One of the important successes of string theory has been the AdS/CFT correspondence which conjectures a mathematical equivalence between string theories (containing gravity) and field theories. The main focus of this thesis is to understand AdS/CFT correspondence more deeply, at the quantum level, in the context of Black Hole Entropy and Holographic Wilson loops.It has been recently shown that the topologically twisted index for 3d supersymmetric Chern-Simons-matter theory (known as ABJM theory) in a certain limit reproduces the Bekenstein-Hawking entropy of magnetically charged asymptotically AdS4 black holes. In the first part of thesis, we investigate sub-leading logarithmic corrections in the large N limit to the topologically twisted index in ABJM theory and black hole entropy in the dual one-loop quantum supergravity, focusing on both the near horizon geometry and the full AdS4 black hole background. We explicitly focus on understanding the quantum aspects of microstate counting of the black hole entropy, which provides an invaluable benchmark for quantum gravity theories. Another aspect of this thesis is precision holography with supersymmetric Wilson loops. The main idea of precision holography is to better understand string perturbation theory in curved spaces beyond the semi-classical approximation, given exact results from localization. The expectation value of Wilson loop operators can be computed exactly via supersymmetric localization. Holographically, these operators are mapped to string configurations in the gravity dual. In the large N limit, the on-shell string action reproduces the large coupling limit of the gauge theory expectation value. There should be a precise match between the sub-leading corrections to these limits as guided by AdS/CFT correspondence. Such precision tests have been done in the literature in the context of N=4 SYM theory revealing various subtleties in the choice of regularization scheme for one-loop computations.In the second part of thesis, we perform a test of this match at next-to-leading order in string theory by computing the ratio between one-loop determinants of the quadratic fluctuations around the classical string configurations dual to BPS latitude and circular Wilson loops in both N=4 SYM and ABJM theory. We find a match for sub-leading corrections in the limit of small latitude angle, using zeta function regularization scheme. Another crucial result of this calculation is that the string partition function is determined entirely by some special modes, which points to a potential bulk localization.
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