Let me start by saying, look at the spec of the PSU! What does it say about the -12V rail?
So, it took me some time to figure out your schematic. Dude, if you want help, make a clear drawing!
But I think you are making this circuit
First of all, this is supposed to go on the low side of the LED’s aka the Cathode side of the LED’s or -LED.
And although it will work the set current can be a bit high. If Vbe really is 0,7V then the current will be 854mA. But checking the datasheet I would say it’s around 0,6V but this would still give 732mA and that’s higher then the maximum rating. And as all datasheet say, it’s the absolute maximum rating. So it’s better to run them @ 600mA or so (use a 1ohm resistor instead)
And you mentioned the spec’s of your LEDs. For example the “Rb 3w 3.2-4.0v at 700mA”. (And I have no idea what Rb means, is it a color?) When you run them towards the maximum current the forward voltages tents to go to the maximum value as well. In this case 4.0V. And if you have 6 LED’s in series this gives 6 x 4.0 = 24.0V. But the current driver also has a voltage drop but there is no room for that. It will probably sort of work because the current is lowered by that but it’s not a good practice, you nullify the purpose of the constant current driver.
But if you want to test this circuit, just connect the PWM pin to positive (12V) and the constant current driver should work without Arduino. But I don’t think the LED’s will light up because the -12V rail can’t supply the current (of maybe it can just light one string).
In my opinion, drop this constant current driver and replace it with 8 of these.
Modify them a bit like I did here. Use a 1ohm 1/2W resistor and you are done. You can connect it to 12V rail without a problem up until a combined forward voltage of 27V.