17

String theory is not so well understood that we can exhaustively enumerate all possible models, nor are we able to calculate all the properties of any given model. What actually happens is that a particular group of researchers will single out a particular narrow class of models which look promising for specific reasons, and then they will investigate that ...


11

None of our known theories of physics makes any predictions before specifying a model in the theory. Think about it: There are many, many choices made to pick the standard model of particle physics out of the huge space of possible local QFTs. Think about how vast that space is, the "landscape of QFT": you can write down pretty much any local Lagrangian ...


9

String theory isn't just a simple quantum field theory with finitely many fields so it is not true that the "string theory potential" is a function of a fixed number of scalar fields (or other fields). Instead, at various points of the configuration space, the number of light (and even massless) scalar fields is changing, at various points of the transitions ...


8

If you spend some time looking in detail at the arguments that string theory requires supersymmetry, you'll find that they are not watertight. (How could they be, since we still can't say/don't know precisely what string theory is?) Basically, some string theorists argue that that the usual classification depends too strongly on choosing nearly trivial ...


7

In my opinion you are exaggerating the power of strings. In my perception it is the all pervading harmonic oscillator potential of quantum mechanical potentials taken to a higher dimensional level. You must know that all symmetric potentials have as a first term the harmonic oscillator in the expansion. When in doubt of the form of the potential, approximate ...


6

It's not a "$G(2)$ lattice" one has to compactify the M-theoretical dimensions upon (after all, the $G_2$ lattice is 2-dimensional); it's the $G_2$ holonomy manifolds. There are lots of different topologies of these seven-dimensional manifolds. They're analogous to the Calabi-Yau manifolds but don't allow one to use the machinery of complex numbers.


6

"10^500 is huge". You're definitely correct there: Suppose it took a Planck time to test each version. It would take $t = 10^{500} \times t_{P} = 10^{457}$ s, or $10^{440} \times$ the present age of the Universe. Thus, it is not feasible to check them all manually. [I like the idea with the electron mass; maybe something could be done with that in a ...


6

Who wrote that passage? It contains some misunderstandings. All I know is that $10^{500}$ is a very large number. It is a finite number. How many theories do you know which have a finite number of solutions? Have you tried to count the number of solutions of plain Einstein-Yang-Mills-Dirac-Higgs theory without its string-theoretic UV completion? There ...


6

I'll add a small disclaimer as well, I am a mathy with little to no physics background, so if any of the below needs expanding, feel free to ask! (Though I'll mention that I felt a lot more comfortable with this stuff when I first computed the induced actions I'll mention below and really got my hands dirty verifying everything.) To see that there is only ...


5

There are currently five distinct string theories, which are related by dualities to M-theory. In addition, bosonic string theory also has many variants though it is not considered a valid candidate due to the tachyon and exclusion of fermions from the spectrum. Bosonic String The variants of the bosonic string theory can be summarised as: Closed oriented ...


5

Is it true that each solution is corresponding to a specific possible universe? This is looking it backwards. One looks at all these vacua for solutions that fit our current cosmological observations, which is a single one out of this huge number. If yes, can we identify and pick a single solution that is corresponding to our universe? Researchers are ...


4

The landscape isn't supposed to be just a set of isolated elements ("depressions" in the landscape, I mean minima) but also the "scenery" in between them. The number $10^{500}$ refers to the number of minima. In 10 dimensions, supersymmetry can't be broken so there are vacua that have moduli – especially the dilaton, i.e. the string coupling (but also the ...


4

First of all, in the most recent decade, string phenomenology isn't talking about strictly Minkowski vacua. E.g. in the KKLT paper, you will see $AdS_4$ vacua uplifted to $dS_4$ by antibranes and no Minkowski space at any place in between. The fact that a nonzero C.C. is generated for the large 3+1 dimensions doesn't mean that one can't find any shape of ...


3

With regards to the follow-up comment: there is no example that covers the most important features, because the only framework where you might understand how to think about a potential with multiple minima is QFT. But there is no evidence that supports this approach in String Theory, and lots of evidence that suggests it is just wrong. Instead, the only ...


3

The place to start is, of course, by finding a prediction of string theory that differs from that of made by competing theories. The prediction made by naive string theory are Extra dimensions. Naively this is a problem, but it can be patched up. All we have been able to do on this front so far is to require that the extra ones be compact and put limits ...


3

Some informal imprecise answers. There is certainly more than one possible Calabi-Yau allowed in string theory. Indeed, a single Calabi-Yau can correspond to many different vacua, because one must additionally specify flux and brane content. Just as a technical point, continuously varying the moduli of one Calabi-Yau can end up with another Calabi-Yau; ...


2

That there are multiple possible solutions isn't seriously questioned, but I note this recent paper The Top $10^{500}$ Reasons Not to Believe in the Landscape. This is not questioning the existance of $10^{500}$ solutions, but it is questioning the interpretation as a landscape. Specifically the paper claims the solutions are entirely separate and you cannot ...


2

One way to understand the landscape is as the space that arises from compactifying a higher-dimensional theory in multiple possible ways. In 10-dimensional string theories, for instance, you usually compactify your theory on Calabi-Yau manifolds with 3 complex (6 real) dimensions, which is convenient because it gives you a compactified theory with $\mathcal{...


2

The example of unnaturalness you describe is the example of the mexican hat for the higgs mechanism ( if you look at this page up on the left you will see the mexican hat in the PHYSICS logo). As all should know this symmetry is naturally broken at our energy levels, as in this the example, which is correct, that the pencil sits precariously and can break ...


2

$10^{500}$ is an approximate number of possible $6D$ Calabi-Yau compactifications of String Theory, which is purely geometrical fact (look at this book on Mirror Symmetry for a very detailed and thorough discussion of the subject). For lower dimensional compactifications the situation is much simpler -- just $S^1 \times S^1$ for $2D$ case, and $S^1 \times S^...


2

The electric field, rather than the associated (string) charge enters into the action. This means that the action is not the Hamiltonian, and does not give you the potential energy for a static configuration. The electric field is like a velocity $\dot q$. To get the Hamiltonian, you have to consider the Legendre transform of the Lagrangian $$ H = p \dot ...


2

As understand it, the 4D string landscape is a function that assigns an energy to every possible compactification of the 6 small spatial dimensions. We expect our universe to lie in a local energy minimum, and if there is a lower minimum at another compactification, then our universe would only be metastable, because we expect that it would eventually ...


1

Currently, the dynamical principle which governs the form of compactified dimensions is not known. It seems that one has to understand String Theory non-perturbatively in order to be able to find the form of entire 10D spacetime doing some pre-Big Bang string cosmology (see, say, this book by Baumann and McAllister on String Inflation where the String Theory ...


1

One answer to your question, which laws of physics should be reproduced in any string compactification, could be the following: If the Weak Gravity Conjecture, see http://arxiv.org/abs/hep-th/0601001, holds true, then gravity should come out as the weakest force in any string compactification. (Notice that there are - as far as I know - only arguments for ...


1

The string one-loop cosmological constant is given by $$\Lambda=\int_{\mathcal{F}}\frac{d^2\tau}{(Im \tau)^2}Z(\tau)$$ where the integration is over the Teichmuller space of inequivalent tori and $Z(\tau)$ is the partition function of the theory. The partition function keeps track of how many particles with any given mass appear in the spectrum of the theory,...


1

I don't think it's a bad question. I think as the comment says, the answer is yes, many Universes may have similar properties. However, it has been argued that our Universe's cosmological constant is finetuned, and that this fine tuning has an environmental explanation. I.e., our constant is untypical, but since observers need e.g. structure in their ...


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