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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112 views

Why don't strings have a Planck mass?

I understand that strings have a size of roughly the Planck length $l_P$ of $10^{-35}$ m. If that is the case then one would expect that their mass would be roughly the Planck mass which is an ...
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70 views

$bc$-system energy momentum tensor

I have a (maybe silly) question regarding the expression of the energy momentum tensor of the $bc$-system in equations $(2.5.11a)$ and $(2.5.11b)$ in Polchinski's String Theory, page 50. I know that ...
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58 views

Why strings, and confusion about string coupling constant

Source: Brian Greene's Elegant Universe 1) I finally understand why string theory is a theory of quantum gravity after reading chapter 6 - the quantum fluctuations/foam that made a mess of the ...
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How does it make sense to talk about the size of a string if the string action is conformally invariant?

From what I understand the Polyakov action in string theory is essentially something like $$S(\xi, g, G)=\kappa \int_{\Sigma} d \mu_{g} \operatorname{Tr}_{g} \xi^{*} G$$ where $\Sigma$ is a given ...
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Polchinski Vol.2 P58 projection under a twist with a discrete torsion in E8$\times$E8 superstring

I don't know how to get the projection Equation (11.3.15) in the book. In the $E_8$$\times$$E_8$ superstring theory, one can introduce the following twist, $$(h_1,h_2)=(\exp[\pi i(k_1F_1+l_1\tilde{F}...
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34 views

$\alpha_n^{i}$ excitations in superstring vs $\psi_r^{i}$ excitations

Perhaps due to a gap in my learning I don't know why I don't see bosonic excitations $\alpha_n^{i}$ discussed in superstring theory, only fermionic excitations $\psi_r^i$. I know the NS sector ...
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29 views

Why worldsheet current associated to spacetime supersymmetry is the integral of the vertex opertor?

Sorry, I just haven't enough reputations for adding a comment in that post. @MISC {389179, TITLE = {Polchinski equation 11.2.7}, AUTHOR = {Nogueira (https://physics.stackexchange.com/users/...
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66 views

Point particles as the limit of a short string

There's a common saying in the domain of the study of classical relativistic strings, that in the limit of a very short string, the action reduces to that of a point particle (there is for instance a ...
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98 views

Are extra dimensions timelike or spacelike?

In special relativity there is a clear difference between spatial and temporal dimensions of spacetime due to the Minkowski metric diag(-1,1,1,1). In higher dimensional theories (10- and 26-...
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102 views

Why any expectation value can be computed by this path integral, and not just the time-ordered ones?

This is quite a basic question about the path integral. In Polchinki's String Theory book, Chapter 2, he says: Expectation values are defined by the path integral $$\langle \mathscr{F}[X]\...
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49 views

CFT correlators and effective string picture

I have been reading https://arxiv.org/abs/hep-th/9702015 by Maldacena and Strominger. Authors derive emission rate of Kerr-Newmann black hole via standard asymptotic matching first. Then rederive ...
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Basic outline of how to compute a string scattering amplitdue

Recently I have been trying to understand how string scattering amplitudes are calculated via integration over the moduli space of Riemann surfaces. I am mathematician with almost no physics ...
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Toroidal compactifications of type IIB string Theory and $SO(5,5)/(SO(5)\times SO(5))$ invariant 6D sugra action

It is usually stated that the compactification of (the bosonic part of the) type IIB ($D=10$, ${\cal N}=(2,0)$) supergravity on $\mathbb{T}^4$ gives a six-dimensional ${\cal N}=(4,4)$ supergravity ...
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K theory and Holography

I have a general or overview question related to charges on D- Branes lies in the K theory of Spacetime. We normally think charges of D branes lies in the Cohomology like $D_0$ branes couple to RR-1 ...
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Is Randall-Sundrum model background independent?

Randall-Sundrum model (https://en.wikipedia.org/wiki/Randall%E2%80%93Sundrum_model) is related on string theory. String theory can be background independent (https://en.wikipedia.org/wiki/...
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Evolution of theories in physics [closed]

I am searching for a book on the theories of (high energy) physics to gain insight, why they are so powerful. Namely, I would like to find a book that uses the evolution of physics from classical ...
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Dirichlet boundary conditions Polyakov action

The most general solution for the equations of motion for Dirichlet is given by: $$ X^{\mu}=a^{\mu}+\frac{1}{\pi}\left(b^{\mu}-a^{\mu}\right) \sigma+\sqrt{2 \alpha^{\prime}} \sum_{n \neq 0} \frac{\...
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Has the conjecture of Guillemin-Sternberg been proven for relevant physics cases?

