3
votes
1answer
65 views

What constrains ghost fields $c^+$ and $b_{++}$ as $z$ going to infinity

In Green's superstring theory, Chapter 3, from equation 3.3.13 to 3.3.18, the author says that the singularity behavior of the ghost field $c^+$ must be no faster than $z^2$ as $z$ goes to infinity. ...
1
vote
1answer
58 views

Ghosts on Torus worldsheet

Why after the expansion, only 0-mode of bc-ghost contributes to the 4-points ghost function on a torus worldsheet? $$<c(z_1)b(z_2)\tilde{c}(\bar{z}_3)\tilde{b}(\bar{z}_4)>_{T^2} ...
4
votes
1answer
112 views

A question about BRST current in bosonic string theory

I have a question about Eq. (4.3.3) in Polchinski's string theory book volume I, p. 131. It is said Replacing the $X^{\mu}$ with a general matter CFT, the BRST transformation of the matter fields ...
1
vote
1answer
64 views

A question of BRST symmetry of bosonic string theory

This question relates to this post I tried to verify Eq. (4.2.7) in Polchinski's string theory book vol I p. 127 but I miserably miss a sign $$ \delta_B (b_A F^A) = i \epsilon (S_2 + S_3) ...
2
votes
1answer
100 views

How do I show the existence of a conserved ghost number with BRST in bosonic string theory?

I have three questions about the BRST symmetry in Polchinski's string theory vol I p. 126-127, which happen together Given a path integral $$ \int [ d\phi_i dB_A db_A d c^{\alpha}] ...
2
votes
2answers
76 views

A question about surface term of ghost fields

(skip disclaimer) Hi, I have a question in Polchinski's string theory vol I p 90, after introducing the ghost fields $b_{ab}$ and $c^a$, it is claimed The equations of motion then provide a ...
6
votes
1answer
239 views

Energy-momentum tensor of Bosonic Ghost Action in String Theory

When quantizing bosonic string theory by means of the path integral, one inverts the Fadeev-Popov determinant by going to Grasmann variables, yielding: $$ S_{\mathrm{ghosts}} = ...
7
votes
1answer
340 views

Clarification on “central charge equals number of degrees of freedom”

It's often stated that the central charge c of a CFT counts the degrees of freedom: it adds up when stacking different fields, decreases as you integrate out UV dof from one fixed point to another, ...
7
votes
1answer
186 views

Who added $\frac{3}{2} \partial^2 c$ to the virasoro BRST current (and why)?

I've been looking at the literature on quantizing the bosonic string, and I noticed that there was a change made in the definition of the BRST current around 1992. However, I haven't found any ...