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First, the entire subject of string phenomenology is not reduced to search by brute force for some internal space that produces a low energy spectrum that reproduces the SM one. See life at the interface between string theory and particle physics for an excellent (and conceptual) string phenomenology overview. Are we regularly finding new vacuua that look ...


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String theory does not avoid black hole singularities, it even generalizes them since in higher dimensions the low-energy supergravity theories have so-called "black brane" solutions which are not point singularities but instead singular on a submanifold of higher dimension (e.g. on a line - the "fundamental string", a surface - the "...


2

$$\partial_m [e^{2 \alpha \phi} (H^{mnp}+H^{pmn}+H^{npm})] = 0$$ Shouldn't be? $$\nabla_m [e^{2 \alpha \phi} (H^{mnp}+H^{pmn}+H^{npm})] = 0$$


2

The spacetime of the string worldsheet is what is fundamental in perturbative string theory, not the target spacetime. You can define the worldsheet and its dynamics in an intrinsic way, without making reference to a "container space". In fact, that was a Gauss great achievement, "manifolds exist with independence of whether or not they accept ...


2

What is the nature of the dilaton? The dilaton is just an scalar field that arises in the spectrum of a quantum closed string. You can work out the details of the quantization of a closed string in any string theory textbook. See for example What is String Theory?. The novelty of the dilaton field $\Phi$ is that it controls the interactions between strings ...


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The answer is that nobody really knows. It is conjectured that the answer is finite (such as in the case of elliptically fibered threefolds), but that is just an speculation. There are no truly physical or mathematical arguments to believe that the answer is not finite.


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No, you must always force the second boundary term $\int_{0}^{\tau_1} d\tau \left[ \delta X^\mu \mathcal{P}^\sigma _{\mu}\right]_{0}^{\sigma_1}$ to vanish as well. In the context of $D_p$-branes for $p \ge 0$, this is done by enforcing the Neumann boundary condition for the variation in $X^0 \dots X^q$, and Dirichlet conditions for the remaining dimensions: ...


2

The conifold singularity is the quadric hypersurface singularity given in complex coordinates by $x_1^2+x_2^2+x_3^2+x_4^2=0$ It is also known as the 3-fold ordinary double point. You can smooth this singularity by perturbing the equation: $x_1^2+x_2^2+x_3^2+x_4^2=\epsilon$ (for some $\epsilon\neq 0$). This variety is smooth ("looks the same everywhere&...


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CFT in 2d is relatively well understood. CFT in higher dimension is still relatively mysterious. Representation theoretic arguments, due mainly to Nahm, IIRC, indicate 6 is the largest dimension in which interacting CFTs can exist, much as 10 is the largest dimension in which supergravities can exist. This is a physics theorem, of course, so it's a mix of ...


1

$D$-branes are as "fundamental" as fundamental strings, at least in the two following precise ways: String dualities (the symmetries of string theory as a whole) exchange fundamental strings with D-branes. As an example, the $SL(2,\mathbb{Z})$ symmetry of type $IIB$ string theory mix fundamental strings and 1-branes (see An $SL(2,\mathbb{Z})$ ...


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In string theory and related theories such as supergravity theories, a brane is a physical object that generalizes the notion of a point particle to higher dimensions They are called generically string theories, but if a theory is based on branes, the concept of one dimensional string representing elementary point particles has developed into two ...


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Your third paragraph is correct. Both the entropy, and the Hawking radiation (if supersymmetry is broken) of a stringy Calabi-Yau black hole depend on the details of the effective low energy theory. It is also plausible that the full black hole partition of a black hole, actually depends on all moduli (vector and hyper multiplets) of the background in which ...


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String fields exist and they have a vacuum as any other quantum field theory. There is an entire subject known as string field theory that studies perturbative string theory via string fields. In string field theory you can define off-shell string states, study the creation of a string, or compute amplitudes for a finite time string scattering process. An ...


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