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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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Can a vector tangent to a spacelike surface be null?

I'm studying the peeling-off behaviour of zero rest-mass fields, as described in Penrose's paper. In it, he talks about the boundary $\mathscr{I}$ of the conformal completion of an asymptotically ...
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How do compact dimensions determine the particle content of string theory?

In string theory, 10 spatial dimensions are required for mathematical consistency. One way to model our 3-dimensional universe is by compactifying the extra dimension on a Calabi-Yau manifold. They ...
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Understanding 4D Gauge Fields in Compactified String Theory

Question: I have a conceptual question regarding $4$-dimensional compactifications in string theory. For example, if we consider flat $10$-dimensional space with D$6$-branes, we obtain $7$-dimensional ...
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Five-form flux in Giddings-Kachru-Polchinski (GKP)

I'm studying the work of Giddings-Kachru-Polchinski (GKP) for hierarchies in string theory and I came across the five-form flux defined in eq. 2.9. Now, if one calculates the Ricci tensor for the ...
Fredrigo6's user avatar
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Cosmological implications of String theory compactification?

Is the process of compactification of hidden dimensions in string theory equivalent to an increasing dilaton field? Would one expect the compactification process to continue indefinitely? Could the ...
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Raising a solution to 4D after having dimensionally reduced it

I am applying the method that Gibbons presents in this article, and it consists of dimensionally reducing a four-dimensional Lagrangian using Kaluza Klein in $S_1$, to a three-dimensional one and ...
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Examples of the Kaluza-Klein dimensional reduction method

I am looking for references or articles that apply or explain how to apply the dimensional reduction method to known metrics such as Minkowski, Schwarzschild, Kerr, etc. The references I found ...
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Do singular $G_2$-holonomy manifolds in M-theory have stable compactifications?

In this paper: Chiral Fermions from Manifolds of G2 Holonomy it is shown that compactifications of M-theory on a $7d$ $G_2$-holonomy manifold $X$, generate chiral fermions, if only $X$ is singular. I ...
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Decomposition of vector bundle in $M$-theory

I was studying this paper where the authors construct some field theory solutions by wrapping M5-branes on holomorphic curves on Calabi-Yau. I have some questions about their construction. What they ...
Davide Morgante's user avatar
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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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2 answers
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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 ...
geocalc33's user avatar
3 votes
3 answers
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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 ...
Beleth_the_wise's user avatar
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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 ...
Bastam Tajik's user avatar
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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 ...
Bastam Tajik's user avatar
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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 ...
Davius's user avatar
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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 ...
ShoutOutAndCalculate's user avatar
6 votes
2 answers
683 views

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 ...
mastershooter77's user avatar
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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 ...
user333644's user avatar
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1 answer
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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 ...
cpollack's user avatar
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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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3 answers
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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 ...
Tachyon's user avatar
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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 $26$...
aitfel's user avatar
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2 votes
1 answer
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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 ...
Bedge's user avatar
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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 ...
Victor Novak's user avatar
2 votes
0 answers
166 views

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 ...
Luke's user avatar
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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_{...
aitfel's user avatar
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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^...
aitfel's user avatar
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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 ...
aitfel's user avatar
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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^{...
aitfel's user avatar
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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 ...
Jesse Flynn's user avatar
2 votes
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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. ...
maarten442's user avatar
3 votes
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101 views

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 ...
user984949's user avatar
1 vote
1 answer
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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 ...
Dr. phy's user avatar
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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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