Just in case you don't deduce it from flowman's post, the ANMs themselves are also on that CIA link.
The Slot Allocation Message includes the most penalising regulation, i.e. the bottleneck that's giving you the slot. You can look up the reg on the CIA.
e.g. if you get
-REGUL LPFRA08
You can look up LPFRA08 to find:
Seq No: 51 FMP: LPPCFMP
Published: 2008-07-08 04:35 State: CHANGE
WEF: 2008-07-08 07:20 Regulation Id: LPFRA08
UNT: 2008-07-08 12:00 Reason: Aerodrome Capacity
Flight Level: ALL Traffic Volume Description: LPFR ARRIVALS
TWY CLOSED. A2027/08