Tag Info

New answers tagged

2

The extra derivative in Polchinski comes from the following version of the Fundamental Lemma of Calculus of Variation (FLCV): $$\tag{1} \left[ \forall g : ~~\int_a^b\! dx~ g(x) ~=~0 \quad\Rightarrow \quad \int_a^b\! dx ~f(x) g(x) ~=~0\right]\quad\Rightarrow \quad f^{\prime}~=~0.\quad $$ FLCV (1) states in words: If it is true that for all functions ...


3

The question of AdS (in)stability is indeed a hot topic in current research of the AdS/CFT correspondence. It is a field that ties together many interesting subjects: Gravity in AdS (i.e a confining box), thermalization in QFTs, the theory of non-linear differential equations and their perturbative treatment, turbulence etc. This explains the explosion of ...


2

There are a few different ways to see that the bosonic string lives in $D=26$. This, by the way, is known as the critical dimension of the theory. I'll give a brief sketch the answer, a more complete one can be found in any textbook, but in particular Polchinski's. Classically, the Polyakov action has 3 main symmetries. These are: 1) Lorentz invariance of ...


2

The torus is special because it's so simple, and because it provides the most tractable example of Mirror Symmetry https://en.wikipedia.org/wiki/Mirror_symmetry_(string_theory), a generalization of T-duality (which relates Type IIB with Type IIA with one another). Toric compactifications are rather special, they're a special case of an incredibly large ...


1

The gamma matrices in a curved space-time satisfy $$ \{ \tau_\alpha(x),\tau_\beta(x)\} = 2 g_{\alpha\beta}(x) $$ Now if you "define" $\tau_a$ by $\tau_\alpha \equiv \tau_a e^a_\alpha$ you find \begin{align*} \{\tau_a,\tau_b\} &= \{\tau_\alpha e^\alpha_a, \tau_\beta e^\beta_b\} \\ &= \{\tau_\alpha , \tau_\beta \}e^\alpha_a e^\beta_b\\ &= 2 ...


1

Let us suppose the holographic principle is indeed correct and that there is a (3+1)-dimensional quantum gravity theory that explains our universe, which has an equivalent description as a (2+1)-dimensional system. This simply means that the two descriptions cannot be distiguished so there is no physical experiment that could determine if we "actually" live ...


1

An uplift is the opposite of a dimensional reduction. Take for example the relation between (the low-energy limit of) M-theory and type IIA supergravity: the former is eleven-dimensional, while the latter lives in ten dimensions. If you find a solution of M-theory, you can get its equivalent in type IIA by Kaluza-Klein reduction. For example, the ...


1

Let us suppress (world-sheet) time $\tau$ in what follows, i.e. consider a fixed time $\tau$. Let there be given a continuous map $\phi:\Sigma\to M$, where the world-space $\Sigma$ and the target space $M$ are both 1D manifolds. We will assume that such a 1D manifold is either a real line $\mathbb{R}$ or a circle $S^1\cong\mathbb{R}/\mathbb{Z}$. That gives ...


2

Notice first that even before restricting the domain of $\phi$, we are considering the theory on the cylinder and identifying the boundary condition $\phi(x + L,t) = \phi(x,t)$. Now to explain the restriction, let's take this example. Consider a field configuration at some fixed time $\phi(x,0)$, we only have to study this in the domain $[0,L]$. Now pick ...


0

To my knowledge you have always a graviton in the closed string string spectrum. The remaining option is to do a theory of only open strings. The problem now is that every loop interactions involves closed strings, so an open string theory is not consistent at the quantum level. See for instance the nice picture of p. 54, in Superstring Theory (Green, ...


0

I think what you want to do is to split away the $-f dt^2$ term from the Schwarzschild piece of the line element, and join it with the $p$-brane directions. Then apply the usual boost to the $(t,z^i)$ coordinates. Because this isn't Minkowski space (the $f$ factor in front of $dt^2$), this won't be a symmetry and will result in the same solution expressed in ...


