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2

I do not agree that $X$ is a primary field. Primary field is defined by its transformation properties under the conformal group (see e.g. yellow book). In particular, under scaling transformation, a correlation function involving primary operators, transforms as $$\langle \mathcal{O}_1(\lambda x_1)\ldots\mathcal{O}_n(\lambda ... 0 Note that under an infinitesimal change in the metric of the form g \to g + \delta g the action changes to$$ \delta S = \int T^{ab} \delta g_{ab} $$Now, under Weyl transformations we have$$ g_{ab} \to e^{2\omega} g_{ab} \qquad \implies \qquad \delta g_{ab} = 2 \omega g_{ab} $$For Weyl transformations \omega is completely arbitrary. If we consider a ... 1 To see why the descendants are primary, you can use$$ \partial\left(T(z)X(w,\overline{w})\right) = T(z)\partial X(w,\overline{w}) = \frac{\partial^2 X}{z-w} + \frac{\partial X}{(z-w)^2} $$And see that it is a primary field of weight h = 1, \overline{h} = 0, and similarly for the other field.... 1 An excellent and clear review of String Field Theory may be found in the paper "Analytical Solutions of Open String Field Theory" by Ehud Fuchs and Michael Kroyter: hep-th/0807.4722. It discusses the CFT and the Oscillator Formalism for covariant string field theory and presents the Schnabl solutions. There is also a detailed discussion of the Sen ... 2 Suppose you have a self-dual five form field strength F_5=*F_5. Kinetic term of this field strength is written as$$ \int F_5\wedge*F_5=\int F_5\wedge F_5=-\int F_5\wedge F_5 $$where in second equality, I used A\wedge B=(-1)^{pq}B\wedge A for p-form A and q-form B. So you can conclude that$$ \int F_5\wedge*F_5=0\,. $$This is the subtlety you ... 1 The quadratic term would give the propagation of the free string, and once ΦΦ and Φ+Φ+ are unpacked we can say what kind of string theory this is. Probably a purely bosonic string if Kaku wrote it in the 1970's. The second term is a standard interaction vertex which splits one string into two or joins two strings into one - a splitting/joining operator. ... 0 The "simplest" link, is NOT to begin with a Superconformal gauge multiplet coupled to a chiral multiplet, but to couple the Weyl multiplet to a superconformal chiral multiplet. It is just a mathematical tool to make your life easier. As a matter of fact, you can take the superconfromal action and make a field redefinition to get the Poincare action, thus ... 2 The main motivation is that string theory incorporates gravitation and gauge theories in a unique framework, avoiding the problems of General Relativity and Quantum Field Theory. Besides this basic fact, I would say that a great theoretical success of the theory is black hole physics. For the first time we have a quantitative framework in which to do ... 4 Where did you hear it's the only way to include gravity? There is also loop quantum gravity on Wikipedia. But even if we leave this aside, the answer is clearly No As with every theory, we can never be sure it is correct or it is "whats really going on". The only thing we can test is, if the theory gives the same results we see in nature. As long as the ... 0 The usual definition of normal ordered product is:$$:X^\mu(z,\bar z)X^\nu(w,\bar w): = X^\mu(z,\bar z) X^\nu(w, \bar w) - \langle X^\mu(z,\bar z) X^\nu(w, \bar w) \rangle $$As you said, this is the regular part of the OPE, since only the divergent part of two operators gives non vanishing contribution to the correlator. Of course$$\langle ...

1

A Schrödinger background is a background with Schrödinger symmetry, and that, in turn, is having the Schrödinger group, which is the central extension of the Galileo group by the non-relativistic mass operator, as a symmetry group. The relevance of the Schrödinger group in string theory and conformal field theory arises because the $d$-dimensional ...

1

Comments to the question (v1): The level matching condition (LMC) for closed strings arises from the reparametrization invariance $\sigma\to \sigma +\sigma_0$ under a constant shift. Open strings do not have this reparametrization symmetry under a constant shift because of the two endpoints, nor do they have the LMC. To more concretely see how the LMC ...

2

The space of semi-infinite forms is basically the name used by mathematicians for the fermionic Fock space please see for example: Friedrich Wagemann lecture, page 8. Given an infinite dimensional vector space with spanned by: $\{ e_i, i\in \mathbb{Z}\}$, let its dual space be spanned by $\{ f_i, i\in \mathbb{Z}\} (\langle f_j, e_i \rangle = \delta_{ij}$) ...

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Veneziano amplitude is a 4 tachyon amplitude in bosonic open string theory. Two tachyons are ingoing and two are outgoing. From the stringy point of view, tachyons are present in both closed and open bosonic theory and are the lowest particle in the spectrum, in particular they have negative mass squared: $m_\textrm{open}^2=\frac{-1}{\alpha'}$. In general a ...

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It's interesting you are asking this question. Just few days ago an article was published in the Quanta Magazine discussing precisely this issue. There it goes beyond what you call “the usual quantum mechanics description of entanglement”. In the new theory, the quantum entanglement (QE) is applied not just across the space but also across the time. By ...

0

Poincare symmetry group of d-dimensional flat spacetime (isometries of flat space) consists of ${\Lambda^{\mu}}_{\nu}$ (Lorentz transformations, i.e. satisfying $SO(d-1,1)$ algebra) and $K^{\mu}$ (translations i.e. commuting algebra). In Nambu-Goto action one interprets $X^{\mu}$ as "flat" spacetime vectors, so the action should be invariant under \$X'^{\mu} ...

1

Killing vector fields correspond to infinitesimal isometry generators of the spacetime manifold and any physical action including the Polyakov action should be preserved under it. In fact, any physical action should be invariant under the (infinitely) larger group of diffeomorphisms of a manifold. Isomotry transformations are just a finite subset of these ...

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