Abstract
We search for the three-generation standard-like and/or Pati-Salam models from the SO(32) heterotic string theory on smooth, quotient complete intersection Calabi-Yau threefolds with multiple line bundles, each with structure group U(1). These models are S- and T-dual to intersecting D-brane models in type IIA string theory. We find that the stable line bundles and Wilson lines lead to the standard model gauge group with an extra U(1)B−L via a Pati-Salam-like symmetry and the obtained spectrum consists of three chiral generations of quarks and leptons, and vector-like particles. Green-Schwarz anomalous U(1) symmetries control not only the Yukawa couplings of the quarks and leptons but also the higher-dimensional operators causing the proton decay.
Highlights
Other hand, the adjoint representation of SO(32) does not contain the spinor representation of SO(10), but it contains the spectrum of the standard model
We find that the stable line bundles and Wilson lines lead to the standard model gauge group with an extra U(1)B−L via a Pati-Salam-like symmetry and the obtained spectrum consists of three chiral generations of quarks and leptons, and vector-like particles
S- and T-dualities tell us that the SO(32) heterotic line bundle models correspond to intersecting D6-brane models in type IIA string theory, where several stacks of branes directly lead to the minimal supersymmetric standard model (MSSM) and/or Pati-Salam model [26,27,28]
Summary
We briefly review the low-energy effective action of the SO(32) heterotic string theory on CY manifolds with multiple line bundles. (For more details, we refer to refs. [10, 11, 32].) At the order of α′, the bosonic part of the low-energy effective action is given by. Since the spinorial representation appears in the first excited mode in the heterotic string [1, 2], we require that the first Chern class of the total gauge bundle lies in second even integral cohomology basis of the CY manifold: c1(W ) = nac1(La) ∈ H2(M, 2Z), a (2.7). When some bundles in eq (2.2) are trivial bundles OM, the U(1) gauge symmetries are enhanced to non-abelian ones as shown in section 3 and corresponding cohomology becomes dim(H0(M, OM)) = dim(H3(M, OM)) = 1 and dim(H1(M, OM)) = dim(H2(M, OM)) = 0 This is because the zero-modes of the Dirac operator are the (0, 0) and (0, 3) forms under the Dolbeault operator ∂ ̄ on manifolds of SU(3) holonomy. Proper internal line bundles have the potential to yield three generations of chiral fermions for a large class of CY manifolds, in the standard embedding scenario, three-generation models are restricted to specific CY manifolds with small hodge numbers
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