-1

Hawking radiation is regarded as true if black holes are true, and we understand event horizons, and they exist in nature. This is because, assuming all that, we already know the vacuum is full of the foaming in and out of existence of pairs that immediately annihilate each other. So it becomes a statistical fact that sometimes these pairs will manifest near ...


3

In fact the answer is "yes", the non-chiral type $II$ sugra thoery is called type $II$ A. You can obtain it by dimensional reduction from the $M$-theory sugra in $d=11$. The (massless) spectrum of type $II$ B contains spinor representations of just one chirality (which one is matter of convention), while type $II$ A contains representations of both ...


0

My guess would be that almost always in physics $x$ stands for a dimensionful quantity, then the logarithm cannot be well defined unless for a dimensionless ratio, i.e. log $(x/x_0)$. In which case you can apply the given formula which becomes perfectly convergent $$-\text{log }\left(\frac{x}{x_o}\right) =\int_0^{\infty}\frac{dt}{t}\left(e^{-tx} - e^{-tx_o} ...


0

In the representation theory of Virasoro algebra there is a mathematically strict theorem: http://en.wikipedia.org/wiki/Goddard%E2%80%93Thorn_theorem for bosonic string theory, and similarly for superstring theory. Intuitively the critical dimensions come from zeta function regularization.


0

The short answer to your question is that, out of the known non-gravitational forces, neutrinos only respond to the weak force, but the weak force only acts on left-handed particles, so right-handed neutrinos would not respond to any of those forces. As for the paper by Arkani-Hamed et al, the idea is that the non-gravitational forces only act within the ...


2

Here the object $\chi_\alpha$ has an explicit 2D vector index, as well as an implicit 2D spinor index. There for it is in the $\textbf{1}\otimes\frac{\textbf{1}}{\textbf{2}} =\frac{\textbf{1}}{\textbf{2}}\oplus \frac{\textbf{3}}{\textbf{2}} $ representation of the $SO(1,1)$ group. Now the question is how do we isolate the $\frac{\textbf{1}}{\textbf{2}}$ ...


1

In supergravity theory, 11d have 3 dimensional scalar object and 6 dimensional anti-symmetric tensor object. This allows that M-theory have M2 brane and M5 brane only. (By studying on following question, D branes Ns brane and p-branes i found some interesting paper, supermembrane, arXiv:9611203, It seems to me that section an "brane scan" describes ...


0

In type IIA string theory, there are D0, D2, D4, D6, D8 branes, and in type IIB there are D1, D3, D5, D7, D9 branes. The D9 is a bit special because it is spacetime filling (p+1 = 10 for p=9). In both theories there are NS5 branes and NS1 "branes", more commonly known as fundamental strings (i.e. the string in string theory). The brane content can be ...


0

If you are thinking to apply renormalization to gravity, I would suggest to look at the explanation from "String Theory" of Kevin Wray: the problem is that we need more and more parameters to absorb the infinities that occur in the theory. String theory solve this particular problem because a string has finite extent lp, the divergent integral is cutoff at ...


2

There are models where the extra dimensions don't need to be curled up. The main issue with extra dimensions is, 'why don't the particles/fields we interact with travel in those directions?' We have extremely good limits on standard model particles (electrons, photons) travelling in extra dimensions. However, it is possible to imagine a string inspired ...


2

I don't think its a weakness in any sense. Because in all string theories, $10+1$ dimensional Lorentz transformations ARE a symmetry of the action itself. However not only in order to agree with phenomenology, but also as an attempt (not completely successful so far) to reproduce the entire structure of the standard model interactions, string theory ...


2

What I think one needs to internalize conceptually is that the program of renormalization is always favourable (and almost always required) in physical theories, be they fundamental or effective phenomenological ones (including condensed matter field theories), be there infinities or not. I think the last point is by far the most important. Yes, ...


9

You seem to be confusing regularization with renormalization. Regularization is the process of removing (or, more properly, parameterizing) infinities in loop integrals. Often in elementary texts a "cutoff" representing an energy scale above which the theory is assumed to be invalid is discussed, and counterterms are added to the Lagrangian in order to make ...



Top 50 recent answers are included