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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.

1 vote
1 answer
67 views

Misconception about closed string worldsheet definition

I'm a little confused about the precise way to define the worldsheet $\Sigma$ of a closed string. Its parametrization must be of the form $X: \Sigma \longrightarrow \mathbb{R}^{1,D-1}$ and one of its …
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4 votes
1 answer
95 views

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' = …
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2 votes
1 answer
136 views

Conformal transformations problem in flat worldsheet

In section 2.2 of David Tong's String Theory lecture notes, he claims that conformal transformations on the flat worldsheet are such that $$\sigma^\pm \to \tilde{\sigma}^\pm(\sigma^\pm).\tag{2.10}$$ I …
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2 votes
1 answer
66 views

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 $( …
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2 votes
0 answers
69 views

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 …
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2 votes
0 answers
85 views

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 …
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0 votes
1 answer
398 views

Functional and total variations in einbein action [duplicate]

I'm currently studying String theory by Becker& Becker, Schwarz textbook. The exercise 2.3 consists in verifying diffeomorphism invariance of einbein action wich is given by $$ S_0 = \frac{1}{2} \int …
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2 votes
0 answers
80 views

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 …
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2 votes
0 answers
53 views

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 …
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4 votes
1 answer
286 views

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 …
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2 votes
0 answers
45 views

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 …
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1 vote
1 answer
327 views

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 …
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2 votes
0 answers
185 views

Residual symmetry of Polyakov action in general backgrounds

In Becker & Becker, Schwarz book String Theory and M-Theory, page $40$ is stated that after choose the conformal gauge $h_{ab} = \eta_{ab}$ in the Polyakov action with background field $G_{\mu \nu}(x) …
1 vote
0 answers
152 views

Background choices that allows static gauge in string theory

Consider the Polyakov action after fixing the conformal gauge $h_{ab}=\eta_{ab}$: $$S_P[X] = -\frac{T}{2} \int \text{d}^2 \sigma \eta^{ab} \partial_a X^\mu \partial_b X^\nu G_{\mu \nu} (X) \tag1$$ whe …
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1 vote
2 answers
146 views

Problems to understand closed string BCs in Polyakov action

I apologize if this is an odd question. In the derivation of equations of motion in the Polyakov action $$S_P = -\frac{T}{2}\int d^2\sigma \sqrt{-h} h^{ab}\partial_a X^\mu\partial_bX^\nu \eta_{\mu \nu …
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