Brane Solutions in Supergravity and the Near-Horizon Geometries

This note represents a summary of a talk given at the 2018 Summer Mathematical Physics seminar, with focus on the physical and the mathematical concepts of the holography principle and large-N dualities. Here, we present an elementary overview of the p-brane solutions in supergravity, setting up a stage for a fairly broad topics on the AdS/CFT correspondence.

DIMENSION EMERGENCE, HOLOGRAPHY AND QUANTUM GRAVITY

In this paper, we try to give an alternative interpretation of the holography principle. We argue that the space or time may be regarded as emerging from quantum mechanics as an evolutive parameter. The lower D-dimensional theory is related to a corresponding (D+1)-theory by a mysterious quantum system. Then from the higher-dimensional theory, under a new dimension reduction mechanism we obtain the corresponding results. We also try to incorporate the gauge field into the reduction, roughly identifying Aμ with Nμ which is the shift vector in the ADM-like decomposition of space–time metric. In the end, we extend to the gravitational field, and obtain a relation [Formula: see text] with a cutoff factor κ, from a different view.

MATCHING CONDITION ON THE EVENT HORIZON AND HOLOGRAPHY PRINCIPLE

It is shown that the event horizon of 4D black hole or ds2=0 surfaces of multidimensional wormhole-like solutions reduce the amount of information necessary for determining the whole spacetime and hence satisfy the Holography principle. This leads to the fact that by matching two metrics on a ds2=0 surface (an event horizon for 4D black holes) we can match only the metric components but not their derivatives. For example, this allows us to obtain a composite wormhole inserting a 5D wormhole-like flux tube between two Reissner–Nordström black holes and matching them on the event horizon. Using the Holography principle, the entropy of a black hole from the algorithm theory is obtained.