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3

What does it mean for a singularity to be resolved into n−1 intersecting two spheres? Just to be sure, the mathematically precise of idea of "resolving a singularity" is given in the realm of algebraic geometry under the name blow up. Now, what is a blow up intuitively speaking? Algebraic geometers have sets of rules to replace singular spaces ...


-2

This is not strictly an answer to the question. A propagator that satisfies most of the properties is: $$\Delta[X,Y]^{-1} = \ln\left( 1- c\int\limits_{-\pi}^\pi \int\limits_{-\pi}^\pi (|\partial_\sigma X||\partial_{\sigma'} X| e^{- |X(\sigma)-X(\sigma')|^2} + |\partial_\sigma Y||\partial_{\sigma'} Y|e^{- |Y(\sigma)-Y(\sigma')|^2} - 2 |\partial_\sigma X||\...


0

The short answer is that it is not exactly known. Strictly speaking $D8$ branes appear in massive type IIA supergravity. Their precise lift to M-theory is not known, as far as my ignorance can tell. Contrary to what is seems, the physics of $D8$ branes and $O8$ planes is delightfully beautiful, it offers wonderful counterexamples to common misconceptions and ...


9

I will discuss the closed string propagator because this case is pictorially closer to the scalar propagator in quantum field theory case. The closed string analog of the (two-leg amputated) line of propagation of a scalar field in a Feynman diagram is a cylinder of finite height $s$ and twist angle $\theta$. At this point you must notice the analogue with ...


0

Let us work with the semi-disk $D$ with radial time flowing from the origin. Let us make the time $\tau=1$ be the contour boundary of the semi-disk while $\tau=0$ be the origin. Also, for simplicity let us neglect $b$ and $c$ for a while. An arbitrary first-quantized state of the string at $\tau=1$ is given by a functional $\Psi(X|_{\tau=1}(\sigma))$. A ...


0

I know that it has been a while since you have asked this question, but here is how I did it, using a trick from the text "String Theory and M theory" by Becker, Becker and Schwarz: The fermionic propagator $\Delta_{\mathcal{F}}$ is given by $(-\partial_{\tau} + m_{\mathcal{F}}) \Delta_{\mathcal{F}} (\tau, \tau' | m_{\mathcal{F}}) = \delta(\tau - \...


2

Clarification: D-branes are defined as categories just in the context of topological string theory. There is no known way to formalize what a D-brane mathematically means in the context of full physical string theory. Also is probably important to recall that while the identification of the B-model branes of a scheme $X$ as the derived bounded category of ...


0

interesting questions. I am currently looking into understanding some of these questions about the connections between heterotic compactifications to 2D and moonshine. In particular from free fermionic CFT approach used in https://arxiv.org/abs/1610.04898 and https://arxiv.org/pdf/0901.3055.pdf, for example. In the former my supervisor and former student ...


1

One proposed test is measuring the strength of gravity. Gravity has the property that if there are $n$ dimensions of space, the strength of gravity when distance increases diminishes by $$\frac{1}{r^{n-1}}$$ In our current understanding of the universe, there are 3 spatial dimensions, therefore the strength of gravity reduces in accordance with the well-...


1

"that elementary particles formed by strings?" Elementary particles are described theoretically by the standard model a well developed and flexible quantum field theory, with the group structure of SU(3)xSU(2)xU(1). The interest in string theories arises because this group structure can be embedded in the group behavior of the vibrations of a ...


0

The question is broater. It strongly depends on what exactly you want to compute and from what string theory you want to obtain it. General comments: The best resource on general grounds is the book "String Theory and Particle Physics: An Introduction to String Phenomenology" written by Ibáñez and Uranga. There you can learn precise relations ...


1

The general idea of a variational principle is that if you have some self-adjoint operator $H$ and any arbitrary state $\phi$, then $\phi$ can be expanded in terms of the (normalized) eigenvalues $\psi_n$ of $H$: $$\phi = \sum_{n=0}^\infty c_n \psi_n$$ It follows immediately that $$\langle \phi,H\phi\rangle = \sum_{n=0}^\infty \lambda_n |c_n|^2 \geq \...


3

Essentially the answer is that the eleven dimensional supergravity is non-renormalizable; to be precise, above two loops, the graviton-graviton scattering amplitude is divergent. A nice review on the specifics of maximal supergravity is Kaluza-Klein supergravity. Some comments to gain intuition about the UV problems in eleven dimensional supergravity: They ...


1

By definition 11 dimensional supergravity is the low energy limit of M-Theory! When calculating loop diagrams, those with higher loops are thought to diverge. (i.e. give infinite results). One can correct these divergences by adding "counter-terms" to the theory which cancel out the divergences. But then the divergences happen at even higher loops. ...


1

Here is a recent comprehensive (200 page) review: Palti, E. (2019). The Swampland: Introduction and Review. Fortschritte der Physik, 67(6), 1900037, doi:10.1002/prop.201900037, arXiv:1903.06239. Abstract: The Swampland program aims to distinguish effective theories which can be completed into quantum gravity in the ultraviolet from those which cannot. ...


0

The conformal weights are included because they come from the conformal transformation which maps the cylinder to the radial plane. Start with the cylinder where $x \sim x + 2\pi$. Define complex coordinates $w=t+ix$ so $w \sim w + 2\pi i$. Then, all operators admit the expansion $$ \Phi(w,{\bar w}) = \sum_{m,n} \phi_{m,n} e^{-m w} e^{-n {\bar w} } , \qquad ...


2

Ten dimensional type IIA string theory is equivalent to M-theory with a compatified coordinate $x^{11}$. Two important aspects of this correspondence should be highlighted. The 256 massless degrees of freedom of eleven dimensional supergravity descend to the ten dimensional type IIA supergravity massless multiplet after compactification. The circle ...


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