Questions tagged [compactification]
Compactification entails changing a theory with respect to one of its space-time dimensions. Instead of this dimension ranging to infinity, the theory is changed so that this dimension has a finite range, and may be periodic. In the limit where the size of the compact dimension goes to zero, no fields depend on this extra dimension, and the theory is *dimensionally reduced*. Further use for dimensional reduction.
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Compactification of Minkowski spacetime
I'm studying Ray D'Inverno's book "Introducing Einstein's relativity". I'm having trouble understanding Fig. 17.7 (pag. 236), which is an illustration of compactified Minkowski spacetime. ...
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The string spectrum with several compactified dimensions
In his String Theory Vol. I book, Polchinski wants to compute the string spectrum when $k$ of the 26 dimensions are compactified $$X^m \sim X^m + 2 \pi R, \quad 26 - k \leq m \leq 25 \, . \tag{8.4.1}$...
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Doubt about the derivation of Casimir Effect
I was reading about Casimir effect from David Tong's QFT notes and I was struggling to understand one thing.
At page 27, equation (2.33) describes the energy in between the plates, then why does the ...
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Simple examples of compactification [closed]
I am starting out on some research and I am trying to find basic examples of compactification to start off with, and then I want to work my way up to more complicated items such as having an action ...
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Is it theoretically possible to get a fermion fields from compactifying a bosonic field theory?
It doesn't seem impossible to me that compactifying a purely bosonic field theory could result in spinor fields.
For example, the spin groups (the double covers of $O(n)$) have representations in $2^{...
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Explanation of Hierarchy Problem in Kaluza-Klein String Scenarios
During the last few days I have been interested in the gravitational hierarchy problem and the different explanations for it/solutions to it.
Among the most "concrete" (insofar as anything ...
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On the Product Structure of Spacetimes after Compactification
I am currently looking into the compactification of spacetimes as it is often done in (super-)stringtheory.
So, say I start with a ten-dimensional Lorentz manifold $(N, g)$, where $N$ denotes the ...
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Do the "extra dimensions" in string theory have equivalent physical value to regular dimensions?
I've seen hyperspace dimensions being discussed in models for superstring theory, where there are 6-7 hyperspace dimensions iirc. But the explanation as to why we don't perceive these extra dimensions ...
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What is the most compact arrangement of superstrings?
I was thinking about crystals and how they might apply to really dense arrangements of matter near the Big Bang or in collapsing stars.
It seems that the bosonic strings and superstrings can form ...
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Small and large extra dimension(s) of the physical space
Trying to make sense of small and large extra dimension(s) of phyiscal space in a simple intuitive example.
Consider a two dimensional manifold like $\mathbb{R}^2$ and we are trying to add a small and ...
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Why don't the extra compact dimensions collapse on themselves?
Why are the extra compact dimensions stable and do not collapse?
I know the anomaly cancellation is the reason why the extra dimensions are necessary.
But I can not visulize how the anomaly ...
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Kaluza-Klein compactifications with ${\cal N}=1$ supersymmetry
I'm trying to understand some of the important properties of KK-compactifications of 10-dim heterotic string supergravity on 6-dim Calabi-Yau ($CY_3$) manifolds to a 4-dim theory with ${\cal N}=1$ ...
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Visualizing the conformal compactification diagram of $G$
I asked a question a year and 3 months ago on mathstackexchange but after 3 bounties and still no answer I've decided to try here. Here's the link: conformal compactification.
Construct a conformal ...
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How to understand Extra Dimensions? [duplicate]
I don't understand how there can be extra dimensions. I've heard it explained to imagine there's a tiny door that we can't perceive, and when you do discover it and walk in, you have discovered a new ...
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Connection between covariant derivative operators upon conformal compactification
I'm having trouble determining the connection between two covariant derivative operators. These are: the one associated with the original space-time (and thus with the metric $ \tilde{g}_{ab}$) and ...
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A way to visualize extra compact dimensions
I'm wondering if it's valid to think of the meaning of compact dimensions in this way:
Suppose a world with two dimensions and a potential $V(x,y)=\kappa\delta(y)$
Then solving the Schrodinger ...
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Poincare transformation and extra compact dimensions
Given that Poincare transformation can mix different different directions of spacetime with each other, does this mean that in the case that some dimensions are compactified, large and compact ...
