Exploring D=26 Anomalies in Bosonic String Theory

  • Thread starter b
  • Start date
In summary, the Weyl anomaly in world-sheet theory means that the conformal symmetry is broken, which in turn leads to the Lorentz anomaly in target spacetime, as the generators of the Lorentz group must include terms for conformal transformations. This is because the reference frame in the light cone gauge changes under a Lorentz transformation, requiring a conformal transformation to stay in the gauge. This results in anomalous Lorentz symmetry in bosonic string theory.
  • #1
b
is there a nice and simple way to see how worldsheet weyl anomaly
translates into target spacetime lorentz anomaly, in bosonic string
theory?
 
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  • #2
Please can you clearly explain by these names what you mean? Actually, bosonic string theory is already a fuss. It will not help you as it is incorrect.
 
  • #3
b said:
is there a nice and simple way to see how worldsheet weyl anomaly
translates into target spacetime lorentz anomaly, in bosonic string
theory?

The presence of a Weyl anomaly in the theory on the world-sheet means that the fields in the world-sheet action don`t satisfy the Einstein equations in the spacetime theory by which I mean General Relativity.
 
  • #4
On Sep 21, 9:28 am, b <bzz...@gmail.com> wrote:
> is there a nice and simple way to see how worldsheet weyl anomaly
> translates into target spacetime lorentz anomaly, in bosonic string
> theory?

I don't know if this is nice and simple, but the idea is this, at
least in part.

The Weyl anomaly implies that the group of conformal transformations
(the group of diffeomorphisms which have the effect of rescaling the
metric)
is no longer a symmetry of the theory. The Lorentz anomaly occurs in
the light
cone gauge (the gauge group is the group conformal transformations).
In the light cone gauge a particular reference frame is singled out.
Under a Lorentz tranformation
this reference frame changes, and you consequently have to make a
gauge
transformation (i.e., a conformal transformation) to stay in the light
cone gauge. Consequently, the
generators of the Lorentz group need to include terms generating
particular conformal transformations.
SInce the conformal symmetry is anomalous this leads to anomalous
Lorentz symmetry.

charlie torre
 
  • #5
On Sep 21, 9:28 am, b <bzz...@gmail.com> wrote:
> is there a nice and simple way to see how worldsheet weyl anomaly
> translates into target spacetime lorentz anomaly, in bosonic string
> theory?

I don't know if this is nice and simple, but the idea is this, at
least in part.

The Weyl anomaly implies that the group of conformal transformations
(the group of diffeomorphisms which have the effect of rescaling the
metric)
is no longer a symmetry of the theory. The Lorentz anomaly occurs in
the light
cone gauge (the gauge group is the group conformal transformations).
In the light cone gauge a particular reference frame is singled out.
Under a Lorentz tranformation
this reference frame changes, and you consequently have to make a
gauge
transformation (i.e., a conformal transformation) to stay in the light
cone gauge. Consequently, the
generators of the Lorentz group need to include terms generating
particular conformal transformations.
SInce the conformal symmetry is anomalous this leads to anomalous
Lorentz symmetry.

charlie torre
 
  • #6
On Sep 21, 9:28 am, b <bzz...@gmail.com> wrote:
> is there a nice and simple way to see how worldsheet weyl anomaly
> translates into target spacetime lorentz anomaly, in bosonic string
> theory?

I don't know if this is nice and simple, but the idea is this, at
least in part.

The Weyl anomaly implies that the group of conformal transformations
(the group of diffeomorphisms which have the effect of rescaling the
metric)
is no longer a symmetry of the theory. The Lorentz anomaly occurs in
the light
cone gauge (the gauge group is the group conformal transformations).
In the light cone gauge a particular reference frame is singled out.
Under a Lorentz tranformation
this reference frame changes, and you consequently have to make a
gauge
transformation (i.e., a conformal transformation) to stay in the light
cone gauge. Consequently, the
generators of the Lorentz group need to include terms generating
particular conformal transformations.
SInce the conformal symmetry is anomalous this leads to anomalous
Lorentz symmetry.

charlie torre
 

1. What is D=26 Anomalies in Bosonic String Theory?

D=26 Anomalies in Bosonic String Theory refers to a specific issue that arises in the mathematical framework of bosonic string theory. In this theory, the equations that describe the behavior of strings in 26 dimensions become inconsistent, or "anomalous", leading to problems in the formulation of the theory.

2. Why is D=26 significant in bosonic string theory?

D=26 is significant in bosonic string theory because it is the critical dimension at which the theory becomes inconsistent. In other words, if the number of dimensions in the theory is less than 26, the equations are under-constrained and the theory cannot fully describe the behavior of strings. On the other hand, if the number of dimensions is greater than 26, the equations become over-constrained and lead to contradictions.

3. How does D=26 anomalies affect the validity of bosonic string theory?

D=26 anomalies have a significant impact on the validity of bosonic string theory. The inconsistencies that arise in this dimension make it impossible for the theory to accurately describe the behavior of strings. As a result, the theory cannot be considered a complete and valid description of the fundamental forces of nature.

4. What are some proposed solutions to D=26 anomalies in bosonic string theory?

There are several proposed solutions to D=26 anomalies in bosonic string theory. One approach is to modify the theory by adding new dimensions or incorporating other fields, such as fermions, to cancel out the anomalies. Another approach is to consider bosonic string theory as a low-energy approximation of a more fundamental theory, such as superstring theory.

5. What are the implications of D=26 anomalies for our understanding of the universe?

The implications of D=26 anomalies for our understanding of the universe are significant. If bosonic string theory is not a complete and valid theory, it means that our current understanding of the fundamental forces of nature is incomplete. It also suggests that there may be other dimensions and fields beyond what we currently know, and that a more comprehensive theory, such as superstring theory, may be needed to fully describe the universe.

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