A class of theories that attempt to explain all existing particles (including force carriers) as vibrational modes of extended objects, such as the 1-dimensional fundamental string. PLEASE DO NOT USE THIS TAG for non-relativistic material strings, such as, e.g., a guitar string.

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15
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1answer
1k views

Do neutrinos refract?

The most benign of interactions is refraction. While neutrinos rarely interact with matter in a sense like the photoelectric effect, does that mean that they don't refract either?
2
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1answer
51 views

What is $\mathcal{N}=2$ QED?

I would like to know is $\mathcal{N}=2$ QED is simply a $\mathcal{N}=2$ theory with gauge group $U(1)$ like in normal QED? If not, exactly what theory is it? Is there some reference for it?
1
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0answers
34 views

Effect of orbifolding on gauge fields

A paper by Lalak et al, entitled "Soliton Solutions of M-theory on an orbifold", considers the brane solutions of 11 dimensional supergravity on a space of the form $R^{10} \times S^1/\mathbb{Z}_2$. ...
2
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0answers
80 views

Mathematician learning theoretical physics [duplicate]

EDIT: I was aware of the supposed duplicate. But I'm interested in a clear and focused path through the basics to advanced theoretical physics such as string theory - a path that avoids studying ...
1
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0answers
30 views

Fourier transformation and mode expansions [duplicate]

Sorry as this is a rather trivial question, but I'm stuck with a certain implication. I'm working on exercise 1.7 from Polchinski where we are given an open string with boundary conditions ...
9
votes
2answers
709 views

Geometric/Visual Interpretation of Virasoro Algebra

I've been trying to gain some intuition about Virasoro Algebras, but have failed so far. The Mathematical Definition seems to be clear (as found in http://en.wikipedia.org/wiki/Virasoro_algebra). I ...
1
vote
0answers
95 views

Fourier transformation and commutators

Sorry as this is a rather trivial question, but I'm stuck with a certain implication. I'm working on exercise 1.7 from Polchinski where we are given an open string with boundary conditions ...
0
votes
1answer
42 views

Open string interactions implies closed string

I am currently reading Polchinski page 81, and am not 100% clear with the explanation given regarding why any open string theory necessarily contains closed strings. It is stated, quoted from page ...
1
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0answers
45 views

Is the Cauchy Horizon of Anti deSitter spacetime stable?

The Cosmic Censorship Conjecture are two mathematical conjectures about the structure of spacetime. In particular the so called Strong Cosmic Conjecture asserts heuristically that generically, ...
3
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0answers
96 views

Mode operators in the Virasoro algebra

This questions concerns Exercise 2.11 in Polchinski. We are asked to compute the commutator $$L_{m}(L_{-m}|0;0\rangle) - L_{-m}(L_{m} |0;0\rangle)$$ By plugging the mode expansions, we use the ...
0
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0answers
65 views

Calculation of OPE in Polchinski

Consider Exercise 2.8 in Polchinski's String Theory book. We are asked to compute the weight of $$f_{\mu \nu}:\partial X^{\mu} \bar{\partial}X^{\nu}e^{ik\cdot X}:$$ I have carried out the usual ...
22
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0answers
919 views

A dictionary of string - standard physics correspondences

Motivated by the (for me very useful) remark ''Standard model generations in string theory are the Euler number of the Calabi Yau, and it is actually reasonably doable to get 4,6,8, or 3 ...
1
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0answers
46 views

Projection that keeps graviton but gets rid of B-field

We consider the closed superstring and the massless states in the (NS,NS)-sector \begin{equation} \tilde{b}^i_{-\frac{1}{2}} |0\rangle_L \otimes b^j_{-\frac{1}{2}} |0\rangle_R. \end{equation} It is ...
1
vote
1answer
108 views

How can extra (non-curled up) dimensions be hidden from us?

Wikipedia says: If extra dimensions exist, they must be hidden from us by some physical mechanism. One well-studied possibility is that the extra dimensions may be "curled up" at such tiny ...
2
votes
1answer
78 views

Operator product expansion energy momentum tensor

We have the following equation from Polchinski (2.4.6) $$ T(z)X^{\mu}(0) \sim \frac{1}{z}\partial X^{\mu}(0) , \tag{2.4.6} $$ where $T(z)$ is defined as $T(z) = -\frac{1}{\alpha'} :\partial X^{\mu} ...
2
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0answers
66 views

Why are there no branes in heterotic string theory?

Why does the heterotic string (or heterotic supergravity) have no brane solutions? According to David Tong's notes: the heterotic string doesn’t have (finite energy) D-branes. This is due to an ...
2
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0answers
49 views

What happens to M2 and M5 brane solutions upon orbifolding?

