A compactified black p-brane in a supergravity theory is not the same as a graviton. Let's break down these concepts:
Black p-brane: In string theory and certain supergravity theories, a black p-brane refers to an extended object (brane) that carries both mass and charge and has a certain number of spatial dimensions (p dimensions). These branes are solutions to the equations of motion in these theories and exhibit properties similar to black holes in general relativity. However, they can have different geometries and carry different charges depending on the specific brane configuration.
Compactification: Compactification is a process in string theory where extra spatial dimensions are "curled up" or compactified to very small sizes. This process allows for the unification of gravity with other fundamental forces. The specific geometry and size of the compactified dimensions determine the properties of the resulting low-energy effective theory.
Graviton: The graviton is a hypothetical elementary particle that is postulated to be the quantum particle associated with the gravitational force. In theories of quantum gravity, such as string theory, the graviton is the carrier of gravitational interactions, analogous to how the photon is the carrier of electromagnetic interactions. Gravitons are massless, spin-2 particles.
In the context of your question, a compactified black p-brane in a supergravity theory is a specific object with extended dimensions, while the graviton is a hypothetical elementary particle associated with gravitational interactions. While both concepts are related to gravity, they refer to different aspects of the theory.
It's important to note that the relationship between branes, gravitons, and gravity in the context of string theory and supergravity is a complex and ongoing area of research. The full understanding of how these concepts fit together is still an active area of investigation in theoretical physics.