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Register a new userR-parity from string compactification
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Jihn E. Kim
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The strategy for assigning $Z_{4R}$ parity in the string compactification is presented. For the visible sector, an anti-SU(5) (flipped-SU(5)) grand unification (GUT) model with three families is used to reduce the number of representations compared to the number in the minimal supersymmetric standard models (MSSMs). The SO(32) heterotic string is used to allow a large nonabelian gauge group SU($N$), $Nge 9$, for the hidden sector such that the number of extra U(1) factors is small. A discrete subgroup of the gauge U(1)s is defined as the $Z_{4R}$ parity. Spontaneous symmetry breaking of anti-SU(5) GUT is achieved by the vacuum expectation values of two index antisymmetric tensor Higgs fields ${bf 10}_{+1}$ and $overline{bf 10}_{-1}$ that led to our word `anti-SU(5). In the illustrated example, the multiplicity 3 in one twisted sector allows the permutation symmetry $S_3$ that leads us to select the third family members and one MSSM pair of the Higgs quintets.
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We construct a supersymmetric standard model in the context of the $Z_{12-I}$ orbifold compactification of the heterotic string theory. The gauge group is $SU(3)_ctimes SU(2)_Ltimes U(1)_Ytimes U(1)^4times[SO(10)times U(1)^3]$. We obtain three chiral families, $3times{Q,d^c,u^c,L,e^c, u^c}$, and Higgs doublets. There are numerous neutral singlets many of which can have VEVs so that low energy phenomenology on Yukawa couplings can be satisfied. In one assignment (Model E) of the electroweak hypercharge, we obtain the string scale value of $sin^2theta_W^0={3/8}$ and another exactly massless {it exphoton} (in addition to the photon) coupling to exotic particles only. There are color triplet and anti-triplet exotics, $alpha$ and $bar{alpha}$, $SU(2)_L$ doublet exotics, $delta$ and $bar{delta}$, and $SU(3)_ctimes SU(2)_L$ singlet but $Y={2/3},-{1/3},-{2/3},{1/3}$ exotics, $xi,eta,bar{xi}, bar{eta}$. We show that all these vector-like exotics achieve heavy masses by appropriate VEVs of neutral singlets. One can find an effective R-parity between light (electroweak scale) particles so that proton and the LSP can live sufficiently long. In another assignment (Model S) of the electroweak hypercharge, there does not appear any exotic particle but $sin^2theta_W^0={3/14}$.
Motivated by results from the LHC and dark matter searches, we study the possibility of phenomenologically viable R-parity violation in $SU(5)$ GUT models from a top-down point of view. We show that in contrast to the more model dependent bounds on the proton lifetime, the limits on neutrino masses provide a robust, stringent and complementary constraint on all $SU(5)$ GUT-based R-parity violating models. Focusing on well-motivated string/$M$ theory GUT frameworks with mechanisms for doublet-triplet splitting and a solution to the $mu/Bmu$ problems, we show that imposing the neutrino mass bounds implies that R-parity violation is disfavored. The arguments can also be generalized to minimal $SO(10)$ GUTs. An experimental observation of R-parity violation would, therefore, disfavor such classes of top-down GUT models.
We construct a supersymmetric standard model in the context of the Z_{12-I} orbifold compactification of the E_8 x E_8 heterotic string theory. The gauge group is SU(3)_c x SU(2)_L x U(1)_Y x U(1)^4 x [SO(10) x U(1)^3] with sin^2theta_W = 3/8. We obtain three families of SO(10) spinor-like chiral matter states, and Higgs doublets. All other extra states are exactly vector-like under the standard model gauge symmetry. There are numerous standard model singlets, many of which get VEVs such that only the standard model gauge symmetry survives and desired Yukawa couplings can be generated at lower energies. In particular, all vector-like exotic states achieve superheavy masses and the R-parity can be preserved.
We study stabilization of an unstable cosmic string associated with spontaneously broken $U(1)_R$ symmetry, which otherwise causes a dangerous roll-over process. We demonstrate that in a gauge mediation model, messengers can receive enough corrections from the thermal plasma of the supersymmetric standard model particles to stabilize the unstable modes of the string.
The nature of R-parity violating interactions in two classes of string inspired supersymmetric grand unified theories (SISUSY GUT), based on the gauge groups $SO(10)$ (and its subgroup $SU(2)_Ltimes SU(2)_Rtimes SU(4)_cequiv G_{224}$) as well as $[SU(3)]^3$, are discussed and their strengths are related to the ratio of symmetry breaking scales present in the model. We first argue that for the R-parity violating couplings $lambda_{R!!!/}$ to be suppressed to the desired level, the $B-L$ local symmetry must break at an intermediate scale $M_{B-L}$ since $lambda_{R!!!/} =M_{B-L}/M_{GUT}$. We then construct scenarios where such intermediate scales arise being consistent with gauge coupling unification in a two-loop renormalization group study. In the resulting $SO(10)$ models, higher-dimensional-operator-induced R-parity violating couplings are potentially large (except in one case), and are therefore inconsistent with limits on the proton life time unless the couplings associated with the higher dimensional terms are fine tuned to very small values. However, the $[SU(3)]^3$ and $G_{224}$ models can be consistent if a certain class of quark-lepton coupling in the superpotential is forbidden by a discrete summetry (unrelated to R-parity). An interesting prediction of these models is neutron-anti-neutron oscillation with observable strength.
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