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Questions tagged [string-theory]

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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What does the word "Observable" mean in Quantum Gravity?

I have seen the statement in several places that the only "observables" in general relativity or Quantum Gravity are measured at temporal or spatial infinity. This is often used as a ...
Josh Newey's user avatar
1 vote
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ADM Formalism for the Effective String Theory

We will consider the following effective action of string theory in leading order of $\alpha'$: $$S=\frac{1}{2\kappa^2_0}\int d^{D}X\sqrt{-G}e^{-2\Phi}\left[R-2\Lambda-\frac{1}{12}H_{\mu\nu\lambda}H^{\...
Daniel Vainshtein's user avatar
2 votes
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How do I obtain the low energy supergravity actions from the 5 superstring theories?

In Domain-Walls and Gauged Supergravities by T.C. de Witt, there is a small table giving the 5 string theories and each of their effective sugras. I am looking for detailed reviews of how these sugras ...
bradas128's user avatar
3 votes
1 answer
106 views

Conceptual Difference Between OPE and Propagator

I'm specifically working with a 2d free scalar CFT. In this case, the propagator is $$\langle X(\sigma) X(\sigma')\rangle=-\frac{\alpha'}{2}\ln(\sigma-\sigma')^2\tag{p.78}$$ while the OPE between $X(\...
Sam's user avatar
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-1 votes
1 answer
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Multiple time dimensions in the eternal inflation model

From a lecture by Prof. Kaiser, I reckoned that according to the Eternal Inflation model, it is possible that all of the 10500 topologies posited by string theory could exist somewhere in the region ...
groaking's user avatar
2 votes
0 answers
58 views

Isomorphism of Virasoro Algebra with Different Highest Weights

Recently I was reading the big yellow book on "Conformal Field Theory" by P. Francesco et.al, and in appendix 8.A.1, it defined a covariant linear map for fusion process among irreducible ...
Mohammad. Reza. Moghtader's user avatar
1 vote
1 answer
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Classical open string in Polchinski -- consistency of Neumann boundary conditions with gauge choice

In Section 1.3 of String Theory, Volume 1, Polchinski derives the open string spectrum from the Polyakov action with Neumann boundary conditions, by first considering the classical open string in ...
Alex's user avatar
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Does LQG break gauge invariance?

So, I'm working with another researcher on a possible connection between Loop Quantum Gravity (LQG) and String Theory (ST). My colleague is proposing and insisting on a action that is not WS ...
Luigi Teixeira de Sousa's user avatar
1 vote
1 answer
58 views

Are the Virasoro constraints generated from the Polyakov action first-class constraints in Dirac's sense?

The Polyakov action for strings reads $$ S[X] = -\frac{T}{2} \int d^2\sigma\, \sqrt{h}h^{\alpha\beta} \partial_\alpha X^\mu \partial_\beta X_\mu, $$ from which the Virasoro constraints follow: $$ T_{\...
Hyeongmuk LIM's user avatar
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Operator Product Expansion (OPE) coefficients of free massless theory

Consider the action of the free massless bosonic theory in $2+1D$ $$ S = \int d^3x \partial_{\mu}\phi(x) \partial^{\mu} \phi(x). $$ The single-particle spectrum (on the surface of a sphere) is given ...
eon97's user avatar
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Derivation of measure for summation over surfaces, including the polyakov action

In his 1981 paper "Quantum geometry of bosonic strings" Polyakov defines a measure for the summation over continuous surfaces. This measure must count all surfaces of a given area with the ...
Jens Wagemaker's user avatar
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39 views

How many dimensions are in string theory? [duplicate]

How many dimensions are in string theroy? I heard that there are 11 but to my understanding, there is an infinite, also can strings be on a 2D plane?
Lucas Dewan's user avatar
1 vote
0 answers
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Which states contribute to the largest gap for WZW model with $so(16)_1$? [closed]

I was told that the WZW model with $so(16)_1$ occurred at $(c,\bar c )=(8,8)$, and it had a gap, i.e. the smallest state with conformal dimension $\Delta = h+\bar h\neq 0$, and it was said to be $2$. ...
ShoutOutAndCalculate's user avatar
1 vote
1 answer
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Number of independent reparametrization gauge invariances of the 'world $(n+1)$-manifold action' of $n$-dimensional objects

