# Coleman-Weinberg formula and one-loop processes in string formalism

1. Jan 6, 2012

### Phy2

Hi !

I have some questions for string specialists.

In stringy approaches, the Coleman-Weinberg formula is used to compute the one-loop vacuum amplitude. Such a formula occurs in QFT but also in string models.

1. I am a bit confused with the achievement of the Coleman-Weinberg formula (I know the paper of Coleman and Weinberg, Phys.Rev.D (1973)).
Can the paper of Polchinski (Commun. Math. Phys. 104, 37-47 (1986)) be considered as a demonstration of the Coleman-Weinberg formula in string formalism?

2. The Coleman-Weinberg formula is pretty nice since it can be expressed according to the string mass spectrum.
Is there a way to keep such a nice expression to compute a one-loop process with two vertices for instance? Are there some papers where such an approach is used?

Thank you.
Mike.

2. Jan 6, 2012

### suprised

This formula just says that the 1-loop vacuum amplitude is the partition function, Z=Tr[exp(-tH)]. Applications of this are everywhere, from stat mech to string theory.

Of course, if you like to put external legs then you need to put vertex operator insertions into the trace and in general this substantially modifies the amplitude. Examples you will find in any textbook.