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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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 ...
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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}...
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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 ...
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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 ...
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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 ...
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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 [ \...
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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}{\...
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Transplanckian energy magnetic monopoles in string theory/M-theory
I was thinking about transplanckian energy $E>10^{19}GeV$ magnetic monopoles in string theory and M-theory. Are they possible in Nature like the Dirac, 't Hooft Polyakov, Julia-Zee monopoles/dyons? ...
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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 ...
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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 ...
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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 ...
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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:
$$S=\frac{1}{2\kappa_0^2}\int d^{26}x\sqrt{-G} \left[ \phi^2\left( R-\frac{1}{12}H_{\mu\nu\...
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Understanding 4D Gauge Fields in Compactified String Theory
Question:
I have a conceptual question regarding $4$-dimensional compactifications in string theory. For example, if we consider flat $10$-dimensional space with D$6$-branes, we obtain $7$-dimensional ...
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Five-form flux in Giddings-Kachru-Polchinski (GKP)
I'm studying the work of Giddings-Kachru-Polchinski (GKP) for hierarchies in string theory and I came across the five-form flux defined in eq. 2.9.
Now, if one calculates the Ricci tensor for the ...
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Wilson lines with Chan-Paton factors in string theory
In the context of compactifying the open string with Chan-Paton factors, Polchinski (Volume I Section 8.6) considers a toy example with a point particle of charge $q$ which has the action
$$ S = \int ...
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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 ...
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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 ...
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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. ...
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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 ...
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On the derivation of Wess-Zumino term
$G$-$\text{WZW}$ model on a Riemann surface $\Sigma$ at the level $k$ is defined as
$${\displaystyle S_{k}(\gamma )=-{\frac {k}{8\pi }}\int _{\Sigma }d^{2}x\,{\mathcal {K}}\left(\gamma ^{-1}\partial ^{...
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Another question about a formula in the book by Green, Schwarz, Witten [closed]
In formula 2.2.62 of Green Schwarz Witten:
$$
(\frac{1}{2}\sum_{n=1}^m\,k\cdot\alpha_{m-n}\,e^{i\, n \,\tau})V(k,\tau)\tag{2.2.62}.
$$
I am having a problem working out the factor of $\frac{1}{2}$. ...
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Description of the center of mass of a string in string theory
For a bosonic closed string, the field describing the string coordinates $X^\mu(\sigma,\tau)$ can be written as: (ethernal thanks to @ACuriousmind for writing it in an answer to another question)
$$X_\...
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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 ...
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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 ...
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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^{...
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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 @...
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Why and how we study different limits in quantum gravity?
While I'm reading an article, I get confused by why and how we study different limits in quantum limit.
In this paper, the author introduced four limits in D0-brane quantum mechanics: the DKPS (...
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References for closed string collisions on finite number of fixed type mutually intersecting orbifolds with D-branes at the orbifold singularities
I don't know if this topic is studied at all but I'm looking for good references for closed string collisions on a finite number of fixed type mutually intersecting football orbifolds with D-branes at ...
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Relationship between CFT coupling constants and gravity parameters in the AdS/CFT correspondence
The AdS/CFT correspondence relates a string theory in AdS to quantum field theory. Various versions of this correspondence exist, and I want to know the map between parameters in the field theory and ...
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Why do spherical M2 branes have no net charge?
In the paper Invasion of the Giant Gravitons from Anti de Sitter Space, the authors claim that
We are interested in the dynamics of a relativistic spherical membrane moving in $S^4$. The
membrane has ...
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$B$-field reducion in the Kaluza-Klein mechanism
Given the following $d+1$ dimensional dilaton-gravity-Maxwell low-energy effective action in the target space of a bosonic string:
$$S=\frac{1}{2\kappa^2}\int d^{d+1}x\sqrt{-\tilde{G}}e^{-2\tilde{\Phi}...
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Correlation function of excited states in the Ramond sector of 2 d free fermion?
$\newcommand{\ket}[1]{|#1\rangle}$
I'm hoping to find an algorithm to do three point function calculation for generic excited states in the Ramond sector of 2d free fermion.
In the NS sector, it's ...
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How scalar field couples to the $B$-field in Dilaton-Gravity-Maxwell action?
Given the following $d$ dimensional dilaton-gravity-Maxwell low-energy effective action in the target space of a bosonic string:
$$S=\frac{1}{2\kappa^2}\int d^dx\sqrt{-G}e^{-2\Phi}\left[R-\frac{1}{12}...