As a generalization of point particle dynamics, one can conceive of a theory of $n-$dimensional objects with 'world-manifold' action given by $$ S[X] = -\frac{T}{2} \int d^{n+1}\sigma \sqrt{h} h^{\...
Hyeongmuk LIM's user avatar
5 votes
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199 views

Modified Special Geometry of SUSY Moduli Space

It is known that the Coulomb branches of 5d $\mathcal{N}=1$ and 4d $\mathcal{N}=2$ SUSY (both have eight supercharges) satisfy special geometry. This means that there exists a holomorphic prepotential ...
TwoStones's user avatar
2 votes
1 answer
96 views

Feynman diagrams in string theory

I am beginning to study string theory, I have a beginner level doubt: If we consider a Feynman torus diagram in string theory, it is a worldsheet. What does it represent? Does it actually mean that in ...
SX849's user avatar
  • 306
1 vote
1 answer
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How do hyperbolic tessellations like {7,3} in Anti de-Sitter space relate to our intuition of 3D space (or 4D structure if you include time)?

I just ran into the AdS/CFT correspondence, as I am looking at various use-cases of hyperbolic tessellations, specifically related to the pentagrid and heptagrid as defined by Maurice Margenstern in ...
Lance's user avatar
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3 votes
0 answers
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Replica wormholes in $AdS_5 \times S^5$ holography

I have a question about replica wormholes and the CFT ensembles in AdS/CFT. To make sure that my question isn't coming from a simple misunderstanding, I'll first sketch out my current understanding on ...
11zaq's user avatar
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4 votes
1 answer
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How do compact dimensions determine the particle content of string theory?

In string theory, 10 spatial dimensions are required for mathematical consistency. One way to model our 3-dimensional universe is by compactifying the extra dimension on a Calabi-Yau manifold. They ...
user34722's user avatar
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0 votes
1 answer
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Is the background independence of dynamics a necessary condition for physical theories?

I read in the answer of Lubos Motl to this question that the dynamics of string theory is demonstrably background-independent while the (manifest) background independence is an aesthetic ...
leonardo ricca's user avatar
0 votes
0 answers
45 views

What exactly is a brane? [duplicate]

what exactly is a brane? i know that in order to get the equations of motion of a relativistic string by varying the Nambu-Goto action one has to impose a Neumann boundary condition and a Dirichlet ...
Tomás's user avatar
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2 votes
1 answer
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Are vibrating strings in string theory perpetual motion?

I have never learned string theory, so please forgive me if my question sounds naive or obvious, but I would like to know and I am most likely wrong. As far as I know, strings vibrate in different ...
Tachyon's user avatar
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0 votes
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Variation of action of non-critical string under Weyl transformation (worldsheet cosmological constant term)

In David Tong's lecture notes on string theory, section 5.3.2 An Aside: Non-Critial Strings, page 121, he describes the non-critical string with the following action: $$S_{\text{non-critical}} = \frac{...
Jens Wagemaker's user avatar
2 votes
1 answer
71 views

Free scalar field deriving Ehrenfest using the path integral

In his lecture notes on String theory, David Tong derives Ehrenfest theorem using the path integral: $$S = \frac{1}{4\pi \alpha'}\int d^2\sigma\ \partial_\alpha X\ \partial^\alpha X\tag{4.19}$$ $$ 0 =...
Jens Wagemaker's user avatar
2 votes
0 answers
65 views

Relation between the Wheeler–DeWitt equation and string theory

Can we derive the Wheeler–DeWitt equations from string theory? Since they are both quantum gravity theory. A simple way seems to be the following logic: The Wheeler–DeWitt equation is the canonically ...
feng lin's user avatar
  • 547
1 vote
1 answer
54 views

Worldsheet action in the presence of background fields in complex coordinates

We will start with the worldsheet action under massless background fields - the graviton $G_{\mu\nu}$ and Kalb-Ramond field $B_{\mu\nu}$ (we choose to exclude the dilaton $\Phi$ that also appears in ...
Daniel Vainshtein's user avatar
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0 answers
44 views

Picture Number in String Vertex Operator

How can I know what is the Picture of a particular vertex operator? For example in 8.3.15 in Polchinski's book Vol.1, the Vertex Operators for the Enhanced Gauge symmetry are given by \begin{equation}...
Roddy 's user avatar
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3 votes
2 answers
177 views

Why does no one add Einstein-Hilbert term to CFT in AdS/CFT?

