponding energy functional. These configurations are static in SO(3) due to the Myers effect and rotate in SO(6) with an angular momentum that is bounded from above. As a first step towards studying their chaotic properties, we evaluate the Lyapunov exponents of their radial fluctuations.