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A classical1 theory of (relativistic) $p$-dimensional membranes exists for any non-negative integer $p$. Such classical membrane-like objects appears in the full non-perturbative formulation of string theory. The problem arises if one tries to quantize a membrane (in a first quantized sense) using standard perturbative quantization methods, which have ...


7

BPS objects are stable because they're the lightest objects with given values of certain conserved charges. So there exists no potential final state that would be lighter and that the BPS state could decay into, by conserving the energy. The excess energy may be invested to the kinetic energy of the final energy but a deficit energy means that the decay is ...


7

The BFSS matrix model is a quantum mechanical model – i.e. quantum field theory in 0+1 dimensions - that describes uncompactified M-theory in 11 dimensions assuming that we study the large $N$ limit of the model with the $U(N)$ symmetry. As myself and later Susskind determined, one may also directly interpret the finite $N$ BFSS matrix model as describing ...


7

Extra-dimensional scenarios may be described as "inspired" by string theory but they are independent hypotheses and they may be true even if string theory is not. However, one has to reduce the ambitions and standards of consistency. Sociologically, it's surely true that the research of models with extra dimensions has been adopted and pursued by many ...


7

In quantum field theory and its extensions including string theory, the electric charge is a generator of a $U(1)$ symmetry which should be promoted to a local symmetry i.e. gauge symmetry. In string theory, the $U(1)$ symmetry and the gauge field often appear as parts of the low-energy effective action. This could be enough to answer the question: we ...


6

In theories with unbroken supersymmetry, the energy can be written as $$E=\sum_i c_i Q_i Q_i $$ where $Q_i$ are some Hermitian supercharges and the coefficients are positive. This is a sum of squares of Hermitian operators which is why it's positively semidefinite. It can't be negative. Tachyons obey $E^2-p^2=m^2$ for a negative $m^2$ so the 4-momentum (or ...


5

There is no 2-D metrics here, because we are working with the boundary $\partial M$ You could imagine a standard action $S_0 = \int_{\partial M} d\tau A_a \frac{d X^a}{d \tau}$, where $A_a$ is constant. With a small perturbation, we will have : $A_a(X) = A_a + \epsilon_a(X)$, and we have an action $S = \int_{\partial M} d\tau A_a(X) \frac{d X^a}{d \tau}$ ...


5

First, the tensor product of two Dirac spinors is the direct sum of differential $p$-forms for all values of $p$. It's because this tensor product is the same thing as the space of all matrices acting on the Dirac spinor space. But all matrices (e.g. $4\times 4$ Dirac-like matrices in 4 dimensions) may be written as linear combinations of $1$, $\gamma_\mu$, ...


5

This formula is actually pretty simple to understand. First, the $2^8$ is the number of possible $D4$ states. Then for each (indistinguishable) $D0$, they can be in either a fermionic or bosonic state, of which there are $8$ each. Next, the coefficient of $q^n$ in $(1+q)^8$ is the number of ways for $n$ independent $D0$ branes to fit in $8$ fermionic ...


5

There exists such a model and it is described in a wikipedia article, the Ekpyrotic Universe. The ekpyrotic model came out of work by Neil Turok and Paul Steinhardt and maintains that the universe did not start in a singularity, but came about from the collision of two branes. This collision avoids the primordial singularity and superluminal expansion ...


5

Matrix string theory http://arxiv.org/abs/hep-th/9701025 http://arxiv.org/abs/hep-th/9702187 http://arxiv.org/abs/hep-th/9703030 is indeed an exact description of fundamental type IIA strings (and similarly $E_8\times E_8$ heterotic strings) at any (e.g. weak) coupling where you can explicitly see the off-diagonal degrees of freedom. You could say ...


4

Yes, there must be branes filling the ordinary large spacetime dimensions in order for gauge fields to propagate there. Even the Type I string theory containing gauge fields (open strings) in 10 dimensions can be understood as having space-filling D9 branes on which the gauge fields live (as well as an orientifold O9 plane). The exception is heterotic ...


3

Yes, whenever the momentum is conserved and T-duality holds, T-duality must map a conserved quantity such as this momentum to another conserved quantity, i.e. the string winding number in this case, and this fact is independent of the carrier of the momentum or the winding charge. In the general nonperturbative case, you shouldn't think about the charges as ...


