Hi(adsbygoogle = window.adsbygoogle || []).push({});

I'd like to show the equation 3.6.24 of Polchinski's big book(string theory volume 1). I think contents of page 35 to 36 is the key for the calculation, but I don't know how to carry out specific calculation. I think I need to know the form of [tex]\left \langle X(z,\bar{z})X(z',\bar{z'}) \right \rangle[/tex].

Using 2.1.18, I can guess [tex]\left \langle X(z,\bar{z})X(z',\bar{z'}) \right \rangle[/tex] is related with [tex]\eta ^{\mu \nu }\delta ^{2}\left ( z-z',\bar{z} -\bar{z'} \right )[/tex], but I don't know specific form because the world sheet is curved. If I naively yield [tex]\left \langle X(z,\bar{z})X(z',\bar{z'}) \right \rangle[/tex], I need to calculate [tex]\int_{-\infty }^{\infty } \frac{e^{ik\cdot (z-z')}}{k^{2}+i\varepsilon }d^{2}k[/tex], and I don't know how to deal with it by dimensional regularization even if the naive calculation is right.

Thus, my questions are

Many thanks in advance.

- If my naive calculation is right, how can I carry out the dimensional regularization of [tex]\int_{-\infty }^{\infty } \frac{e^{ik\cdot (z-z')}}{k^{2}+i\varepsilon }d^{2}k[/tex] .
- If wrong, I'd like to know how to get [tex]\left \langle X(z,\bar{z})X(z',\bar{z'}) \right \rangle[/tex] by dimensional regularization.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A How to prove 3.6.24 of Polchinski's big book

Tags:

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**