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Problems with fuzzball black hole creation and low energy physics
The fuzzball proposal intrigues me, but I doubt its ability to match up with semi-classical low energy physics. A variation of my question was asked by the awkwardly titled post:"At the instant ...
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Is there an exact correspondence between Seiberg-Witten theory and mirror symmetry?
Seiberg-Witten solution gives an algebraic geometrical description of the quantum moduli of 4d $\mathcal{N}=2 $ SUSY gauge theory. However, the solution seems purely constructive and does not enjoy ...
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Why $N\to \infty$ limit implies $g_s \to 0$ in holographic QCD?
One basic difficulty in QCD is that it does not contain a small dimensionless quantity that would allow for perturbative calculation of low-energy observables.
A remarkable feature of holographic ...
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"Penrose Functional Degrees of Freedom" ( PFDoF) as a source of dark mass
In his book "Fashion, Faith, and Fantasy in the New Physics of the Universe" Sir Roger Penrose mention ( referring to his older works and specially Penrose-Hawking Theorem) the possibility ...
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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 ...
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Virasoro constraint under the static gauge
I am reading an article on introduction to string theory.
Consider an open string of length $L$, rotating around its center of mass with angular velocity $\omega$. Here we fix the gauge by the static ...
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Gravity dual of the string world-sheet CFT?
The AdS/CFT correspondence conjectures a duality between a $(D+1)$ dimensional gravity theory in asymptotic AdS spacetime with a $D$ dimensional conformal field theory. Is there any sense in asking ...
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A question on BRST current of the Bosonic string, why we choose $c(z)$ as generator?
I'm new to the forum, I will try to make my asking as clear as possible.
I'm currently writing a 40-minutes talk on the BRST quantization of the Bosonic string, mostly following Polchinski's Book. The ...
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Why is empty AdS identified with CFT vacuum and what do excited states correspond to?
I have a few questions regarding the AdS/CFT dictionary regarding the state-state map.
I have seen people identifying the empty AdS spacetime with a CFT vacuum.
What do they mean by "empty" ...
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References for Hanany-Witten setups
What are some good, possibly modern, references for Hanany-Witten brane setups? I know the one of Giveon and Kutasov: Brane Dynamics and Gauge Theories, but I would like to have some more since this ...
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How is negative mass related to string theory according to Eric Weinstein?
Eric Weinstein suggest in his interview that string theory comes from Hermann Bondi's famous paper related to negative mass in 1957 Chapel Hill Conference and that gravitoelectromagnetism and string ...
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Open bosonic string with boundary conditions representing D-branes
(This is the first part of Polchinski's problem 1.6, here it my attempt). I have the following boundary conditions on the $X^{25}$ component being $X^{25}(\tau,0) = 0$ and $X^{25}(\tau,l) = y$ for ...
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Mismatch in the mass dimensions of the dilaton field
In chapter 7 of David Tongs' string theory lectures, the low-energy effective action of string theory is presented, and given by eq.(7.16):
$$S=\frac{1}{2\kappa^2_0}\int d^{26}X\sqrt{-G}e^{-2\Phi}\...
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Sugawara construction in $G$-WZW models
Lorenz argues that Virasoro generator $L_n$ admits a mode expansion in terms of conserved currents
$$L_n = \gamma\sum_{\alpha}\sum_{m\in\mathbb{Z}}:J^{a}_{n}J^{a}_{m-n}:\space\space\space \gamma = \...
user361492
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Semidirect product of Diffeomorphism group and Weyl transformations
This is more a mathematical question but in my string theory lecture we always divide in the Polyakov path integral by $$\mathrm{Diff}\ltimes \mathrm{Weyl}$$ and I was wondering why there is the ...
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Mathematical objects on crystal meltings and their relation to particle physics
I am a mathematician interested in analytic number theory, and I found the paper Dimers and Amoebae
, which shows how many mathematical objects like the Mahler measure, the Ronkin function and the ...
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Calculating the Bekenstein-Hawking entropy for 1+1 black hole with dilaton background
According to this paper the Bekenstein-Hawking entropy of a 1+1 black hole which described by the $SL_k(2,\mathbb{R})/U(1)$ WZW cigar geometry is given by the following formula appearing in eq. (5.7):
...