All Questions
Tagged with quantum-anomalies string-theory
58
questions
18
votes
5
answers
27k
views
Why does string theory require 9 dimensions of space and one dimension of time?
String theorists say that there are many more dimensions out there, but they are too small to be detected.
However, I do not understand why there are ten dimensions and not just any other number?
...
11
votes
1
answer
1k
views
Mathematically rather than physically speaking, is there something "special" about 10 (or 11) dimensions?
As I understand it, string theory (incorporating bosons and fermions) "works" in $9+1=10$ spacetime dimensions. In the context of dual resonance theory, I've read descriptions of why that is "...
- 457
10
votes
1
answer
671
views
Confusion about two definitions of anomalies
As I am currently studying for an exam about quantum field theory and string theory, I got confused about the notion of "anomalies" and how they are actually defined. Similar questions have already ...
- 7,309
10
votes
1
answer
1k
views
Why does tachyon arise in bosonic string theory?
I am looking for precise mathematical and physical reasons which cause the presence of tachyon in bosonic string theory(specially closed bosonic string theory). Has it to do with the specific form of ...
- 2,057
8
votes
2
answers
3k
views
Weyl anomaly in 2d CFT (string theory lectures by D.Tong)
In his lectures on String Theory (http://www.damtp.cam.ac.uk/user/tong/string.html), Tong gives a proof of the Weyl anomaly, using equation $(4.37)$. It seems wrong to me.
Here he uses the OPE between ...
- 106
8
votes
1
answer
448
views
Critical dimension in quantization of p-branes
So I have what might be a fairly basic question, but my understanding that in the quantization of the the string, or the 1-brane, there are conditions on the number of spacetime dimensions to ensure ...
- 746
8
votes
1
answer
827
views
About the general expression of trace anomaly and CFT partition functions
I have put up a question here,
https://mathoverflow.net/questions/139685/proof-of-the-general-expression-for-anomaly-in-a-cft-and-its-partition-function
Here I am putting up a slightly different ...
- 4,619
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
7
votes
1
answer
483
views
Target Space Lorentz Invariance vs. World Sheet Weyl Invariance
The Polyakov action, $S\sim \int d^2\sigma\sqrt{\gamma}\, \gamma_{ab}\partial^a X^\mu \partial ^b X_\mu$, has the well known classical symmetries of world sheet diffeomorphism invariance, world ...
- 3,492
6
votes
1
answer
456
views
Polchinski's first derivation of the Weyl anomaly
So, i've been reading volume 1 of Polchinski's String Theory text book and have a doubt.
His first derivation of the Weyl anomaly goes as follows:
From dimensional analysis, we know that:
$$\begin{...
- 63
6
votes
0
answers
298
views
Holomorphic instantons in target torus
For computing instantons contributions from worldsheet torus to target torus, one can evaluate zero modes contribution of genus 1 partition function given by following expression:
$$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
2
answers
1k
views
How exactly do superstrings reduce the number of dimensions in bosonic string theory from 26 to 10 and remove the tachyons?
In bosonic string theory, to obtain the photon as the first excited state, the ground state must have a negative mass (tachyon). By applying $1 + 2 + 3 + \cdots = -1/12$, it can be shown (in a ...
- 9,581
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
631
views
Is this explanation of "Why nine space dimensions?" correct?
In Gordon Kane's Supersymmetry and Beyond (p. 118), he states:
String theory has to be formulated in nine space dimensions or it is not a consistent mathematical theory. There doesn't seem to be a ...
- 6,745