Particles hold themselves together in a vacuum through the fundamental forces of nature, specifically the strong nuclear force and the electromagnetic force. These forces act between the particles and keep them bound together.
The strong nuclear force is responsible for binding together particles that make up an atom's nucleus, such as protons and neutrons. This force is extremely powerful, overcoming the repulsive force between positively charged protons. In a vacuum, this force is still present and allows particles to hold themselves together.
The electromagnetic force is responsible for the attraction or repulsion between charged particles. In a vacuum, particles with opposite charges (such as protons and electrons) will be attracted to each other due to this force. This allows for the formation of atoms and molecules, as well as other particles to hold together.
Aside from the strong nuclear force and the electromagnetic force, there are also weak nuclear force and gravitational force. However, these forces are not as significant in particle bonding in a vacuum as they are over larger distances. The strong nuclear force and electromagnetic force are the main forces at play in this scenario.
At extremely high energies, particles may break apart due to the collisions and interactions between them. This is seen in particle accelerators, where particles are accelerated to high speeds and collide with each other, breaking apart into smaller particles. In a vacuum, there is less interference from other particles and the energy levels can reach higher levels, potentially leading to particle decay or the creation of new particles.