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## Hot answers tagged string-theory

7

The operator-state correspondence says that all states in the theory can be created by operators which act locally in a small neighborhood of the origin. That is to say that the entire Hilbert space of a CFT can be thought of as living at a single point. The key here is that for CFTs we have radial quantization, and states evolve radially outwards unitarily ...

6

It is incorrect to say that the energy of a string directly gives us the mass of the particle. While it is true that more the oscillations on the string, higher the mass, the relation between the oscillations and the mass it not that of a simple proportionality. What's really happening is that the string has some energy $E$ (due to oscillations on it) and a ...

6

The dimension of the string is a special case of the concept of dimension for a much more general class of objects called manifolds. Manifolds are a mathematical abstraction and generalization of the concept of a surface (like the surface of a sphere). The dimension of a (real) manifold is, roughly speaking, the number of coordinates (real numbers) ...

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

the article in wikipedia says that in string theory the particles at lower level are broken down into one dimensional strings, but I understand that only a straight line can be one dimensional, how are these loop like strings still said to be one dimensional ? Maybe this will help: In mathematics, the dimension of an object is an intrinsic property ...

5

It's a scenario that has heavy scalars and relatively light gauginos, so it's one example of a class of "split SUSY" or "mini-split SUSY" scenarios that have survived most of the constraints. In this kind of scenario, collider bounds put the lightest superpartners, namely the winos, above about 270 GeV. Gluinos are constrained to be somewhere north of a TeV, ...

3

One of the points of F-theory is that it may be imagined to be a 12-dimensional theory – however one in which two dimensions are compactified on a tiny, infinitesimal two-torus. But the supersymmetry generators are exactly those that are fully compactible with the 12-dimensional interpretation – after all, all "type IIB supercharges" in F-theory transform ...

2

The value $R=\alpha^{\prime 1/2}$ is the self-dual radius under T-duality. One may indeed extract the massless spectrum – the spectrum of all fields much lighter than $\alpha^{\prime -1/2}$. Because the CFT has an $SU(2)\times SU(2)$ symmetry, as can be seen from the OPEs of the currents, the spacetime physics has this symmetry, too. Because one finds ...

2

Ref : Polchinski Vol $1$, pages $146-150$ With a torus topology, with identifications $(\sigma_1, \sigma_2) \sim (\sigma_1, \sigma_2) + 2\pi(m,n)$, one may bring the worldsheet metrics to the form $ds^2 = |d\sigma_1 + \tau d\sigma_2|^2 = dw d \bar w$, where $\tau$ is a complex constant (the moduli). The periodicity is expressed by $w \sim w + ... 2 The 16 toroidal dimensions have a stringy radius because it has to be self-dual under T-duality, $$R \to \frac{\alpha'}{R}$$ This is needed for these 16 dimensions to be purely left-moving. A fast semi-heuristic way to see it is that the left-moving dimensions obey $$\partial X = 0, \quad \partial_\sigma X = \partial_\tau X$$ If you integrate the latter ... 2 Say we have a supercharge$Q$in$\mathbb{R}^{10}$. To turn this into a supercharge on the$\mathbb{R}^4$effective theory obtained by compactifying on$X$, we need to contract$Q$with a covariantly constant spinor on$X$. The reason why we want it to be covariantly constant is because we want to take the size of$X$to zero. Covariant constant spinors are ... 2 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 ... 1 Let me elaborate on Ryan's correct comments. The flat background makes all components of the spinors covariantly constant; so the geometry is compatible with all of SUSY. A generic curved 6-real-dimensional manifold has an$O(6)$holonomy or$SO(6)\sim SU(4)$if it is orientable. The$SU(3)$subgroup preserves 1/4 of the original supercharges – it is the ... 1 This result follows from i) Uniformization theorem and ii) Gauss-Bonnet theorem in 2d. According to the statement of uniformization theorem from this wiki page : every connected Riemann surface X admits a unique complete 2-dimensional real Riemann metric with constant curvature −1, 0 or 1 inducing the same conformal structure On the other hand, ... 1 Why not use explicit construction for such a surface? From The Manifold Atlas: Any hyperbolic metric on a closed, orientable surface$S_g$of genus$g\ge 2$is obtained by the following construction: choose a geodesic$4g$-gon in the hyperbolic plane${\Bbb H}^2$with area$4(g-1)\pi$. (This implies that the sum of interior angles is$2\pi$.) Then ... 1 What you're missing is that the condition $$\Pi |\psi\rangle = |\psi\rangle$$ does not imply$X(\sigma)=X(\ell-\sigma)$– a condition which would force the closed string to go back and forth along the same path and effective become an open string. Instead, the condition above implies (is equivalent to) a much weaker condition that the complex amplitude ... 1 No. You quantize strings using the same methods as for other classical theories, but these methods are postulated, so you can't use this to explain anything. There is also no such thing as wave-particle duality, that's a terribly out-of-date term. We have neither particles nor waves, but instead wave-functions and operators that correspond to observables. 1 Modern mathematicians would use a very rigorous approach to your question but i'll retain the old approach(Euclid's approach) which might be technically wrong but it is how i understand the word one dimensional. i'll mention the informal definition of point and line from the work of Euclid :Euclid's Elements. A point is that of which there is no ... 1 In the first action the$A_{\mu}$are Hermitian. In the second action the$A_{\mu}$are anti-Hermitian since we let$A_{\mu}\to\frac{i}{g}A_{\mu}$. The commutator of anti-Hermitian matrices are also anti-Hermitian. If we have$\text{Tr}(M^{2})$, with$M$being anti-Hermitian, then we can write it as$\text{Tr}(M^{2})=-\text{Tr}((iM)^{2})$, with$iM\$ ...

1

Ok, this question requires a more careful answer than what was presented here. First, extra-dimensions appear in string theories or M-theory (which is in fact not a well defined or well known theory, if any). Considering only the bosonic string we have the Weyl invariance. If you calculate the energy momentum tensor then the Weyl invariance implies that its ...

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