Goldstone Fields in the Superstring Theory
Abstract
If global supersymmetry is broken by gaugino condensation in the hidden sector of the E_{8} × E_{8}^{'} heterotic superstring theory after compactification, then the auxiliary field F_{B} of the modulus B ≡ (B_{r}, B_{i}) attains a finite value, while that of the dilaton A ≡ (A_{r}, A_{i}) vanishes, F_{A} = 0, the Goldstone fermion being the modulino ∼ {B}, the spin½ component of the complex chiral supermultiplet {B} ≡ (B,∼ {B}). The Goldstone boson of the scale symmetry that is broken when the radius of the internal space is fixed at a constant value is B_{r}, which is determined from the goldstino Lagrangian, compared term by term with the superstring Lagrangian, including higherderivative gravitational terms {R}^{2} and {R}^{4}, after linking the spacetime curvature to the energymomentum tensor of the goldstino via the Einstein equations. This nonlinear formulation of supersymmetry, due to Volkov and Akulov, is expressed in terms of the goldstino alone, whose Lagrangian contains a negative cosmological constant, which can be cancelled by the superHiggs mechanism of Deser and Zumino to make the gravitino massive and break supersymmetry at the level m_{s} = √ {√ {6}m_{3/2}/k }≈ 2.5(1.39/A_{r})^{1/4} (B_{r} /B_{r} ^{H})^{1/2}× 10^{18} GeV, while m_{3/2} ≈ (1.39/A_{r}) ^{1/2}(B_{r} /B_{r} ^{H}× 10^{18} GeV. Here, the modulus has been scaled to the Hagedorn value for the heterotic superstring theory, B_{r} ^{H} = 1/4π ^{2} T^{2} Hα ' = 2.914, and A_{r}, identified with the inverse square of the treelevel gauge coupling, has been scaled to the calculation in the minimal supersymmetric standard model due to Weinberg, that g^{2} = 1.39 at the unification mass M_{X} = 2.2 × 10^{16} GeV, assuming three generations of elementary particles and two Higgs doublets. In the presence of gravitino condensation in the internal space, however, there is an arbitrary additional contribution to the cosmological constant, facilitating reduction of m_{s} to 100 TeV, say, and m_{3/2} to 1 eV.
 Publication:

International Journal of Modern Physics D
 Pub Date:
 2008
 DOI:
 10.1142/S0218271808011882
 Bibcode:
 2008IJMPD..17...81P
 Keywords:

 Goldstone theorem;
 heterotic superstring theory;
 superHiggs effect;
 supersymmetry breaking