Having put all of this in place, we see that Finally, theŜ parameter iŝ Notice that for ∆ → +∞ one findsŜ → 3 4 ε 2 cos 2 θ W , which is the AdS result with IR Dirichelet boundary conditions [24,29]. The reason for this is that by taking ∆ → +∞ in practice the background becomes identical to the AdS with an IR hard-wall at r = 0.
As a side remark, notice also that our result forŜ vanishes for ∆ = 1. The reason for this is that in this case the bulk dynamics is controlled by a free scalar in the dual theory. However, there is no light dilaton in the spectrum for ∆ < 2. For values of ∆ > 2 the result is very close to the asymptotic one, with a modest reduction for values close to ∆ = 2, for whichŜ → cos 2 θ W ε 2 (2π − 1)/π 2.

### Language ###
English

### Assessment ###
The text mentions a specific value that Ŝ approaches when ∆ → +∞, which could be a straightforward information request.

### Query ###
What is the value of S in the AdS result with IR Dirichelet boundary conditions?
What is the value of S in the AdS result with IR Dirichelet boundary conditions?