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In a nutshell, the $1+1=2$ extra dimensions of spacetime can (in an appropriate gauge) be viewed as a longitudinal spatial direction and a temporal direction. This makes sense because of Minkowski signature of spacetime. The point is that the physical modes of the string can be identified with the 24 (8) transversal directions of the critical bosonic ...


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The two notions are indeed related. Take for example the Weyl anomaly of bosonic string theory: the classical (Polyakov) action $S$ is invariant under Weyl rescalings of the worldsheet metric $\gamma_{ab}$, i.e. $$S[\gamma_{ab}(\tau,\sigma)]=S[\exp(2\omega(\tau,\sigma))\gamma_{ab}(\tau,\sigma)]=S[\gamma'_{ab}(\tau,\sigma)].$$ Since this is a conformal ...


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In general you cannot, but in your special case it works out. You should be aware of what the objects in your expression actually are, and how they relate to each other. $X$ is a bosonic field and as such does not feel the presence of gamma matrices at all. Your first line could be rewritten as $$ S = \int \mathrm d^2 \sigma \, \bar \epsilon \gamma^\alpha ...


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I've got the answer by myself. Simply do Taylor expansion of the left hand side. Expand both the exponential, and the field around $H(0)$ or $\psi(0)$, then the right hand follows naturally after plugging in definitions of $T_B$.


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Check out Richard Feynman's QED lectures. It's not quantum gravity yet but it might be what you're after.


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D-branes also arise in perturbative string theory on flat backgrounds as hypersurfaces in space on which strings can end due to Dirichlet boundary conditions. The equivalence of D-branes and p-branes is completely independent from the AdS/CFT correspondence and was discovered before the correspondence by Polchinski in 1995 (see here). D-branes and p-branes ...


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if my paper is correct then for every divergent integral $ \int_{0}^{\infty}x^{m}dx $ will depend on the value $ \zeta (-m) $ http://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation/ and http://vixra.org/abs/1305.0171 for a recurrence realting divergent series and ...


3

I figure that string theory is a new breed of QFT which looks at fields in terms of a network of strings and also incorporates gravity into its module, You should read some reviews of what string theory is . String theory rejects the idea of a point particle as the fundamental constituent of the theory, which is the central concept in quantum field ...


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For a quick (and somewhat dirty) way of deriving the bound, do the following: Recall, that in Poincaré coordinates, the metric of $AdS_{d+1}$ is $$ ds=\frac{1}{z^2}\left(dz^2+\eta^{\mu\nu}dx^\mu dx^\nu\right). $$ The equation of motion for a scalar is $$ (\Box-m^2)\,\phi(z,x)=0, $$ where $\Box=\frac{1}{\sqrt{-g}}\partial_a \sqrt{-g}g^{ab}\partial_b$. ...



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