Tag Info

New answers tagged

0

One way to think about this is the following. In general, the partition function (which is the integrand of the vacuum amplitude and not the vacuum amplitude itself) will be of the form $Z_\psi^{\pm}\propto\sum_{a,b}C[^a_b]Z^a_b(\tau)$ where $a$ and $b$ sum over the different sectors as given in the text and the $C$s are some phases. Many of these phases ...


1

The electric field, rather than the associated (string) charge enters into the action. This means that the action is not the Hamiltonian, and does not give you the potential energy for a static configuration. The electric field is like a velocity $\dot q$. To get the Hamiltonian, you have to consider the Legendre transform of the Lagrangian $$ H = p \dot ...


1

Using the Dolbeault bigrading, the (2,0) and (0,2) components of the Kähler metric $g_{zz}=0$ and $g_{\bar{z}\bar{z}}=0$ do indeed vanish, respectively. In particular, the formula $$g_{z\bar{z}}=\partial_{z}\partial_{\bar{z}}K$$ for the mixed (1,1) components does not generalize to the (2,0) and (0,2) components.


0

To make the math work. Ever since Einstein determined that time is actually another dimension, Physicists have used that notion to expand the conception of the Universe to include added (by not sensible) dimensions to get their math and theories to work. Of particular note is Witten's unification of string theories which "only" required the addition of yet ...


0

An answer you might find satisfactory is that our model of spacetime is "larger" than what we observe. Yes, there is a preferred direction which gives us a (1,3) signature, but actual, real objects in spacetime must travel on timelike curves (we normalize the length of their geodesics to -1). These timelike curves only transverse part of the entire ...


0

As other answers have pointed out already, String theory describes not only one string, the basic objects are open and closed strings, also there are some other fundamental ones such as D-branes. As a firrst book to read I would recommend Zwiebach, "A first course in String Theory".


-1

It is relatively easy to imagine 4th dimension. That would be time. But time as if we had a time machine with which we we could arbitrarily move through it. Higher dimensions would be more difficult but possible as if "destinies". For example imagine that in destiny1 you see a car going from A to B in a given hour but in alternate destiny2 you see the same ...


3

In differential geometry, a space of a given number of dimensions can be curved rather than Euclidean, so for example the surface of a sphere is understood to be a 2-dimensional space in spite of the fact that we can't help but visualize the sphere sitting in a higher-dimensional 3D Euclidean space. This 3D space that we imagine the 2D surface sitting in is ...


5

The definition of dimension used here is that of a dimension of a manifold - essentially, how many coordinates (=real numbers) we need to describe the manifold (thought of as spacetime). Manifolds may carry a notion of length, and one of volume. They may also be compact or non-compact, roughly1 corresponding to finite and infinite. E.g. a sphere of radius ...


2

There is a very direct relationship which answers your question, and I'll state it in the way I first learned about it (but you can derive a different connection by passing between dimensions): The 2-dimensional reduction of the Seiberg-Witten equations are the (abelian) vortex equations. The $SU(2)$-vortex equations on $\mathbb{R}^2$ are a ...


0

You can think of a solution describing rotating string with finite length, the existence of which is based on the nonlinear aspect of EOM, contrast to other linear equations. More generally the strings can move as arbitrarily as they like, relating to variant of initial conditions and boundary conditions. Similar for the infinite length string t'Hooft ...


2

The motivation for the holographic principle is independent of string theory. It is that the entropy of a black hole increases with its surface area rather than with its volume. So thermodynamically, a quantum theory with black holes in it, behaves like an ordinary quantum theory with one less dimension of space. This became the idea that a theory of quantum ...


3

When the Hamiltonian of theory is constructed out of creation and annihilation operators the S-matrix automatically satisfies the cluster decomposition principle given that in momentum space the coefficient of the interaction contains only one delta function. However this does not apply to the (first quantized) string theory because there even though the ...


2

The "singleton" and "doubleton" language comes from the oscillator method of finding group representations. Given a (non-compact) group $G$ admitting lowest weight representation with maximal compact subgroup of the form $H\times\mathrm{U}(1)$ for some other compact group $H$, the oscillator method is to describe (unitary irreducible) representations by ...


0

This is either a partial answer or partially incorrect. I had to research this, as I did not know the answer immediately. As I see it, your question has three parts. Why don't the constraints matter for the commutation relations? The derivation of the commutation relations with constraints taken into account is given in the historical reference on the ...


0

In general, once you fix the high energy theory, then there will be a unique EFT following from running down that theory to some lower energy $E_L$ (which will depend of course on $E_L$). Note however that deriving this EFT can be highly complicated sometimes. If for any reason the EFT you get at $E_L$ is not what you wanted, then you have to modify the high ...


0

I understand that the field theory is nonlinear, but what does that have to do with stretching the string with strong excitations? Maybe you're overthinking this one. Find a washing line or a guitar string, and twang it. As you do, look carefully. The string started off straight, but as you were about to let go, it was stretched. The string is elastic, like ...


1

Let $\Omega^2=\exp\phi/2$ so that $\gamma=\Omega^2 g$. Then we have the standard formula $$R_\gamma=\Omega^{-2}\big(R_g-2(n-1)\Delta\ln\Omega-(n-2)(n-1)[\nabla\ln\Omega]^2\big)$$ This is proven in any number of General Relativity texts, but the one in R.M. Wald, General Relativity (1984), is particularly easy to follow and is proved in the form shown here. ...


1

The name T-duality stands for Target-space duality, see e.g. this preprint.


1

It comes from S matrix theory, long before quarks were imagined, S,T and U characterize the type of exchange in the Feynman diagrams entering the S matrix calculation, and they are called Mandelstam variables. s channel-------------------------- t channel------------------------u channel duality meant that the sums could be done either in S ...



Top 50 recent answers are included