From a working physicist's perspective, the conjecture of Guillemin-Sternberg (and its generalisations) seems to state in a highly technical manner that quantization commutes with gauge-fixing. In ...
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48 views

Factor of $1/2$ in $TT$-OPE [closed]

I'm trying to calculate the TT OPE in a bosonic theory. I'm missing a factor of 1/2 in the least-singular term. We have (following Di Francesco) $$\langle \partial \phi(z) \partial \phi(0) \rangle = \...
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Quantum corrections to metric on non-linear sigma model target space

I am trying to make sense of what physicists mean when they talk of quantum corrections to the metric on the target spaces of nonlinear sigma models, for example [GHL99]. First some quick notation. ...
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72 views

Polchinski Vol.2 10.6.4 mutual locality condition

I'm reading String Theory Vol.2 by Polchinski. In the book, Polchinski claimed that to define a consistent superstring theory, we need to impose several constraints. One of them is the mutual locality ...
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65 views

Diffeomorphisms on Polyakov action

The Polyakov action is invariant under arbitrary transformations of the sort: $$ \sigma^{\alpha} \rightarrow \tilde{\sigma}^{\alpha}(\sigma). $$ How do I show that the metric will transform like a ...
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54 views

Wheeler-deWitt equation as a renormalization group flow

I recently heard a comment that Wheeler-deWitt equation can be interpreted as RG flow equations. However, I haven't been able to find appropriate references for the same. Could someone suggest any ...
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94 views

Is the gauge/gravity (or AdS/CFT) duality believed to be exact?

I was wondering about the implications of the gauge/gravity (or AdS/CFT in a more restrictive sense) duality for the way we deal with physical theories, and I was wondering if the duality was believed ...
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145 views

What's the connection between cosmic strings and the strings hypothesized in string theory?

I read somewhere that Edward Witten, the (once) big hotshot of string theory, said that the discovery of cosmic strings (at the beginning of this Wikipedia article it is written: "Not to be confused ...
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118 views

Why is so much work spent on String Theory (despite lack of evidence), contrary to the Rishon Model? [closed]

I read this interview with Nathan Seiberg, one of the most outspoken physicists of String Theory. In this interview he writes: There are two correct statements. One is that at the moment there is ...
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84 views

Supercurrent of the $bc$-$\beta\gamma$ SCFT

In Polchinksi's Sec. 10.1, the $bc$-$\beta\gamma$ SCFT is introduced with action $$S_{BC} = \frac{1}{2\pi} \int d^2z (b \bar \partial c + \beta \bar \partial \gamma)$$ and supercurrent $$T_F = -\...
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1answer
158 views

What is dimension? What is the size of dimension?

Recently I heard a TED talk by Brian Greene where he was speaking about String Theory working on $(10+1)$ dimensions. Plus he said that we live in only in $(3 +1)$ dimensions. So where are others? ...
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97 views

Why the full conformal symmetry is $Vir\otimes \overline{Vir}$ instead of $Vir\oplus \overline{Vir}$

In 2D CFT, we have the Virasoro generators $L_m$ and the generators $\bar L_m$, which are such that $[L_m,\bar L_n]=0$. Hence I thought that the full conformal algebra was $Vir\oplus \overline{Vir}$. ...
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Tachyon mode in Brane-Antibrane system (Type II)

Lets First start with coincident $D3$ brane- $D3$ Brane system. Superstring stretch between these two contain a Tachyon mode But GSO projection removes this. For open string, $D$ branes serve just as ...
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92 views

Which AdS/CFT correspondences have been found so far?

When I read about AdS/CFT correspondence, there always comes the most famous example of conjectured correspondence, which is the one between type IIB string theory (AdS side) and $\mathcal{N}=4$ ...
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29 views

Will string theory ever be provable? [duplicate]

Some time ago I saw a documentary in which they said that to have the experimental certainty of the existence of a string we would need a particle accelerator with the same diameter of the milky way. ...
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A simple question about equation of motion in polchinski's String theory?

