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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 ...


5

The type of branes a theory has in constrained by the p-form fields it contains. There is only one supersymmetric gravity theory in 11d, and it has a single $p$-form with $p=4$, call it $G_4$. This means that the theory can possess brane solutions that either couple electrically to $G_4$ (M2 branes) or magnetically to $G_4$ (M5 branes). To understand the ...


3

A string is a one-dimensional object, and not a zero-dimensional like a point. This means that the object traced out by it following its trajectory is a two-dimensional surface, the worldsheet, while particles - points - trace out one-dimensional objects, the worldlines. Much of the difference between string theory and theories with particles as the ...


2

The fact that the boundary theory is conformal means that renormalization does not induce running of the coupling. However, there are divergences which have to be regularized and renormalized. The regularization requires the introduction of an arbitrary scale, which is not Weyl invariant and leads to a conformal anomaly (in even dimensions). ...


2

I just want to point out that the dimensionality of spacetime is a bit of a fluid concept in string theory. Superstring theory can only be formulated in 10 dimensions, but it can be shown to be dual to an 11-dimensional theory called M-theory. It has also been conjectured to be dual to a 12-dimensional theory known as F-theory, although whether or not this ...


2

Comments to the question (v5): If an action functional $S$ is invariant under a Lie algebra $L$ of symmetries, the corresponding Noether currents & charges do not always form a representation of the Lie algebra $L$. There could be (classical) anomalies. In some cases such (classical) anomalies appear as central extensions, cf. e.g. Ref. 1-3 and this ...


2

The first part of the question If a theory gets two predictions right, how likely it is that the rest of the predictions are true too? << can not be answered since even the wrongest assumption can lead to 2 right predictions (and an uncounted bunch of wrong ones). Two opposite theories can have two simililar predictions which of course does not ...


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, ...


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

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

Comments to the question (v1): We will not discuss tachyonic states here, because they are pathological and signal an instability of the theory. Then $$\tag{1} p^{\pm}~\equiv~\frac{p^0 \pm p^1}{\sqrt{2}}~\geq~0 $$ is manifestly non-negative, since the energy $p^0\geq |p^1|$. In the light-cone formalism $p^{+}>0$ is strictly positive, since the special ...


1

I am not aware of a procedure to get the global AdS-metric from a decoupling limit type argument directly. You might already be aware of this, but usually the extension of the equivalence of type IIB string theory on the Poincaré patch of AdS and the super Yang-Mills theory on $\mathbb{R}^{1,3}$ to global AdS and the field theory on $\mathbb{R}\times S^3$ ...


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 ...


1

As a matter of opinion, I would say: absolutely. In fact, The Elegant Universe was one of the books that really got me interested in theoretical physics. It uses examples that are easy for the layman to grasp and visualize, yet illustrate the essential properties of the physics. More objectively speaking, I would recommend looking at the table of contents ...


1

Probe brane means that the brane is not backreacting on the geometry. It's very similar to the idea of a test particle in GR. A test particle follows geodesics of the spacetime. In reality, of course the particle will backreact on the geometry, but for small objects it's a good approximation to neglect this backreaction. In the context of AdS/CFT, this ...


1

It might help to think of obtaining Klebanov-Witten theory in a limiting proceedure. Imagine a dynamical setting where the branes don't start out at the singularity, but instead at some smooth point near the singularity. Then move them to the conifold point. And the conifold point can be located because it's a singular point. If we choose coordinates so that ...


1

ADE refers to the ADE classification, which refers to simply-laced simple Dynkin diagrams and corresponding Lie algebra and Lie group. refers to finite subgroups $\Gamma$ of $SU(2)$, which is related to orbifolds $M/\Gamma$, i.e. manifolds with singularities. See also elementary catastrophes. An ADE gauge theory means that the gauge group is an ADE ...



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