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What is the principal/more actual strategy in order to find the definitive form of M/String theory?

I mean, you have a (for example) $10^{500}$ string theory possibilities landscape (given by the combinations of Calabi-Yau compactifications and different fluxes) and you need to find the one which describes our universe. But you don´t have an algorithm to pre-select the correct one.

I see lots of works which try to understand in a more general way the underlying string theory but I don´t see a concrete strategy or approach to achieve this.

And in this context: which is the role that AdS/CFT correspondence plays? I also see lots of works trying to find new dualities (for example http://arxiv.org/abs/1410.2650) but I don´t know how this help to find (directly) the definitive theory.

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  • $\begingroup$ To be honest, there is no strategy. 90% of the community is working on applications of the theory, instead of completing the foundation (yes, after 50 years the foundation is not yet complete). You may want to look for String Field Theory. $\endgroup$ – Rexcirus Feb 16 '17 at 21:58
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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 implications to inflationary physics are presented) dynamically from certain symmetric initial condition. There are some phenomenologically reasonable stationary compactifications of String Theory which lead to low-energy 4D physics resembling the Standard Model. See, for example, the 2nd volume of Green, Schwarz, Witten.

The role of AdS/CFT is two-fold. First, it allows one to describe full String Theory on a certain background, which is, in particular, a quantum theory of gravity, using techniques of 4D SUSY gauge theory, which is much simpler. The problem is that even 4D gauge theory is still too complicated to be studied quantitatively in most interesting range of coupling constants. The most famous example of ${\cal N}=4$ $SU(N)$ SYM theory dual to Type IIB String Theory on $AdS_5 \times S^5$ background with $N$ units of 4-form cuvature strength through $S^5$ allows one to study String Theory using SYM only for the case of $g_{YM}^2 \ll 1$ and $g_{YM}^2 N \ll 1$, when the perturbative QFT works well. Second, it allows to study strongly coupled gauge theory using classical Supergravity, which is a classical and low-energy limit of String Theory ($g_{YM}^2 \ll 1$ and $g_{YM}^2 N \gg 1$ limit of the aforementioned case of AdS/CFT). This route is quite effective and allows to uncover interesting dynamics of gauge theories which cannot be done using standard perturbative techniques (see this classical review of Aharony et al. on the subject). Finally, it is very interesting example of duality between theories living in different dimensions, which is believed to be inevitable consequence of the fact that String Theory describes quantum gravity among many other things. The possibility of such a duality was put forward before AdS/CFT correspondence, being based on certain quantum black holes considerations -- it is known that the entropy, which counts degrees of freedom of BH is proportional to the area of its horizon, not the volume of the interior.

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  • $\begingroup$ @Chequez For example, it is known how the symmetry is broken in the Standard Model. It is described by the Higgs Mechanism -- we start with a symmetric Lagrangian, but vacuum is not symmetric, and blah-blah-blah... Here we (probably) should start with a target space symmetric in all the dimensions and end with what we have -- 6 compact dimensions times 4 non-compact resembling de Sitter space. It is known known how to achieve this. $\endgroup$ – Andrey Feldman Feb 16 '17 at 12:26
  • $\begingroup$ Two things: First, what do you exactly mean with "dynamical principle which governs the form of compactified dimensions " and secondly: as to non perturbative formulation: different objects, (branes etc ) which arise in a non perturbative way have been studied; isn´t there any (string?) theory which doesn´t use perturbative approach (and what is the main difficult on it)? Sorry for not being concrete enough, I´m just a beginer in string theory $\endgroup$ – Chequez Feb 16 '17 at 12:28
  • $\begingroup$ @Chequez In principle, there is an non-perturbative approach to String Theory, namely, String Field Theory. But this approach is complicated, hides all the dualities, and what was achieved using this approach is just repetition of what was known before from usual first-quantized String Theory. $\endgroup$ – Andrey Feldman Feb 16 '17 at 12:37
  • $\begingroup$ Using integrability techniques, some aspects of N=4 SYM can be studied outside the perturbative regime. $\endgroup$ – Antoine Feb 17 '17 at 9:14

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