M-theory has M2 and M5 brane solutions. Suppose M-theory is compactified on $\mathbb{R}^{10} \times S^{1}/\mathbb{Z}_2$, what happens to the M2 and M5 brane solutions? How does one define the near ...
1
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2answers
53 views

What equation do we use to measure the energy level of a string, to determine it's “particle correlation”

If string theory happened to be correct, and a point-particle is replaced with a string, there is a direct correlation between the vibrating frequency of the string and the particle it produces. I was ...
2
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0answers
30 views

When can a $k$-cycle wrap around a manifold?

According to the paper ``Heterotic and Type I String Dynamics from Eleven Dimensions'' (page 7): Even when the topology is wrong -- for instance on $\mathbb{R}^{11}$ where there is no two-cycle ...
7
votes
2answers
881 views

Critical Dimension of Bosonic Strings and Regularization of $\sum_{n=1}^\infty n$

If $D$ is critical dimension of Bosonic strings, a particular derivation goes like the following, where we arrive finally at $$ \frac{D-2}{2}\sum_{n=1}^\infty n + 1 = 0. $$ Now mathematically this is ...
1
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0answers
32 views

How to find de Sitter and almost de Sitter solutions in (super)string theory

From Cosmology, we have learned that we live in an almost de Sitter (positively accelerated!) Universe. It seems that dS space solutions in superstring/theory are problematic and there are some no-go ...
0
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0answers
15 views

Given the extension of a NS5-brane, can we find the extension of the T-dual KK5-brane?

My question is about the relation between the Kaluza-Klein 5-brane and the NS5-brane and the effective dimensionality of the KK5 brane. To my knowledge, the KK5 is defined as the T-dual of the NS5, ...
2
votes
0answers
58 views

AdS/CFT-duality: How does the $U(1)$ decouple form the $U(N)$?

A stack of N coincident D3-branes on its world-volume describe, at the lowest order in $\alpha'$ and in absence of non-trivial background fields, a supersymmetric $U(N)$ gauge theory as explained in ...
3
votes
0answers
59 views

Projector and delta function on a cycle $\Sigma$ of a manifold $\mathcal{M}_6$

In the paper ``Hierarchies from Fluxes in String Compactifications'' by Giddings, Kachru and Polchinski, the following example is considered for a localized source that may have negative tension (my ...
2
votes
1answer
74 views

Canonical commutation relations in Light-cone gauge

It seems that when trying to identify the physical degrees of freedom for the string some authors$^1$ use: $$ q^-=\frac{1}{\ell}\int_0^{\ell} X^-(\tau,\sigma)d\sigma$$ Then, the commutation relation ...
2
votes
1answer
349 views

Advantage of string theory over other theory-of-everything candidates

I am getting curious over why string theory, especially M-theory, is the most popular candidate for the theory of everything. It seems that all candidates of the theory of everything lack substantial ...
0
votes
1answer
36 views

Polchinski, (0,0) picture vertex operator

I am currently working through chapter 12 of Polchinski and am confused as to how the equation $(12.3.39)$ for the (0,0) picture vertex operator arises. From the text: The state–operator mapping ...
0
votes
1answer
52 views

How many Dimension do we have? [duplicate]

I know that Einstein described three dimensions for space and one for time. But I also have heard something about a world with so many dimensions or 11 dimensions of space or ... On the whole due to ...
3
votes
0answers
53 views

Charged black holes and AdS/CFT

People generalize the statements of AdS/CFT correspondence by adding black hole (charged black hole) in the gravity theory to provide the dual gauge theory finite temperature (finite density). I have ...
0
votes
1answer
54 views

Equations of motion for Polyakov action

In Polchinski 2.1.10 we have the action in terms of complex coordinates $$S = \frac{1}{2\pi \alpha'} \int d^{2}z \partial X^{\mu}\bar{\partial}X_{\mu}\tag{2.1.10}$$ This should be a rather trivial ...
7
votes
2answers
1k views

Recommendations for time-line and road map in graduate school towards specializing in Maldacena's conjecture

This question was asked on Theoretical Physics Stackexchange and was grossly misread and closed. I am again posting the question here hoping to get some valuable insights. Also some people were ...
3
votes
1answer
70 views

Question regarding moduli space of a Calabi-Yau manifold

On page 132 of "Introduction to Supergravity" by Horiatiu Nastase, the author says: On $M = CY_3$ (Calabi-Yau space) there are $b_3$ topologically nontrivial 3-surfaces, for which we can define a ...
2
votes
2answers
158 views

How to find the rank of the matrix $\frac{\partial ^2\mathcal{L}}{\partial \dot{X^\mu} \partial \dot{X^\nu} }$ for the Nambu-Goto string Lagrangian?

