All Questions
Tagged with quantum-anomalies string-theory
58
questions
6
votes
0
answers
298
views
Holomorphic instantons in target torus
For computing instantons contributions from worldsheet torus to target torus, one can evaluate zero modes contribution of genus 1 partition function given by following expression:
$$Tr(-1)^FF_LF_Rq^{...
- 662
5
votes
2
answers
759
views
Inconsistency in the normal ordered Virasoro algebra
I seem to have found a basic contradiction when it comes to the commutation relations of the Virasoro algebra with normal ordered operators and I am not sure what the resolution is.
If we have a ...
- 11.6k
5
votes
1
answer
167
views
Holomorphic anomaly at genus 1
Partition function on torus can be defined using a generalized Witten like index as given below:
$$F_1=\int_\mathbb{T}\frac{d^2\tau}{\tau_2} Tr(-1)^F F_LF_R \;q^{L_0} \bar{q}^{\bar{L_0}},$$
where $\...
- 662
5
votes
1
answer
243
views
Anomalies in the self-dual Yang-Mills theory and $\mathcal{N}=2$ open-string theory
I am reading a paper, written by G. Chalmers and W. Siegel - https://arxiv.org/abs/hep-th/9606061, where they discuss the action of self-dual Yang-Mills theory, which in light-cone formalism is ...
- 4,883
3
votes
1
answer
123
views
How do we know there doesn't exist an anomaly that implies that there is no good choice of dimension for the bosonic string?
By considering $\langle T^\alpha_\alpha\rangle$, the Weyl anomaly, we can show that the critical dimension, $D=26$ is the only possible choice of dimension for the bosonic string.
However, how do we ...
- 857
3
votes
0
answers
264
views
Weyl Anomaly Derivation in Polchinski Eq (3.4.21)
In Polchinski's longer derivation of the Weyl anomaly, he arrives at the result (equation 3.4.19):
$$ \ln{\frac{Z[g]}{Z[\delta]}} = \frac{a_1}{8\pi} \int d^2\sigma \int d^2\sigma' g^{1/2} R(\sigma) G(\...
- 41
3
votes
2
answers
225
views
Are there versions of String Theory formulated in $D$ spacetime dimensions or even in infinitely many dimensions?
There are a lot of different versions of string theory, and almost all of them differ in the number of dimensions. The most famous ones are formulated in 10, 11 or 26 dimensions.
But are there any ...
- 2,462
3
votes
0
answers
339
views
Polchinski Weyl Anomaly from perturbing the flat background. Eq (3.4.22)
In deriving the Weyl anomaly for the bosonic string using a perturbation around a flat background, Polchinksi uses Eq. (3.4.22), i.e.
$$
\ln \frac{ Z[\delta+h] }{Z[\delta]} \approx\, \frac{1}{8\pi^2}\...
- 3,126
3
votes
1
answer
515
views
OPE of stress tensor in CFT
I come aross an OPE between stress tensor components in CFT which is
\begin{equation}
T(z)\bar{T}(\bar{w})\sim -\frac{\pi c}{12}\partial_{z}\partial_{\bar{w}}\delta^{(2)}(z-w)+...
\end{equation}
I am ...
- 669
7
votes
1
answer
260
views
Casimir Force and bosonic String Theory dimensions
I was reading the lecture notes on Quantum field theory by David Tong. In the section on Casimir force he derived the force of attraction felt by the plates due to the field vacuum energy in $1+1$ ...
- 1,490
0
votes
0
answers
66
views
Critical dimension from the symmetries of the string action
(Related: This post and this post.)
In this thesis it is said (on page 13) that just by assuming that we have some general action with the same symmetries as the Polyakov action (Poincare invariance, ...
- 787
2
votes
0
answers
295
views
Is there a way to make this simple "derivation" of the Trace Anomaly correct?
I think I came up with a simple yet sketchy almost-proof of the trace anomaly (A.K.A. Weyl anomaly) in 2D CFT, but it has the wrong prefactor. I was wondering if anyone could assess whether this "...
- 11.6k
1
vote
1
answer
279
views
Gauge anomaly in Polyakov string and Faddeev-Popov method
I am currently trying to gain a better understanding of the gauge fixing procedure used in chapter 5 of David Tong's notes.
Since the central charge of the Polyakov action for, say, the bosonic ...
- 261
1
vote
1
answer
256
views
Is string theory self-consistent? (Conformal anomaly)
Recently I attended a very short course on string theory. We went through the standard presentation in light-cone gauge for brevity. We ‘derived’ the Einstein field equation in the following manner. ...
- 516
4
votes
0
answers
300
views
How does the Weyl anomaly imply $\langle T^{\mu}_{\mu} \rangle \neq 0$?
I want to consider the case of euclidean field theory in 2 dimensions with the action
$$S[\phi]=\int \! d^2\!x \sqrt{\det(g)}g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi$$
which leads to a partition ...
- 261