In the case of a Dirac operator, the index is the (signed) excess dimension of the space of vacuum modes of one chirality w/r/t the other: i.e., the number of anomalous “ghost” states in a chiral field theory.

Anomalies arise when the classical/quantum symmetry correspondence breaks down under renormalization (a global anomaly could be responsible for quark mass in QCD; resolving the local chiral anomaly in the SM accounts for quarks and leptons; resolving it in superstring theory fixes the gauge group [to either SO(32) or E8 x E8], and the resolution of a conformal anomaly fixes the dimension of spacetime and the fermion content). When trying to turn string theory into actual physics, one asks 


Can it explain three generations of chiral fermions? 
Can it explain the experimental results on proton decay?
Can it explain the smallness of the electron mass? 
Can it explain [things about the cosmological constant]?


and AST helps to answer these questions.

Where is the Atiyah-Singer index theorem used in physics?
Can anyone point me towards examples of Browser Games / Browser Game Sites that use RESTful web services?

I have been convinced time and again that building web sites using RESTful principles is a good idea. And I agree.  But I just can't wrap my head around what RESTful means when the service you're providing is just a single (or a few) games.

Any ideas or thoughts would be nice, but I'd also love to see some solid examples.
