An A320 number 2 ND MAP failed and the autopilot did not track correctly causing a track deviation although the FMA indications remained green and the FMGCs entered independent operations.

Narrative

Early in the Cruise Phase; First Officer was pilot flying. It was brought to my attention by the First Officer that his ND was displaying 'Map Not Available' in red color; no map was displayed on the number 2 ND. Seconds later a level 2 ECAM (single chime) with the message of CAB PR LDG ELEV FAULT; which was then accompanied by another fault; the lower ECAM GW display was amber XX LBS. As the pilot not flying I began to troubleshoot what seemed to be the most critical aspect of the multiple failures. At the time it seemed that the Cabin Pressurization was the most critical; not to mention; it was that problem that triggered the Level 2 caution. Once I determined that the integrity of the pressurization system was not compromised; I moved on to the other issue; the lack of the map display on the First Officer side. It seemed that the number 2 FMGC had failed; however; the PFD indications were consistent with no failures. FMA's displayed MACH ALT CRZ NAV all in green; no mode reversions had occurred. Even the FD mode was 1FD2. Yet; as I scanned over to my display; I realized the aircraft failed to make a turn upon passing the previous fix so I immediately went to HEADING Mode turning the aircraft back to re-intercept the course and engage AP1. The deviation was 6.1 NM left of course. At that moment; ATC had queried our position and asked what our next FIX was; I told ATC what our next fix was. I then requested DIRECT; and was cleared direct. This lateral deviation would have been avoided had the aircraft been equipped with a lateral deviation alert similar to altitude deviation alerts that most aircraft are equipped with. Although flying the airplane is the priority at all times; it was very deceiving to the pilots when the aircraft indicated that it is flying based on what the PFD FMA's were displaying. As a former instructor on this airplane; I always used to tell my students to believe what the FMA displays. In this case; it lied about its NAV capability; even though it displayed a normal green NAV display; it wasn't. There must be a communication link between the ND and the PFD.