Exploring D=26 Anomalies in Bosonic String Theory

[b]

is there a nice and simple way to see how worldsheet weyl anomaly
translates into target spacetime lorentz anomaly, in bosonic string
theory?

 

[Lakshya]

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.

 

[josh1]

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.

 

[torre@cc.usu.edu]

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?[/color]

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

 

[torre@cc.usu.edu]

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?[/color]

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

 

[torre@cc.usu.edu]

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?[/color]

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