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Why the extra compact dimensions of superstring theory must form a Calabi-Yau manifold? [duplicate]
In superstring theory, extra dimensions are conjectured. Then, the obvious observation that, macroscopically, we observe only three spacelike dimensions and one timelike dimension, leads to the ...
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The momentum live in the dual lattice in the toriodal compactification (book reading)
(D-Branes Clifford V. Johnson section 4.5 )
$G_{mn}=\delta_{ab} e^a_m e^b_n$
$X^a=X^m e_m^a$ where the equivalence of the toriodal compactification $X^a\sim X^a 2\pi e^a_mn^m$ or identify the ...
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Compactification in String Theory and Compactification in Topology are they the same thing?
In topology, there is a concept of compactification which is defined as follows.
A space $Z$ is a compactification of $X$ if $Z$ is compact Hausdorff and there exists an
embedding $j:X \rightarrow Z $ ...
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Is it necessary that the compactified manifold in string theory must be complex?
I have learned that there are some restrictions imposed on the manifolds which are used to compactify the extra-dimensions of string theory. The most important being the "Ricci flatness" ...
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What is a specific example of a Calabi-Yau manifold? are there simple ones like a 6-torus, $T^6=(S^1)^6$ or $S^3\times T^3$
What is a specific example of a 6D Calabi-Yau manifold? are there simple ones like a 6-torus, $T^6=(S^1)^6$ , $S^3\times T^3$, or similar structures with products of Spheres and Torus?
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Can any other manifold be used for compactifying the 6 extra dimensions of string theory? [duplicate]
I'm a layman interested in string theory. I read about how the 6 extra dimensions of superstring theory are compactified into 3-dimensional complex manifolds (so real dimension 6?) called Calabi-yau ...
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Why is (1,1) worldsheet SUSY enhanced to (2,2) SUSY after compactification of type II string theory on a CY threefold?
I have a quick question. In case of compactification on an Calabi Yau cutting off 3/4th SUSY from the type-II string in 10D leads to an enhancement of worldsheet SUSY. It has been claimed since time ...
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String Compactification on a Circle Results in a Moduli Space?
I have been reviewing some string theory for a project I'm working on and I have some questions regarding string compactifications on a circle and the precise definition/origin of the moduli space ...
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Does compactification of a Nambu-Goto string in one direction break Diff invariance?
Assume we have a Nambu-Goto action, in phase space, for a closed string. If I compactify one coordinate of the target space, do I reduce the diff invariance of the system.
We have
$$S=\int d^2\sigma \...
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Could mass just be light moving in another dimension?
Could mass just be perceived as light moving along a geodesic through an additional spatial dimension (either invisible or somehow curled up into itself)? Since the light would be moving in another ...
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Doubt for open string toroidal compactification
Let $(\tau,\sigma)$ be our coordinate system on a local path of worldsheet. For open string $\sigma \in [0,\pi]$ and the end points are different. Now if we do compactification on this string in $26$...
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Coordinates on a compactified dimension in bosonic string theory
In the simple case of compactification on the circle of radius $R$, $S^1_R$, most sources on string theory, e.g. here (Kevin Wray, An Introduction to String Theory, page 197), it is stated that the ...
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Is there a room for "another SUSY" to reduce extra dimensions?
I've heard that supersymmetry already dropped dimensions count in String theories from 26 to 10 (11 - after Witten).
So, is there any space left in the rest of the math to introduce some "another ...
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Why does one need to compactify space in a Euclidean CFT?
It is often claimed [1] that in Euclidean CFT's on $\mathbb{R}^d$ one needs to first compactify space to the sphere $S^d$, as $\mathbb{R}^d$ is not invariant under conformal transformations. I cannot ...
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Quantized momentum in compactified direction
I'm reading Szabo's book. Here is exercise 6.1. :
A relativistic particle of mass $m$ and charge $q$ in $d$ Euclidean
spacetime dimensions propagates in a background electromagnetic vector
potential $...
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Meaning of $A^{25}$ in toroidal compactification of open strings
In ch-$8$ sec-$8.6$ (String theory vol $1$) Polchinski starts with “a constant background” U$(1)$ gauge field when doing toroidal compactification of an open string and mention this gauge field
$$A_{...
