A Clifford algebra approach to bosonic strings with fermionic boundaries

Area of Science:

• Theoretical Physics
• High Energy Physics
• Geometric Algebra

Background:

• The Brauer-Weyl theorem establishes an isomorphism between spinor tensor product algebras and Clifford algebras.
• The Standard Model's fermion-boson relationships align with the Brauer-Weyl theorem, but not with supersymmetry.
• Supersymmetry is often considered essential for string theory due to perceived issues with non-supersymmetric bosonic string theory.

Purpose of the Study:

• To rebut common objections to non-supersymmetric bosonic string theory.
• To demonstrate how bosonic string theory can accommodate fermions and a Higgs-like field.
• To propose bosonic string theory as a unified framework for fundamental forces.

Main Methods:

• Re-examination of the Brauer-Weyl theorem's implications for particle physics.
• Analysis of fermionic states within the D-brane boundary of open strings.
• Characterization of the open-string tachyon as a Higgs field.

Main Results:

• Bosonic string theory admits fermions on D-brane boundaries.
• The open-string tachyon exhibits properties consistent with the Higgs field.
• The 1970s formulation of bosonic string theory, when viewed as a theory of all forces, aligns with the Standard Model.

Conclusions:

• Supersymmetry is not a necessary requirement for string theory.
• Bosonic string theory provides a viable framework for unifying fundamental forces and describing the Standard Model.
• Geometric algebra offers powerful tools for understanding modern physics.