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Results tagged with string-theory
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user 251344
A class of theories that attempt to explain all existing particles (including force carriers) as vibrational modes of extended objects, such as the 1-dimensional fundamental string. PLEASE DO NOT USE THIS TAG for non-relativistic material strings, such as, e.g., a guitar string.
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Are the one-loop beta functions in bosonic string theory written in terms of bare or renorma...
Given a bosonic string theory defined by the action
$$\tag1 S = \frac{1}{4\pi \alpha'}\int_\Sigma \! \mathrm{d}^2 \sigma \, \sqrt{|g|} \, \left[ G_{\mu\nu} \partial_\alpha X^\mu \partial_\beta X^\nu …
- 434
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Reason to consider only compact world-sheets in string theory
Generally speaking, the "sum over world-sheets" in string theory involves summing over all possible topologies of compact, orientable and connected, as Polchinski says in page $100$ of his first volum …
- 1,330
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answer
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Help with strange notation involving fractions of tensors
I'm currently reading the paper Open strings in background gauge fields by Callan et.al. It is frequently used a notation that is not explained anywhere. If $F_{\mu\nu}$ is the electromagnetic field …
- 1,330
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RG equations for renormalized metric in string theory
I'm studying these PDF notes on strings on curved backgrounds and the author introduces the dimensional regularization of the theory by first defining the bare and renormalized target space metric, $G …
- 213k
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1
answer
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How is the dimensionful renornalization scale $\mu$ related to break of scale invariance in ...
In the $7.1.1$ of David Tong's String Theory notes it is said the following about regularization of Polyakov action in a curved target manifold:
$$\tag{7.3} S= \frac{1}{4\pi \alpha'} \int d^2\sigma \ …
- 55.4k
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Confusion about choosing an Euclidean world sheet metric in String Theory path integral
When it comes to construct a well-defined path integral for the Polyakov action in Bosonic String Theory, most authors assume that the world sheet metric $g$ is Riemannian (i.e. it has Euclidean signa …
- 1,330
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On what space of maps is Polyakov path integral actually defined?
This is a question more concerned about mathematical detail involving the Polyakov path integral.
In section $3.2$ of Polchinski's 1st String Theory book it is stated the following about Polyakov path …
- 1,330
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Why $C^{\infty}(\Sigma, \mathbb{R}^D)$ instead of $\text{Emb}(\Sigma, \mathbb{R}^D)$ in stri...
In most String Theory textbooks, e.g. Polchinski, Blumenhagen et. al., GSW, Becker & Schwarz, Zwiebach, the dynamics of the string is firstly motivated geometrically by the Nambu-Goto action $S_{NG} \ …
- 1,330
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answer
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Logical consistence in Neumann BC in the Nambu-Goto action
Background: In Zwiebach's A First Course in String Theory, 2nd ed. equation $(6.50)$ define a kind of momentum along the $\sigma$ direction on the worldsheet (Here $\dot{X} = \partial_\tau X, \, X' = …
- 1,330
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Physical and mathematical relation between $(\tau, \sigma)$ parameters and coordinates $X^\m...
When we define the parameter space for a string Worldsheet $\Sigma$ to be diffeomorphic to, say, $\mathbb{R} \times [0,1]$ or $\mathbb{R}\times S^1$, and use standard coordinates $(\tau, \sigma)$, $\s …
- 1,330
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Trying to understand the conformal gauge "derivation" in Polyakov action symmetries [duplicate]
In section 2.3 on p. 16 of the book "Basic Concepts of String Theory" by Blumenhagen, Lüst, Theisen, 3 symmetries of Polyakov action are discussed: Poincarè invariance, diffeomorphism invariance and w …
- 213k
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What does really mean to glue the endpoints of a closed string?
I'm almost all string theory standard textbooks such as Polchinski, Barton Zwiebach's book, etc. It is stated that the Worldsheet (or parameter space) flor the closed string is such that the points $( …
- 4,842
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1
answer
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Precise definition of a string worldsheet as a manifold in string theory
I've spent some time studying some definition in smooth manifolds theory in order to give a proper definition of a worldsheet in classical string theory at least. My attempt is the following:
Definiti …
- 1,330
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1
answer
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Energy-momentum tensor normal ordering in Polchinski
In Volume 1 of Polchinski's String Theory book, the author works with energy--momentum tensor of CFTs till chapter 3 in a normal ordered mode, i.e. $T(z)= : \text{something}: (z)$. However, in chapter …
- 1,996
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answer
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On the finiteness of worldsheet area
It is commom to define the wordlsheet of a classical open string, for example, as the $2$-dimensional smooth manifold with boundary as $\mathbb{R} \times [0,\pi]$. With the appropriate embedding $X: \ …
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