The concept of particles and anti-particles in the context of Hawking radiation is slightly different from the notion of fundamental particles and their vibrations as described in string theory. Allow me to explain.
In the framework of quantum field theory, particles and anti-particles are considered as excitations of their respective fields. For example, an electron is an excitation of the electron field, and a positron is an excitation of the positron field. These particles and anti-particles have opposite electric charges and other quantum numbers.
Hawking radiation is a theoretical prediction made by physicist Stephen Hawking, which suggests that black holes are not completely black but emit thermal radiation due to quantum effects near the event horizon. According to Hawking's calculations, this radiation involves the spontaneous creation of particle-antiparticle pairs near the black hole's event horizon. One of these particles can fall into the black hole while the other escapes to infinity, resulting in the apparent radiation from the black hole.
In the context of Hawking radiation, the creation of particle-antiparticle pairs does not involve string vibrations or the underlying structure of particles as described in string theory. Rather, it is a consequence of the quantum nature of fields near the black hole's event horizon. These particles are not directly related to the vibrations of strings but are rather an outcome of quantum field fluctuations in the curved spacetime around the black hole.
In summary, while string theory provides a framework for understanding the fundamental particles and their vibrations, the concept of particle-antiparticle pairs in Hawking radiation is not directly connected to the vibrational modes of strings.