As I work through AdS/CFT exercises, it struck me that there seemed no one doing the following. Suppose we have a holographic CFT. By some reeconstruction method, we can write CFT operators in terms ...
Bulldozer's user avatar
1 vote
0 answers
23 views

Action formalism of braneworld gravity and effective field equation on the brane

Is it possible to derive the effective gravitational field equation on the brane by simply varying the action? Context: The popular way to derive that equation is by starting from Einstein's field ...
SCh's user avatar
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0 votes
0 answers
32 views

Howe-Tucker to Nambu-Goto Action

Aim to find from the Howe-Tucker action: $$S_{\text{HT}}=-\frac{1}{2}\int d^d\sigma\sqrt{-\gamma}(\gamma^{ab}\partial_a X^{\mu}\partial_b X^{\nu}\eta_{\mu\nu}-m^2(d-2))$$ (which is a Polyakov-like ...
cable's user avatar
  • 1
0 votes
0 answers
27 views

Supersymmetric Wess Zumino term and Fierz identities in $d=10$

When studying the Green-Schwarz formalism of superstring, we came across the following term (the Wess Zumino term) in the action \begin{align*} S_{WZ} = \frac{1}{2 \pi \alpha} \int d^2 \sigma [ \...
LSS's user avatar
  • 980
1 vote
0 answers
51 views

Integral of Theta function [closed]

I'm trying to compute the following integral, useful to calculate Amplitudes in String theory \begin{equation} \int \frac{d^2z}{\tau_2} \;\partial^2_z \log \vartheta_1\left(z\right) = - \frac{\pi}{\...
Roddy 's user avatar
  • 11
0 votes
0 answers
22 views

How to decompse kinetic term operator in string compactification

In general textbook, when we want to calculate the dimension of moduli space of string compactification, i.e. calculate the number of massless modes after dimension reduction, we use the following ...
AlphaNotKnows's user avatar
4 votes
1 answer
79 views

Where does the "arbitrary constant" in the $L_{0}$ Virasoro operator come from?

In the 2007 "String Theory and M-Theory" textbook by Becker, Becker, Schwartz there is the following claim about the canonical first quantization of a bosonic string: the quantization of the ...
Daigaku no Baku's user avatar
0 votes
0 answers
49 views

Energy conservation in string theory?

From what i understand string theory usually lives in a Minkowski Spacetime or AdS spacetime. In Minkowski Spacetime conservation of energy is usually very straightforward, is this also the case in ...
FACald's user avatar
  • 117
2 votes
0 answers
36 views

Is the Kalb-Ramond $B_{\mu\nu}$ equivalent to Kaluza-Klein $A_\mu$?

The low-energy effective action of the bosonic string in the critical dimension $D=26$ can be written as: $$S=\frac{1}{2\kappa_0^2}\int d^{26}x\sqrt{-G} \left[ \phi^2\left( R-\frac{1}{12}H_{\mu\nu\...
John Eastmond's user avatar
0 votes
0 answers
51 views

Understanding 4D Gauge Fields in Compactified String Theory

Question: I have a conceptual question regarding $4$-dimensional compactifications in string theory. For example, if we consider flat $10$-dimensional space with D$6$-branes, we obtain $7$-dimensional ...
Nathanael Noir's user avatar
1 vote
0 answers
35 views

Five-form flux in Giddings-Kachru-Polchinski (GKP)

I'm studying the work of Giddings-Kachru-Polchinski (GKP) for hierarchies in string theory and I came across the five-form flux defined in eq. 2.9. Now, if one calculates the Ricci tensor for the ...
Fredrigo6's user avatar
3 votes
0 answers
78 views

