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4

No, it's not possible. The reason is that string theory is a quantum theory. That means it includes all of the properties of quantum theory among its basic assumptions. That includes the Born rule, which relates wavefunctions to stochastic probabilities ("randomness") when measurements are made. Because string theory includes quantum randomness as an ...


3

As far as I know, "a" Universe is caracterised by fundemental constants such as the speed of light, Newton's gravitationnal constant, the Planck constant and so on. You could distinguish between two different universe from the variation of these values I think.


3

A "fifth force" can be given by a scalar field. This field arises in many theories, for example from the dilaton scalar field of string theory, that is non minimally coupled to $R$ in the action. In the low energy limit we can phenomenologically treat string theory as a Scalar Tensor Theories of Gravitation (see the Wikipedia Link for details) in which you ...


3

Define $$ N \equiv \sum_{i=0}^{D-2} \alpha_{-n}^i \alpha_n^i,~~~~{\tilde N} \equiv \sum_{i=0}^{D-2} {\tilde \alpha}_{-n}^i {\tilde \alpha}_n^i $$ The formula you have written tells us un particular that for any state, we must have $N = {\tilde N}$. This condition is known as the level-matching condition. The state $\alpha^i_{-1} |0;k\rangle$ has $N = 1$ but ...


2

If one calculates expectation value $\langle\Psi| M^2|\Psi\rangle$ of the mass-square operator $M^2$ of the state $|\Psi\rangle~=~ \alpha^j_{-1}| 0; p\rangle $, then the level-matching condition (2.25) would be violated.


2

Both $h$ and $\tilde{h}$ are usually called weights. Their sum, $\Delta=h+\tilde{h}$ is the (scaling) dimension of the operator, while the difference, $s=h-\tilde{h}$ is called the spin. This is due to their association with scale transformations (dilatations) and rotations, respectively. To see this, note that the dilatation operator is given by ...


1

One comes to this conclusion due to the fact that the contraction of a symmetric tensor with an antisymmetric one vanishes. Writing down the loop diagrams involves a contraction of both vertices. If you get expressions proportional to $\epsilon_{\mu\nu}\eta^{\mu\nu}$, this will be zero due to the fact that the metric is symmetric and the epsilon tensor is ...


1

As stated in another answer already, your definition of the holographic principle is misleading. More precisely, the holographic principle says the following: A theory of quantum gravity in a compact space should be equivalent to some theory on the boundary of this space. This statement (which is a conjecture) is motivated from the result of Bekenstein and ...



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