I think that they are talking about the various ways in which the particles could be interacting. You can count dimensions as the number of ways in which things interact. In this case I think they are saying that they have 103 different ways that the interactions could occur.

I think another way of saying it is that they have 103 degrees of freedom. In a strictly classical physics view that would mean that they could have 103 ways of moving. That would include right/left, up/down, forward/backward, rotating clockwise/counterclockwise, tumbling forward/backward, .... on and on.

Bill Gill

C is not the speed of light in a vacuum.
C is the universal speed limit.