Wilson lines with Chan-Paton factors in string theory

In the context of compactifying the open string with Chan-Paton factors, Polchinski (Volume I Section 8.6) considers a toy example with a point particle of charge $q$ which has the action $$ S = \int ...
Adrien Martina's user avatar
0 votes
1 answer
42 views

Large central charge limit for Virasoro blocks

On page 3 of this paper (https://hal.science/hal-00627906v3/document), the authors say that in the $c\to\infty$ limit only the global generators will survive when computing the conformal block. In ...
furious.neutrino's user avatar
0 votes
0 answers
31 views

Should dilaton field be at Planck energy everywhere?

I understand that the consensus view is that the dilaton field has been ruled out by solar system experiments like the time-delay measurements of the Cassini probe. But surely that assumes the rest of ...
John Eastmond's user avatar
7 votes
1 answer
204 views

How to get the factor of $n^{-27/4}$ in number of open string states from the calculation in GSW's book?

In section 2.3.5 of Green, Schwarz, Witten's book on string theory (volume-1) pp. 116-118, the objective is to calculate an Asymptotic Formula for Level Densities $d_n$ for open bosonic string theory. ...
Sanjana's user avatar
  • 785
0 votes
1 answer
70 views

Cosmological implications of String theory compactification?

Is the process of compactification of hidden dimensions in string theory equivalent to an increasing dilaton field? Would one expect the compactification process to continue indefinitely? Could the ...
John Eastmond's user avatar
1 vote
0 answers
56 views

On the derivation of Wess-Zumino term

$G$-$\text{WZW}$ model on a Riemann surface $\Sigma$ at the level $k$ is defined as $${\displaystyle S_{k}(\gamma )=-{\frac {k}{8\pi }}\int _{\Sigma }d^{2}x\,{\mathcal {K}}\left(\gamma ^{-1}\partial ^{...
user avatar
1 vote
0 answers
34 views

Another question about a formula in the book by Green, Schwarz, Witten [closed]

In formula 2.2.62 of Green Schwarz Witten: $$ (\frac{1}{2}\sum_{n=1}^m\,k\cdot\alpha_{m-n}\,e^{i\, n \,\tau})V(k,\tau)\tag{2.2.62}. $$ I am having a problem working out the factor of $\frac{1}{2}$. ...
DavidGSW's user avatar
2 votes
1 answer
119 views

Description of the center of mass of a string in string theory

For a bosonic closed string, the field describing the string coordinates $X^\mu(\sigma,\tau)$ can be written as: (ethernal thanks to @ACuriousmind for writing it in an answer to another question) $$X_\...
Wolphram jonny's user avatar
1 vote
2 answers
111 views

What do we learn from quantizing the relativistic point particle?

In many textbooks on string theory, some time is spend on quantizing the relativistic point particle as a warming-up for quantizing the Nambu-Goto action for relativistic strings. However, I have not ...
Fraxinian's user avatar
  • 168
2 votes
1 answer
91 views

Why is the Ramond vacuum a Majorana fermion in type II string theory?

I understand that in order to have a supersymmetric spectrum in string theory, the vacuum has to be a MW (Majorana-Weyl) spinor under $SO(1,9)$. But I don't see where the Majorana condition on the R ...
Ballanzor's user avatar
  • 496
5 votes
1 answer
106 views

Low-energy string effective action valid for large dilaton field?

The low-energy effective action of the bosonic string in the critical dimension $D=26$ is given by: $$S=\frac{1}{2\kappa_0^2}\int d^{26}x\sqrt{-G} \left[ \phi^2\left( R-\frac{1}{12}H_{\mu\nu\lambda}H^{...
John Eastmond's user avatar
1 vote
0 answers
56 views

Question about the first two terms in the mode expansion in string theory

I am confused about the mode expansion in string theory. For instance, for a bosonic closed string, the field describing the string coordinates $X^\mu(\sigma,\tau)$ can be written as: (many thanks to @...
Wolphram jonny's user avatar

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