Guptaroy, ankita and Roy, Shubho Ranjan
(2018)
Holographic computational complexity in
non-relativistic field theories.
Masters thesis, Indian Institute of Technology Hyderabad.
Abstract
The aim of the project is to study the holographic complexity of black holes and black branes.
We discuss basic concept of complexity. We see how quantum computational complexity is
related to black hole physics. In the process we look at the difference between classical and
quantum complexity. We solve for the holographic complexity of pure AdS and pure Lifshitz
spacetime. We then study the AdS black hole in detail. We first try to find the nature of
the maximal volume slice at a finite time, and then see the small black hole limit of it using
the perturbation method. We perform similar late time analysis on the Lifshitz black hole as
well. Lastly we try to understand the notion of complexity from first principle calculations. We
retrace the procedure of calculating the complexity of a system and try to compare with the
holographic quantity. However, although the two approaches are similar in a lot of aspects, they
don't match perfectly.
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