3

The higher-dimensional objects are the "branes", which were first found as extended black holes in supergravity. In M-theory, the fundamental objects are the 2-brane and the 5-brane, and strings arise from compactifying a brane, e.g. a 2-brane is wrapped around the eleventh dimension, and shows up as a string in the 10-dimensional limit. The classical ...


3

There can not only, there have to be heavy higher dimensional objects (as for example D-branes) in string theory, as Joseph Polchinski discovered. So it is strictly speaking no longer appropriate to talk about "string theory", since M-theory is now known to relate all the different string theories known before by dualities and which contains these higher ...


2

This is not a constraint which appears at the level of perturbative open string worldsheets! Where does this additional constraint come from? Your problem has absolutely nothing to do with any special features of string theory; the very fact that you introduced string theory into this discussion only has one effect, namely to completely mask the actual ...


2

From what we understand today, p-branes are honest degrees of freedom, on equal footing with strings. Shop you have a good question. But I don't think anyone had so far managed to consistently quantize a p-brane. Loosely, a brane has much more degrees of frerdom than a string and it's difficult to get them under control. So quantizing it is a technical ...


2

First of all, if a stack of $M$ branes is rotated relatively to a previously coincident stack of $N$ branes, it's clear that the degrees of freedom that encode the relative angle $\theta$ are nothing else than the transverse scalars determining the position/orientation of these two stacks. Any D-brane or any stack of D-branes may be rotated in any way and ...


2

Maybe it should be remembered that the late 90s not only saw M(atrix) speculation, but also the observation that most, if not all, higher branes in string/M-theory, at least as far as their "worldvolume theory" is concerned, have a quantum description in terms of AdS-CFT duality. Notably the quantum M2-brane (which is the super-membrane in 11-dimensional ...


2

There is. They're all included in the name "string theory". While it originally began as a theory of 1-dimensional strings, today it describe a quantum theory of many other $p$-dimensional (D$p$-branes, membranes, etc.). We just didn't bother finding another name for the theory. The key difference is that while a fundamental string is perturbative, the ...


2

D-branes are not restricted to planar geometries. They can take on many different forms, and you often encounter branes wrapped around spherical manifolds, like $S^1$ or $S^4$. To determine whether a given configuration is stable, you have to evaluate the action of the D-brane configuration, which is given by the Dirac-Born-Infeld action. For a $Dp$-brane, ...


1

The counting of the dimensions is the same for D1-branes and the fundamental F1-strings. There are 24 physical scalars because the embedding of a 2-dimensional world sheet (of either F-string or D-string) may be locally specified by 24 functions. For example, as long as the coordinates $X^0,X^1$ are changing at least "a little bit" in a region of the world ...


1

I'm no expert on the subject, but according to one of the proponents of this model (http://wwwphy.princeton.edu/~steinh/npr/), the 2 branes "stick" to create the universe. Hope that helps.


1

He doesn't really "state" the result without deriving it. He derives it. See e.g. this sentence on page 2: It is further shown that since the D-brane tension arises from the disk, it scales in string units as $g^{−1}$, $g$ being the closed string coupling The tension of D-branes goes like $1/g_s$ because the tension may be calculated from the disk ...


1

Have a look at these lecture notes by David Tong. When you vary the Polyakov action to obtain the equations of motion for the open string, you get two boundary terms. As usual, you want these to be zero so that you can invoke the principle of least action. You can do this by requiring 1) Neumann boundary conditions, 2) Dirichlet boundary conditions or 3) ...


1

There are no actual states with zero energy, $P_0=0$ (I don't even need to talk about $P_i$), unless they correspond to modes of massless states and only massless scalars – moduli – should be considered real. Note that relativity implies that $P_0=0$ states would have to have zero mass and zero spatial momenta in both compact and noncompact dimensions, too. ...


1

By T-dualities along the finite directions on which the D-brane is wrapped, your first problem is equivalent to the problem of a D0-brane moving on a circle. The massless open-string scalar corresponding to the direction of the circle produces the field $X(\tau)$ living on the world line of the D0-brane. And indeed, by assumption, the global topology of the ...


1

They are allowed to move. In fact, if you think about it for a minute you can see that Lorentz invariance requires that they be allowed to move because given a static brane I can always boost to a reference frame where the brane is moving. In order for this to be an equally good description of the physics we must allow branes to move. As an aside, the same ...



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