I'm not familiar enough with the SEPIC topology to understand why this should be the case.
Papabravo, look at the transformer windings. One end sits on "ac ground" and the other is connected together by large capacitors. AC Ground can be ground or "+12V" either way there is not AC signal.
One of the windings sits on +12V or 0V with no ac at all just DC.
The other end of the windings has large AC signals.
The two large capacitors C8 & C9 from post #5 could be small and the circuit will work. With small caps, they work as a snubber. This kills ringing on the transformer.
As you know a Boost supply, the output voltage must be more than the input voltage.
This is a Boost/Buck supply where the output can be smaller or larger than the input.
At 50% duty cycle the primary winding will have one end sitting on 12V and the other end will be at 0V or 24V at 50%.
The secondary winding starts out at ground and will have an output at -12V and +12V at 50%.
The cold end of the two windings have a capacitor that shorts them together. C1,2,3.
The hot end of the windings have a capacitor that shorts them together. C8,9. See post #5.
If the two windings are not exactly 1:1 there will be massive current circling around and never leaving the power supply. If the windings are exactly 1:1 things are happy.
I have built many of these supplies and they work. I do not know why this one does not. I hope you can help. I have given up.