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Using $c$ function to calculate $H$ spectrum in bosonic string theory
Ch-$8$ sec-$8.4$ Polchinski (String theory vol I) states
In the canonical approach, focus on the zero-mode contribution to the world-sheet action. Inserting $$\color{red}{X^m(\sigma)=x^m(\sigma^2)+w^...
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Scalar in compactification in several dimension
In sec-$8.4$ $($String theory vol $1$$)$ Polchinski states that
With more than one compact dimension, the anti-symmetric tensor also has scalar components $B_{mn}$
I am not understanding why the ...
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Identical OPE behaviour of CFT of T-dual $X’^{\mu}$ of $X^{\mu}$
In chapter $8$ (String theory vol $\mathrm{I}$) sec $8.3$ Polchinski states that
The field $X’^{25}$ has same OPE and energy momentum tensor as $X^{25}$ the minus signs always entering in pair
$$X^{...
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Question about dark matter/energy and other dimensions
According to drummer and lyricist Henrik Ohlsson, the title Dark Matter Dimensions refers to the "appreciation and acknowledgement of the unseen worlds and dimensions, because without the ...
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Dimensional Reduction and Supersymmetry
I am working my way through "Basic Concepts of String Theory", by Blumenhagen, Lüst and Theisen. Currently I am working on the compactifications of string theories on Calabi-Yau manifolds.
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Why open strings must all end on same D brane?
Consider 10-d open string theory with a D9 brane (i.e. an open string), and $X^9$ compactified on a circle. T-dualising, we find a D8 brane. Why is it that the endpoints of all open strings in this ...
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The volume of infinitly large extra dimension
What I understand is that, according to the string theory our universe is a membrane parallel to several other membranes or (universes). These parallel universes are separated by the bulk or extra ...
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Constraints on non-compactified extra dimensions
I'm reading this paper
An introduction to extra dimensions and string phenomenology
Which according to it, in string theory the 4-dimensional Plank scale is related to the Planck scale of ...
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How many different vacua really are there in the string theory landscape?
How many different vacua are there in the string theory landscape? Different sources give different estimates: some sources talk about the number $10^{500}$, others $10^{272\ 000}$, still others say ...
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Number of unbroken supersymmetries in compactifications
In type II compactifications, we take a 10/11-d spinor $\epsilon$ to decompose into internal $\eta$ and external $\zeta$ pieces, $$\epsilon^1=\zeta^1\otimes\eta^1\ \ (+c.c.)$$ $$\epsilon^2=\zeta^2\...
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Do we have an upper bound to the size of the six hypothetical curled up dimensions in string theory?
String theory requires ten (or eleven for M-theory) extra dimensions. These dimensions are not observed at large scales and so it has been hypothesised that they are curled up and invisible at larger ...
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Basic confusion about interpretation of the 5th dimension in Kaluza-Klein theory
As has been mentioned in other posts, Kaluza originally didn't require the 5th dimension to be curled up/compactified.
So how exactly would our 4D world emerge from a non-compactified 5D manifold? I ...
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Some questions about the compact boson in David Tong's notes on Gauge Theory
The notes can be found at http://www.damtp.cam.ac.uk/user/tong/gaugetheory.html.
In Sec. 7.5.1, T-Duality, around Eq. 7.51, it says that the Bianchi identity $\partial_\mu(\epsilon^{\mu\nu}\partial_\...
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The M2 brane of M theory creates the Type IIA string and D2; the M5 brane creates the D4 and NS5. What are the other objects grouped with the D0?
Type IIA string theory is related to M theory with the 10th spatial dimension compactified on a circle. The origin of the F1 string, D2 brane, D4 brane and NS5 branes is simple: they come from the M2 ...
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Are "Selective Extra Dimensions" possible?
The large extra dimensions model also known as the ADD model proposes that the six hidden dimensions implied by string theory are not rolled up to the Planck length and some (or all) of them are ...
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Structure of Planck volumes in String theory
This question (as the previous one) is mostly arose from such pictures:
As explained by Brian Greene, this is something what our Universe should look like at a Planck scales in superstring theories.
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How Strings move from 1 CY manifold to another?
M-theory says that there's a Calabi-Yau manifold, representing $n = 7$ extra spatial dimensions (here simplified to $n = 3$; check out animated video) curled up and compactified inside every 3D Planck ...
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