3
votes
1answer
220 views

Gregory-Laflamme Instability of Black Strings and $p$-Branes

In a paper by Gregory and Laflamme (http://arxiv.org/abs/hep-th/9301052) in 1993, it was demonstrated that black strings and $p$-branes which were solutions to certain low energy string theories were ...
2
votes
1answer
143 views

Spin connection in higher dimension

I have a problem regarding computation of spin connection in the case where One or more dimension is compactified. For example if we take a $D+1$ dimensional bosonic string action and write the $D+1$ ...
3
votes
1answer
91 views

Can a D-brane be closed and contractible?

Let's consider for simplicity D-branes in bosonic string theory. I have a very basic question whose answer I couldn't find clearly stated in the few textbooks where I looked for it. Take for ...
4
votes
0answers
74 views

Is it possible to build up holography in a closed manifold, i.e., in a manifold with a mathematical boundary?

I was wondering about the AdS/CFT correspondence basics. It is constructed on the idea of conformal compactification, in which a open manifold $M$ is homeomorphic related to a closed one $N$ through a ...
3
votes
1answer
63 views

What is the need to consider a singular spacetime?

To have a consistent superstring theory (which is to avoid the conformal anomaly on the worldsheet CFT) we are forced to build our theory on the critical dimension $n=10$. However, the Standard ...
6
votes
2answers
184 views

What happens if the holonomy group lies in $SU(2)$ for a CY 3-fold?

I am a mathematician and reading a physics paper about the holonomy group of Calabi-Yau 3-folds. In that paper, a Calabi-Yau 3-fold $X$ is defined as a compact 3-dimensional complex manifold with ...
4
votes
2answers
125 views

Proof that higher genus surface admits a metric of negative Ricci scalar everywhere

In the Green, Schwarz and Witten Superstring Theory textbook, the paragraph below equation 3.3.15 says, For genus greater than one, it can be shown that the surface admits a metric of everywhere ...
1
vote
1answer
80 views

How can a string be unidimensional if they can be open ended or close ended?

I just don't understand how a object with 2 ends can be unidimensional.
4
votes
2answers
235 views

Dimensions of strings in string theory

In the above image taken from wikipedia, at the string level the strings have been shown as some loops, the article in wikipedia says that in string theory the particles at lower level are broken ...
1
vote
1answer
41 views

Pre-gauge-fixed superspace action of the RNS superstring

When writing down the the action of the RNS superstring in superspace, all of the sources I have checked (BBS, GSW, Polchinski) seem to just write down the action in conformal gauge, that is $$ ...
3
votes
1answer
101 views

Hyperkahler manifolds and their use in theoretical physics

Just as the title says: What is the easiest definition of a Hyperkahler Manifold? Could you give some examples of Hyperkahler manifolds, and manifolds which fail to be hyperkahler? Why are such ...
8
votes
2answers
238 views

What are orbifolds and why are they useful and interesting for physics?

Just what the title says. What's the basic definition of an orbifold? How do they arise in physics and why are they interesting?
1
vote
1answer
53 views

A question about variation of metric under Weyl and coordinate transformations

I have a question about deriving variation of metric under Weyl and coordinate transformations in Polchinski's string theory (3.3.16). Under transformation $$\zeta: g \rightarrow g^{\zeta}, \,\,\, ...
3
votes
1answer
173 views

Deriving the transformation under Weyl rescaling in Polchinski eq. (1.2.31)

I have another question in Polchinski's string theory book volume 1, namely how to derive Eq. (1.2.32)? $$(-\gamma')^{1/2} R'=(-\gamma)^{1/2} (R-2 \nabla^2 \omega) \tag{1.2.32}$$ I have awared his ...
3
votes
1answer
108 views

Energy Functional

I am a graduate student in pure mathematics, during my study on Ricci Flow I faced some functional known as energy functional. For example Einstein-Hilbert functional is called an energy functional, ...
3
votes
2answers
371 views

Polyakov action: difference induced metric and dynamical metric

The Polyakov action is given by: $$ S_p ~=~ -\frac{T}{2}\int d^2\sigma \sqrt{-g}g^{\alpha\beta}\partial_{\alpha}X^{\mu}\partial_{\beta}X^{\nu}\eta_{\mu\nu} ~=~ -\frac{T}{2}\int d^2\sigma ...
3
votes
0answers
59 views

Expectation of 2-form field $B_{MN}$ in string theory

In the context of string theory, in particular when we're dealing with a low energy effective action, if we have an effective action of the form: $$S_{eff} \sim S^{(0)} + \alpha S^{(1)} + (\alpha)^2 ...
5
votes
3answers
254 views

Extending General Relativity with Kahler Manifolds?

Standard general relativity is based on Riemannian manifolds. However, the simplest extension of Riemannian manifolds seems to be Kahler manifolds, which have a complex (hermitian) structure, a ...
6
votes
1answer
165 views

If a fundamental theory exibits e.g. a mirror symmetry, in what sense it the underlying geometry real?

Are the more recently discovered symmetries in string theory such that the theories based on mirroring geometries are absolutely the same from an observable point of view? I have mirror symmetry ...
3
votes
0answers
82 views

Relating the deformation of Calabi-Yau metrics and the conformal quantum field theories

(v2) As I read e.g. in this question, the nice holonomy group features of Calabi-Yau manifolds are valuable regarding supersymmetry (I suspect because it's a symmetry involving the target manifold, ...
3
votes
0answers
188 views

What are the topics of string theory that are comprehensible with only a mathematical background on Manifolds and Algebraic Topology?

What are the topics of string theory that are comprehensible with only a mathematical background on manifolds and algebraic topology? Also, I have read only the first four chapters in Peskin & ...