Goldstone bosons and gauge bosons are both types of elementary particles in quantum field theory, but they have distinct properties and roles.
Goldstone bosons arise in the context of spontaneous symmetry breaking in quantum field theories. When a system undergoes spontaneous symmetry breaking, the ground state of the system no longer possesses the full symmetry of the underlying theory. As a consequence, massless particles called Goldstone bosons emerge. These bosons are associated with the broken symmetry and can be thought of as the "residue" of the symmetry-breaking process.
Goldstone bosons are characterized by their zero mass and their coupling to the broken generators of the symmetry group. They typically have spin-0, meaning they are scalar particles. Examples of Goldstone bosons include the pions, which emerge in the context of spontaneous chiral symmetry breaking in quantum chromodynamics (QCD).
On the other hand, gauge bosons are particles that mediate the fundamental forces in nature. They are responsible for transmitting the forces between particles. Gauge bosons arise from the gauge symmetry of the underlying theory. Each fundamental force is associated with a specific gauge boson. For example, the photon is the gauge boson associated with the electromagnetic force, while the W and Z bosons are the gauge bosons of the weak force.
Gauge bosons have nonzero mass and specific spin values. The photon is a massless spin-1 particle, while the W and Z bosons are massive and have spin-1. In contrast to Goldstone bosons, gauge bosons do not arise from spontaneous symmetry breaking but are part of the fundamental structure of the theory.
In summary, Goldstone bosons emerge from spontaneous symmetry breaking and are associated with broken symmetries, while gauge bosons are the particles that mediate the fundamental forces in nature and are associated with the gauge symmetries of the underlying theory.