All Questions
12 questions
1
vote
0
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62
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Light-cone gauge
I'm trying to understand the existence of the light-cone gauge for the closed bosonic string in a more mathematical precise language.
Namely, when looking for critical points of Polyakov action, we ...
- 538
1
vote
0
answers
50
views
On the Gauge-fixing for the case of the Polyakov string action
In the book "String theory and M-theory" by Becker-Becker-Schwarz, the author says that
"reparametrization invariance of the string sigma-model action $$S_{\sigma}=\frac{-T}{2}\int d^2 ...
- 834
4
votes
1
answer
352
views
Stückelberg mechanism and the axion
In the so-called Stückelberg mechanism we have the BF term
$$
\sim \int m\; B_2\wedge F ~,
$$
where the field $B_2$ is a 2-form and $F$ is the field strength arising from a $U(1)$.
The Stückelberg ...
- 706
3
votes
0
answers
171
views
Why string theory action needs to be manifestly diffeomorphism invariant?
A typical QFT action is obviously not diff invariant, in other words, the integration parameters have physical significance as time and position. For example action for massless free scalar field on ...
- 1,439
3
votes
1
answer
141
views
Difference between field-antifield and light-cone quantisation
I have learnt field-antifield quantisation and know that it can be used for very general gauge theories - open and reducible. I have not got much into light-cone quantisation but I am unable to see ...
- 81
2
votes
0
answers
122
views
Nambu-Goto action and zweibein
Consider the Nambu-Goto action
\begin{equation}
S=\int d\sigma d\tau \sqrt{(\partial_\sigma X^\mu \partial_\tau X_\mu)^2-(\partial_\sigma X^\mu\partial_\sigma X_\mu)(\partial_\tau X^\mu\partial_\tau ...
- 335
2
votes
1
answer
368
views
String coupled to Kalb-Ramond field under gauge transformation
I'm studying how a string coupled to a Kalb-Ramond 2-form $B_{\mu \nu}$ is affected by a gauge transformation of the K-R field, $\delta B_{\mu \nu} = \partial_{\mu} C_{\nu} - \partial_{\nu} C_{\mu}$ ...
- 1,115
4
votes
1
answer
388
views
What kind of fields can couple naturally to a $p$-form gauge fields in a Lagrangian?
Ordinary $U(1)$ gauge fields can naturally couple to classical fields such as spin-$1/2$ fields via the Dirac Lagrangian, or to complex spin-$0$ fields via the obvious covariant derivative coupling, ...
1
vote
1
answer
571
views
Derivation Of The Equation Of Motion Of String from Polyakov action
I'm stuck at a step in the derivation of the equations of motions of a string using the Polyakov action.
In Polchinski's textbook in String Theory , Page 14 ; Equation ( 1.2.25 ) ,
Varying the ...
- 415
6
votes
1
answer
2k
views
Reduction of Nambu-Goto action to true degrees of freedom
I) First consider the point particle
$$S=m\int\sqrt{-\dot{X}^2}d\tau.$$
If you choose the static gauge $$\tau=X^0$$ and replace it in the action you get
$$=m\int\sqrt{1-\dot{X}^j\dot{X}^j}d\tau.$$
...
- 1,734
12
votes
1
answer
3k
views
Infinitesimal transformations for a relativistic particle
The action of a free relativistic particles can be given by
$$S=\frac{1}{2}\int d\tau \left(e^{-1}(\tau)g_{\mu\nu}(X)X^\mu(\tau)X^\nu(\tau)-e(\tau)m^2\right),\tag{1.8}$$
with signature $(-,+,\ldots,+)$...
- 459
8
votes
1
answer
246
views
"Gauge fixed world-sheet action"
My question is in reference to the action in equation 4.130 of Becker, Becker and Schwartz.
It reads as,
$$S_{matter}= \frac{1}{2\pi}\int (2\partial X^\mu \bar{\partial}X_\mu + \frac{1}{2}\psi^\mu \...
- 4,739