Semi-Classical Brane in AdS-Spaces

We briefly review a semi-classical analysis of static branes in AdS spaces. First, fluctuations of a 1/2 BPS F-string in AdS5 ×S5 whose world-sheet extends along AdS2 are examined. They are three massive and five massless scalars propagating in AdS2. It is shown that they can reach the boundary to deform the Wilson line and so result in operator insertions in the Wilson line. We see that there exists SO(3) × SO(5) symmetry in both sides. Second, fluctuations of a D3-brane in AdS5 × S5 whose world-volume extends along AdS2 × S2 in AdS5 are examined. They are six massless scalars and a U(1) gauge field propagating in AdS2 × S2. The spectrum on AdS2 is derived via a KK-reduction on S2. Third, fluctuations of an M2-brane in AdS4 × S7/ℤk whose world-volume extends along AdS2 × S1 is examined. After a KK-reduction on S1, it is shown that for k = 1,2 the spectrum degenerates to form eight N = 1 scalar supermultiplets for each µ∈ℤ/2. Among them, sixteen bosonic fluctuations can reach the boundary.