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Tagged with string-theorymetric-tensor
80 questions
2votes
0answers
45views
Global conformal gauge
I'm reading the Blumenhagen-Lust-Theisen book on string theory. On page 18, They want to discuss whether a global conformal flat metric can exist, namely $$ h_{\alpha\beta}=e^{2\phi}\eta_{\alpha\beta} ...
- 222
1vote
1answer
80views
Einstein Frame from String Frame
Consider the following low-energy effective action in $D$ dimensions for the bosonic sector: $$ I=\frac{1}{2\kappa_0^2}\int d^Dx\sqrt{-g}e^{-{2\Phi}}\left[R-2\Lambda+4g_{\mu\nu}\partial^\mu\Phi\...
1vote
0answers
27views
Make the worldsheet metric in Polyakov action flat [duplicate]
The polyakov action is $$ S=-\frac{T}{2}\int d\tau d\sigma \sqrt{-h}h^{ab}\partial_ax^\mu\partial_b x^\nu g_{\mu\nu} $$ where $g$ is the background spacetime metric and $h$ is worldsheet metric. I've ...
- 222
3votes
1answer
461views
String Theory in Curved Spacetime
As far as I know, String Theory (ST) is usually defined on a spacetime background such as a flat Minkowski space or AdS/CFT. Is it also possible to define ST in a curved spacetime (similar to QFT in ...
0votes
0answers
71views
Isn't this reparameterization just a coordinate transformation?
I'm studying the Polyakov action in string theory. I know that it's invariant under reparameterizations $\sigma \rightarrow \xi(\sigma)$, which in case of the world sheet metric is given by $$\delta ...
0votes
1answer
100views
Has Carl Brans got the wrong Brans-Dicke parameter ($w=1$) for String Theory?
In his 2005 paper The roots of scalar-tensor theory: an approximate history Carl H.Brans claims his Brans-Dicke Theory whose field equations can be derived from the following action accords with ...
- 6,073
2votes
0answers
37views
RNS string action in complex coordinates
The action for the Ramond-Neveu-Schwarz string in conformal gauge $h_{\alpha \beta}=\eta_{\alpha \beta}$ of the world-sheet is (for $\alpha '=1/2$ or $T=1/\pi$) $$S=-\frac{1}{2\pi}\int d^2 \sigma \Big(...
- 834
2votes
0answers
45views
Getting the Double Field Theory action from the projectors
I am mainly focusing on the following paper by Olaf Hohm and Barton Zwiebach: On the Riemann Tensor in Double Field Theory, so I'll give broad brushstrokes as to what my qualms are. The DFT (Double ...
- 123
1vote
0answers
50views
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 $$S_{\sigma}=\frac{-T}{2}\int d^2 ...
- 834
3votes
1answer
113views
Where this definition $T_{\alpha\beta}=-\frac{2}{T}\frac{1}{\sqrt{-h}}\frac{\delta S}{\delta h^{\alpha \beta}}$ come from?
In the book "String theory and M-theory" by Becker, Becker and Schwarz, the author says that the Nambu-Goto action $$S_{NG}=-T\int d\sigma\, \tau \sqrt{(\dot{X}\cdot X')^2 -\dot{X}^2X'^2}$$ ...
- 834
1vote
1answer
123views
Classical open string in Polchinski -- consistency of Neumann boundary conditions with gauge choice
In Section 1.3 of String Theory, Volume 1, Polchinski derives the open string spectrum from the Polyakov action with Neumann boundary conditions, by first considering the classical open string in ...
- 23
0votes
0answers
60views
Derivation of measure for summation over surfaces, including the polyakov action
In his 1981 paper "Quantum geometry of bosonic strings" Polyakov defines a measure for the summation over continuous surfaces. This measure must count all surfaces of a given area with the ...
0votes
0answers
52views
Variation of action of non-critical string under Weyl transformation (worldsheet cosmological constant term)
In David Tong's lecture notes on string theory, section 5.3.2 An Aside: Non-Critial Strings, page 121, he describes the non-critical string with the following action: $$S_{\text{non-critical}} = \frac{...
0votes
0answers
49views
Howe-Tucker to Nambu-Goto Action
Aim to find from the Howe-Tucker action: $$S_{\text{HT}}=-\frac{1}{2}\int d^d\sigma\sqrt{-\gamma}(\gamma^{ab}\partial_a X^{\mu}\partial_b X^{\nu}\eta_{\mu\nu}-m^2(d-2))$$ (which is a Polyakov-like ...
2votes
0answers
90views
Confusion about choosing an Euclidean world sheet metric in String Theory path integral
When it comes to construct a well-defined path integral for the Polyakov action in Bosonic String Theory, most authors assume that the world sheet metric $g$ is Riemannian (i.e. it has Euclidean ...
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