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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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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Motivation of Keeping Supersymmetry in String Compactification

In Candelas, Horowitz, Strominger, and Witten's famous paper [1] about string compactification, they ask that supersymmetry should not be broken in the resulting 4d theory. Then combined with other ...
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Is classical Kaluza Klein theory stable or not?

Set Up In the original classical Kaluza Klein theory, you have a $d+1$ dimensional manifold where one space dimension is a circle $S^1$. In the "low energy limit," none of the metric ...
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Twistor and Calabi-Yau spaces

The twistor space of Penrose's twistor theory is a projective space of three complex dimensions. This can be understood as six orthogonal dimensions, three with real metric and three with imaginary ...
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Why do you need to count curves on Calabi-Yau manifolds in string theory?

One of the mathematical fields that string theory is said to have had a large bearing on is enumerative geometry which, roughly, deals with counting rational curves on hypersurfaces and its ...
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$T$-duality in effective gauge theories of a $D(p+1)$-brane

I am considering a $D(p+1)$-brane in a space $\mathbb R^{1,p}\times S_R^1$ where $S_R^1$ is the circle of radius $R$. I am assuming low energies $ER\ll1$, so that only the massless spectrum of the ...
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Rolled-up dimensions vs surfaces in a higher dimensional space

All the accounts of dimensions higher than 4 seem to talk about them being 'rolled up'. Is this different to being confined to a 4D surface that exists in a higher dimensional space?
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How and why does toroidal compactification fail to capture observed physics?

My question is motivated by a statement in this chapter (emphasis added, off-topic statements about supersymmetry elided): Compactifying on tori ... is very interesting for its simplicity ... but not ...
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How many fields are there in most flux compactifications?

Quoting from this paper: At first sight, the most striking thing about these compactifications is how many fields they have compared to the Standard Model. While the particle physicists of the 1930s ...
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What are compact dimensions in string theory?

It is often said that string theory describes the world at the most fundamental level and is independent of the background, that is, not the strings are in space-time, but the space-time itself is ...
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Compactification of additional dimensions [duplicate]

The extra dimensions in string theory are supposed to close in on themselves to form circles. Are there other possibilities for compactification? For example a compactification in segment.
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Can string theory be background independent?

Are there any models in string theory which are background independent? If there are, would this mean that these models could be built in any number of dimensions? (Instead of assuming a fixed number ...
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Different symmetries or no symmetries in string theory?

I was reading the book "A Fortunate Universe" by Geraint Lewis and Luke Barnes and something caught my attention: At page 195 the authors say that universes with different symmetries could ...
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Might the Kaluza-Klein scalar provide a solution to the dark puzzles?

Kaluza-Klein theories of a five-dimensional spacetime yield not only the equations of general relativity and electromagnetism, but also a scalar field. This scalar field, sometimes quantised as the ...
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String Theory for beginners: what is a scale?

I'm reading this introduction to string theory by Mariana Grana and Hagen Triendl and I have understanding problems around the method of compactification in string theoretical sense. The ...
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Polchinski String Theory (8.4.38) T-duality of two compactified dimensions

I am confused about a sentence in Polchinski's String theory chapter 8 p 255 when he works out the example of the full $T$-duality with two compact dimensions. He writes "A simultaneous $T$-...
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How to test extra dimensions?

It is predicted in string theory that our world has some extra dimensions. I'm wondering if we want to prove this experimentally, what should we do
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How to compute Physical Constants from given Calabi-Yau Compactification of Effective Field Theory of corresponding String Theory?

I got some interest in String Theory when I was listening to lectures of David Tong and Brian Greene. I remember them stating that the spacetime manifold is compactified to resemble our usual 3+1 ...
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Alternatives to Calabi-Yau spaces? [duplicate]

Are there alternatives to Calabi-Yau spaces describing dimensions in superstring theory? If yes, what are they? If no, why?
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Dimensional regularization and (dimension) compactification [closed]

I believe I read that "additional dimension" in dimensional regularization can be understood as spatial dimensions compactified, but I could not find resources related to this. Is this view correct? ...
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How to explain "compactification of a dimension"

The first paragraph of the wikipedia entry on "compactification (physics)" explains that it "means changing a theory with respect to one of its space-time dimensions. Instead of having a theory with ...
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Is one dimension the same as one space-time?

In this Cern article, https://home.cern/science/physics/extra-dimensions-gravitons-and-tiny-black-holes, it states: "In our everyday lives, we experience three spatial dimensions, and a fourth ...
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