In page 14 to get the equation of motion, it takes the variation of the action $$ S_P[X,\gamma]=-\frac{1}{4\pi\alpha'}\int_Md\tau d\sigma(-\gamma)^{1/2}\gamma^{ab}\partial_a X^\mu\partial_b X_\mu $$ ...
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33 views

String theory question

If string theory proposes that the point like particles observed are actually different vibrations of a string. Is the way the see them equivalent to various harmonics and fundamental frequencies? So ...
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69 views

Motivation behind action when deriving ''Strings as Harmonic oscillators" in Zwiebach's book on String theory

Page 248 gives us this action and he simply says that we will assume it correct. $$ S=\int d \tau d \sigma ~\mathcal{L}=\frac{1}{4 \pi \alpha^{\prime}} \int d \tau \int_{0}^{\pi} d \sigma\left(\dot{X}...
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174 views

How to derive the Hamilton-Jacobi equation for the area of a minimal surface on a Riemannian manifold?

The action for a string in this background $$G_{IJ}\tag{1}$$ can be written as the Nambu-Goto action $$S_{NG}=\int d\sigma^1d\sigma^2\sqrt{g}\quad\quad\Rightarrow\quad\mathcal{L}=\sqrt{g}\tag{2}$$ ...
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Finite size energy levels

I am reading this paper. In section 5 they consider a 2d QFT in finite size geometry (cylinder of radius $R$). They say that the energy levels of stationary states ($|n \rangle$) therein will behave ...
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37 views

Can we ignore the scalar field (dilaton) term in the Polyakov sigma-model action when deriving the classical equations of motion?

I have the full Polyakov sigma model action: \begin{equation} \begin{split} &S=S_P + S_B + S_\Phi = \\ &- {1 \over 4 \pi \alpha'} \Big[ \int_\Sigma d^2\sigma \sqrt{-g} g^{ab} \partial_a X^\mu ...
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Idea behind boundary states in BCFT

In Blumenhagen's book on CFT, in the BCFT chapter he introduces the concept of a boundary state. TO do this, he first explains how there is a duality between the one-loop open string worldsheet and ...
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48 views

Does the string theory landscape apply to M-theory?

I had read about "string theory" having a large number of solutions (~$10^{500}$). Does this apply to the 11 dimensional M-theory or only to it's five 10-dimensional limiting cases?
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Minimal area for circular Wilson loops in these coordinates

In all references you can see that the Poincare coordinates are used to get the minimal area for the circular wilson loop. I want to use the metric that is used also for the D3-brane (e.g. see ...
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49 views

Nambu-Goto action using ADM metric

I start from the Nambu-Goto action:$$ S=-\frac{T_{0}}{c} \int_{\tau_{i}}^{\tau_{f}} d \tau \int_{0}^{\sigma_{1}} d \sigma \sqrt{\left(\dot{X} \cdot X^{\prime}\right)^{2}-(\dot{X})^{2}\left(X^{\prime}\...
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Veneziano amplitude from 3-point constants

Consider an open bosonic string in the critical dimension at $g_s = 0$ (only the sphere contributes to the string amplitude). The scattering of 4 tachyons is given by the Veneziano amplitude. I'm ...
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56 views

Systematic way of calculating 3-point worldsheet amplitudes

I'm looking for a systematic way of deriving the 3-point functions $\left< V_1(z_1, \bar{z}_1) V_2(z_2, \bar{z}_2)V_3(z_3, \bar{z}_3)\right>$ of the worldsheet CFT of a closed bosonic string. ...
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71 views

Mobius invariance of the worldsheet 3-point function

Consider the CFT that corresponds to a gauge-fixed closed bosonic string. Ground level string states are described by vertex operators such as $$V(p) = :\exp(i p_{\mu} X^{\mu}(z, \bar{z})):$$ which ...
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77 views

Are there other theories (apart from string theory) that combined with inflation, would produce universes with different laws?

In chaotic inflation, space would stop expanding in some points, creating hubble volumes that could experience different spontaneous symmetry breaking, which would result in different properties, such ...
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44 views

Book with explanation of Kazama-Suzuki models

The book "Introduction to Conformal Field Theory" by Blumenhagen and Plauschinn (BP) covers coset construction and minimal models, but it stops there. The original papers by Kazama and Suzuki seem to ...
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47 views

String Theory with a background B-Field

i was reading some articles about open string theory with a background B-Field, and i was wondering if this B-field can carry a mass or not? i mean, can we find in the expression of the mass operator ...
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73 views

String topology in string theory

How do string topology, string field theory and topological strings interact? Does anybody see a global picture? By string topology I mean the TQFT based on the homology of the space of loops ...
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54 views

Are the factors in the de Broglie identities operators, scalar real numbers, or both? Or something else?

I understand that $\hbar$ is an honest element of $\mathbb{R}$. But I am trying to understand how the de Broglie wavelength is related to the wave function mathematically. In the identity $p = \hbar k$...

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