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0

So actually they are compatible. It says that a string theory in 3D for AdS (anti deSitter) spacetime which describes a universe with quantum gravity can be mapped (i.e., there is some correspondence) to a conformal field theory (CFT) in 2D, in the spatial boundary of that universe. This gave rise to the holographic principle, unproven but also not disproven,...


3

If you take a classical string with a constant tension (NB unlike a rubber band the tension doesn't depend on how far the string it stretched) and let it relax then it will shrink to a point. However once you quantise the string you have the Heisenberg uncertainty principle to contend with. That means if you were to shrink the string to a point its ...


0

The quotient of locally free sheaves is not necessarily locally free, i.e. the first two terms being locally free does not force the third to be locally free, cf. this math.SE post. You have no guarantee that, given a map $f: E\to F$ of vector bundles, that the quotient $\mathrm{coker}(E\to F)$ (which we would also like to write as $F/\mathrm{im}(E)$) ...


5

I will try to illustrate the sizes for you in my answer. However, with the examples you gave from the article and TV show, that is nonsense...they may be right with the size comparisons, but that is not an illustrative point. You kind of have to take that type of pop-science with a (large) grain of salt. First, let's familiarize ourselves with units. We'll ...


3

The mass of the neutrinos are estimated to some tenths of an $\mathrm{eV}$. The masses of atoms are mostly between 1 and 300 $\mathrm{GeV}$. Thus, considering the masses, this golf ball comparison isn't okay in my opinion. In my mind, comparing the mass of the Moon to the mass of the Solar System would be more realistic. Their sizes can't be easily compared,...


3

In a nutshell, no. Part of the problem seems to be that you misunderstand the fundamentals of string theory. The strings do vibrate. The frequency of these vibrations determines the type of particle and the energy of the string determines the energy of the particle. Second, your understanding of the uncertainty principle isn't quite right. Yes, we cannot ...


0

See https://arxiv.org/pdf/hep-th/9905111v3.pdf (page 58), and references therein. I hope it helps.


1

(Note that I am only starting to study these works and I may be wrong on some points.) The paper you are quoting is indeed providing a full definition of (type II and heterotic) superstring theory (type I is missing), valid at the quantum level and for both the NS and R sectors. The definition is basically following the construction of Zwiebach (arxiv:hep-...


3

Recall that the path integral formulation comes in (at least) two versions: Lagrangian & Hamiltonian. It is often argued that the Hamiltonian version is more fundamental, cf. e.g. this Phys.SE post. Thus we should compare the Polyakov (P) Hamiltonian Lagrangian density $${\cal L}_{P,H}~=~P^{\alpha} \cdot \partial_{\alpha}X +\frac{\gamma_{\alpha\...


7

The path integral involving the Nambu-Goto square root in the exponent is a very complex animal. Especially in the Minkowski signature, there is no totally universal method to define or calculate the path integrals with such general exponents. So if you want to make sense out of such path integrals at all, you need to manipulate it in ways that are ...


2

Let me take parts 2. and 3. of the question first: The 10 dimensions of string theory are, a priori, not "coiled up" or anything else. They are derived for a string theory where the classical version of the string propagates in d-1 spatial dimensions and 1 temporal dimension, i.e. Minkowski space $\mathbb{R}^{1,d-1}$. "Dimension" here is dimension of a ...


0

The problem is that the thickness of the torus is related to its external curvature, whereas a metric only gives information about its intrinsic curvature. Think of a sheet of paper: when it is flat, its metric is clearly zero. Now warp it into a cylinder. This in fact does not change its metric, indeed any transformation that does not crease the paper ...


0

String theory gives some mathematical structure that resembles what we would like quantum gravity to appear as. The closed string has spin 2 fields that are a graviton for instance. The most recent major result is the AdS/CFT correspondence. This says that the interior of an anti-de Sitter spacetime has gravitation which corresponds to a conformal field on ...


2

String theory does not say that GR or quantum field theory hold at those scales. It posits strings, and gets to the Planck scale and predicts what it might look like, foam or stringy things arising and changing and so on. At lower energies it is consistent with quantum field theory and GR. So, GR is a low energy description, and does not worry about the ...


0

Please asks just one question. For the first one: The thickness of a 2 torus does not enter in. It is simply a 2D manifold, it has length and diameter, and only the outside surface matters. At least classically. And by the way a 2 torus is a flat space. It is one of a number of possible compact flat spaces in 2D. See https://en.m.wikipedia.org/wiki/...


1

First, what objects M-theory actually contains is not finally settled because we don't know the full extent of the conjectural theory that is M-theory. Second, M-theory does so far not contain any strings - instead, it contains two-dimensional branes, the M2-branes, that reduce to the strings of the various string theories by having one of their two ...


-1

Spacetime in string theory is a kind of strings field. Some said that this field is infinite - or in infinite expansion - other that spacetime strings appear in the same as the universe grow; others that the strings stretch. If you consider the spacetime a string field it is easy to understand how and like and how occured the born of a strings of matter and ...


3

M-theory M-theory is a theory that shows that the many different string theories people have come up with are connected by underlying dualities. Each of the different theories it compromises are useful in different situations, and each of the different theories allow different types of strings. For example, type I theory includes both open and closed ...


2

As you say, $\gamma_{\mu \nu}$ is a metric. Then, $\gamma_{\mu \nu}=\gamma_{ \nu \mu}$ and it makes no difference which one you write down. This already deals with one half of your discrepancy. Now for the trace: In the einstein summation notation, a the trace of $\gamma_{\mu \nu}$ is $\gamma_{\mu}^{\; \mu}$. The looking at your $$\frac{\partial (det \gamma)...


2

Part 1: The branch of string theory which actually tries to match experiment is called string phenomenology. The state of the art in string phenomenology is that, starting from different forms of string theory (heterotic string theory, M-theory, F-theory...), it is possible to define space-time geometries, arrangements of branes, background fluxes... such ...


1

I will address the title question: does string theory explain the existence of 3 generations of quarks leptons because of the word "explain". Physics is about measurements and observations and mathematical models which not only fit the measurements and observations but also have predictive power. Otherwise the model is just a map, not a physics theory....


0

The official string theory website says this: Theoretical physics has not explained why there are three generations of particles that make up matter. Maybe string theory will come up with an answer for this. That's really where it stands. In fact, there's another question on physics SE here, where one of the answers says The question as to why ...



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