In this case $$\mathcal{L}~=~-T\sqrt{-\dot{X^2}X'^2+(\dot{X}\cdot X')^2}.$$ I was reading some books and papers about the constraints in the Nambu-Goto action, and all of them say something like ...
2
votes
1answer
210 views

Reduction of Nambu Goto action to true degrees of freedom

First consider the 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 $$=m\int\sqrt{1-\dot{X}^j\dot{X}^j}d\tau$$ So now, you ...
5
votes
3answers
147 views

What happens at the center of a black hole according to holographic theory?

As far as I understand, the AdS/CFT correspondence proposed by Maldacena is an exact duality to a four-dimensional theory, which interpolates between one well-defined conformal field theory in the UV ...
0
votes
0answers
50 views

Ishibashi states and Cardy states in CFT

What are the Ishibashi states and Cardy states in CFTs? I am familiar with conformal field theory language. It would be great if someone can discuss about the basic idea of these states and their ...
5
votes
2answers
113 views

What laws are the same in all string theory compactifications?

In the string theory landscape, the set of particles we observe, their masses and interaction strengths originate from one of many different possible compactifications. What fundamental physical ...
2
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2answers
60 views

Topological strings: Why is the complex structure for $T^2$ denoted as $\tau$ in string theory?

In these notes by Vafa on topological string theory he says in page 7 that the moduli of the 2-torus can be repackaged into two quantities: $$A=iR_1/R_2 \,\,\,\,\,\,\,\,\, \tau=iR_2/R_1$$ where $A$ ...
1
vote
1answer
185 views

Why are right hand neutrinos unaffected by all forces except gravity

I'm curious as to something I read on Berkeley's website. Does anyone happen to know why, according to this model,right hand neutrinos are unaffected by all forces except gravity? (Model taken from ...
6
votes
0answers
122 views

Monstrous Moonshine outside of String Theory

My question concerns applications of monstrous moonshine, which is the connection between the $j$-function and the monster group. Recently, physicists have applied it to string theory and, ultimately, ...
0
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0answers
28 views

Why are closed strings with different perioidicities equivalent?

I was typing up some lecture notes the other day when I saw something unclear. While talking about bosonic open and closed strings and the Polyakov action, the notes say we don't need to distinguish ...
4
votes
2answers
165 views

Traces in different representation

I am actually working with Green-Schwarz anomaly cancellation mechanism in which I have came across a strange formula which relates trace in the adjoint representation (Tr) to trace in fundamental ...
1
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1answer
81 views

Facing a problem in Katrin Becker, Melanie Becker, John Schwarz's String Theory

In BBS's string theory book, in the equation (2.143), it says that $$\text{tr} \omega ^N=\prod _{n=1}^{\infty } \left(\prod _{i=1}^{24} \text{tr} \omega ^{\alpha _{-n}^i \:\alpha _n^i}\right)=\prod ...
1
vote
1answer
66 views

Quark-gluon plasma: status [closed]

Can we say that a QGP has been observed or is there only suggestive evidence? Is the idea that string theory, through the AdS/CFT correspondence, could help to understand this new state of matter ...
4
votes
1answer
724 views

Conversion of the Polyakov action into the Nambo-Goto action?

I've read that the Polyakov action using an intrinsic metric $h_{\alpha\beta}$ $$\tag{1} S_P ~=~ -\frac{T}{2}\int d^2 \sigma \sqrt{-h}h^{\alpha\beta} \partial_{\alpha}X^{\mu}\partial_{\beta}X^{\nu} ...
1
vote
1answer
69 views

Elementary question about global supersymmetry of a worldsheet [closed]

I'm reading chapter 4 of the book by Green, Schwarz and Witten. They consider an action $$ S = -\frac{1}{2\pi} \int d^2 \sigma \left( \partial_\alpha X^\mu \partial^\alpha X_\mu - i \bar \psi^\mu ...
1
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0answers
76 views

Branes at the conifold

Consider $N$ $D3$-branes at the singularity of the conifold. This particular example can be viewed as a $AdS_{5} \times T^{1,1}$ in the near horizon limit, where the Einstein manifold has isometry ...
1
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0answers
25 views

Polchinski equation 11.2.7

In Polchinski's string theory volume 2, when discussing the GSO projection for the heterotic string he says: In the IIA and IIB superstrings the GSO projection acted separately on the left- and ...
152
votes
11answers
21k views

What experiment would disprove string theory?

I know that there's big controversy between two groups of physicists: those who support string theory (most of them, I think) and those who oppose it. One of the arguments of the second group is ...
2
votes
1answer
116 views

Does Conformal Invariance of the Polyakov Action in Conformal Gauge imply Conformal Invariance of the Pre-gauge-fixed Polyakov Action?

In bosonic string theory the Polyakov action can be put in into conformal gauge. It is then possible to show that the resulting gauge fixed action is conformally invariant. Actually it's shown that ...