All Questions
Tagged with quantum-anomalies string-theory
19
questions with no upvoted or accepted answers
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:
$$Tr(-1)^FF_LF_Rq^{...
- 662
6
votes
1
answer
819
views
String theory and trace anomaly in semiclassical gravity?
what does string theory have to say about the trace anomaly in the expectation value of the stress-energy tensor of massless quantum fields on a curved background and its interpretation as the ...
- 648
5
votes
0
answers
232
views
Where does chiral matter at conical singularities "come from" in M-theory?
It seems to be accepted that to produce chiral fermionic matter in a compactification $\mathbb{R}^4\times X$ of M-theory/11d SUGRA to four dimensions, we need the seven-manifold $X$ to have isolated (...
- 126k
4
votes
0
answers
132
views
Normalization of zero point energy in string theory
Following Joe Polchinski’s Little Book of String, page 12, he use the sum $$1+2+3+...=-1/12$$ to find the zero point energy of the bosonic string (and later used the result to argue that we must have ...
- 1,734
4
votes
0
answers
300
views
How does the Weyl anomaly imply $\langle T^{\mu}_{\mu} \rangle \neq 0$?
I want to consider the case of euclidean field theory in 2 dimensions with the action
$$S[\phi]=\int \! d^2\!x \sqrt{\det(g)}g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi$$
which leads to a partition ...
- 261
3
votes
0
answers
112
views
Why are there only two 496-dim. gauge groups $E_8\times E_8$ and $SO(32)$ allowed in string theory? Why not $E_8\times U(1)^{248}$ or $U(1)^{496}$?
While constructing anomaly-free string theories with $\mathcal N=1$ supersymmetry (16 supercharges constituting a Majorana-Weyl spinor), we learn that the gauge group must be 496-dimensional in order ...
- 71
3
votes
1
answer
123
views
How do we know there doesn't exist an anomaly that implies that there is no good choice of dimension for the bosonic string?
By considering $\langle T^\alpha_\alpha\rangle$, the Weyl anomaly, we can show that the critical dimension, $D=26$ is the only possible choice of dimension for the bosonic string.
However, how do we ...
- 857
3
votes
0
answers
264
views
Weyl Anomaly Derivation in Polchinski Eq (3.4.21)
In Polchinski's longer derivation of the Weyl anomaly, he arrives at the result (equation 3.4.19):
$$ \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
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.
$$
\ln \frac{ Z[\delta+h] }{Z[\delta]} \approx\, \frac{1}{8\pi^2}\...
- 3,126
2
votes
1
answer
174
views
Light-cone quantization of open string as derived in Polchinski
Polchinski uses the following gauge conditions, but I don't follow this procedure of gauge fixing and quantization:
\begin{align}
X^+ = \tau, \tag{1.3.8a} \\
\partial_\sigma \gamma_{\sigma \sigma} = 0,...
- 433
2
votes
0
answers
65
views
How does one arrive at the relation of commutator $\left[M^{-i}, M^{-j}\right]$ of Lorentz generators $M^i$ in terms of the string modes $\alpha_n^i$?
I am reading the book "String theory demystified" by David McMahon.
On page 149, the author discusses the "critical dimension" for superstrings.
the number of spacetime dimensions ...
- 251
2
votes
0
answers
130
views
How do I understand this conformal transformation?
I am learning conformal transformation, and this is by far the most confusing transformation for me.
For the 2D bc system
$$S=\frac{1}{2\pi}\int d^2 z b\overline{\partial}c,$$
we have the ghost ...
- 216
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
2
votes
0
answers
240
views
Faddeev-Popov-Determinant of Polyakov Path Integral
I'm currently trying to understand the paper "Quantum Geometry of bosonic Strings" by Polyakov. I think I roughly understand the X integration, but when it comes to the integration over the metric ...
- 21
2
votes
0
answers
144
views
Anomalies from a Renormaization Group Equation (RGE)
This is an approach to anomalies which seems unfamiliar to me..
Firstly what is this function $W$ which seems to satisfy the equation, $\frac{\partial W }{\partial g^{\mu \nu} } = \langle T_{\mu \nu}...
- 4,561