Reference for Quantum field theory in $S^1 \times R$

I am looking for a reference where it is considered QFT on a space given in a circle, plus a time coordinate, namely QFT in $$S^1\times R$$.

• I studied $S^1 \times R$ in Birrell and Davies. The calculated expectation value of $T\mu \nu$. Yeah that's it by 2 different methods. – aitfel Oct 8 '19 at 14:44

You should check out basically any introductions to string theory. QFT on $$S^1 \times R$$ is exactly what you study when looking at closed strings.
• The string worldsheet is described by conformal field theory on $S^1 \times R$. OP didn't mention anything about conformal symmetry. – Prof. Legolasov Oct 8 '19 at 13:10