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.
2,861 questions
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Riemann 2-manifold volume form: complex vs real
Question 1: is it always possible to write the metric in that form? Is it sufficient the local conformally-flat form to obtain the volume?
Question 2: Is the volume form in (4.1) well-defined? Going ...
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Can a universe with only one spatial dimension and one time dimension still produce complex physical behaviour? [closed]
Can a universe with only one spatial dimension and one time dimension still have meaningful physics? For example, can quantum fields in 1+1 dimensions produce effects similar to higher dimensions, or ...
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Worldsheet ADM Formalism & Hamiltonian Path Integral
Consider the following bosonic NS-NS sector of closed string worldsheet action, having the following spacetime fields - metric tensor $G_{\mu\nu}(x)$ Kalb-Ramond Field $B_{\mu\nu}(x)$ and scalar ...
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EOM of Nambu-Goto in second fundamental form
I am computing the EOM of the Nambu-Goto action $$S[X] = -T\int d^2 \sigma \sqrt{-\det{(\partial_a X^\mu \partial_b X_\mu)}}$$ and I want to write this in a specific form using the second fundamental ...
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D-branes, string field theory, and Chern-Simons
Reading the book$^{\dagger}$ Chern-Simons Theory, Matrix Models, and Topological Strings by Marcos Marino, I'm trying to understand the argument in 7.3.2: here are my main questions which can also be ...
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How to calculus the corresponding operators of bosonic beta-gamma ghost systems? [closed]
In Polchinski's book, it states that the corresponding operators of $|1\rangle, |-1\rangle$ are $\delta(\beta),\delta(\gamma)$, and suggests that it can be shown by path integral. I'm a little ...
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Structure constants of quantum cohomology of (partial and complete) flag varieties [closed]
I have an extremely efficient way to compute the structure constants of the quantum cohomology rings of partial flag varieties (which are modeled by quantum (parabolic) Schubert polynomials, the three-...
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Integrals in Euclidean plane with complexified coordinates?
Calculations are carried out in Euclidean plane with complexified coordinates $z,\bar{z}$ as we do in CFT. I need to derive the following:
$$\int{\frac{d^2 z_1}{(z-z_1)(\bar{z_1}-\bar{w})}}=\pi\ln{|z-...
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Why are strings in string theory considered as elementary?
I was reading "The classical theory of fields" by Landau & Lifshitz and, in the beginning of the third chapter of the 4th edition, they explain that the existence of a rigid body is ...
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How does string theory handle non-renormalizability of QED in $d>4$?
Quantum electrodynamics is non-renormalizable in more than four dimensions (see Peskin & Schroeder, chapter 10). This would seem to put it on similar footing as gravity for $d>4$ in the sense ...
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Why is the string worldsheet theory a CFT?
Why do we say that the (gauge-fixed) worldsheet theory in string theory is a conformal field theory (CFT)? Where exactly does this conformal invariance come from? Is it simply because, after gauge ...
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Why conformal gauge?
In the path integral of the bosonic string, we fix the gauge by setting the metric $ h $ to a reference metric $ \hat{h} $. A common choice is the conformal gauge:
\begin{equation}
h_{\alpha \beta} \...
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Is it true that string theory is definitively wrong on account of it being a theory of an anti de Sitter space?
I'd like to preface this by mentioning that I come from an experimental astrophysics background, and am woefully ignorant of string theory. I apologize if I ask something particularly ignorant or ...
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Wick contraction in CFT
I am reading Tong's lecture notes on CFT and I can't reproduce a result at pag. 82
$$T(z):e^{ikX(w)}:=-\frac{\alpha'^{2}k^{2}}{4}\frac{:e^{ikX(w)}:}{(z-w)^{2}}+ik\frac{:∂X(z)e^{ikX(w)}:}{z-w}+...\tag{...
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Chan-Paton factors and gauge symmetries?
In Ammon and Erdmenger's book on AdS/CFT there is a short discussion on Chan-Paton factors. They state in chapter 4
Although the Chan–Paton factors are global symmetries of the worldsheet action, the ...
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How does requiring the string scale to exceed the GUT scale constrain the QCD axion mass in string theory?
In the recent paper String Theory and Grand Unification Suggest a Sub-Microelectronvolt QCD Axion the authors combine grand unification and explicit type-IIB string compactifications to argue that the ...
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Spin generators for bosonic string for $SO(D-2)$ transverse directions
On page 24 in Polchinski's String Theory Volume 1, he states that the spin generators for the transverse directions (all but the two directions $i=1,2$ that are combined in lightcone gauge) are
Can ...
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Explanation of statement concerning static gauge in flat metric
I am reading Tong's notes about string theory, the second chapter, and I encountered this part that I don't know how is derived. We are considering the worldsheet $(\tau,\sigma)$ whose gauge we set to ...
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How to prove the transformation $\tau \to \frac{a\tau +b}{c\tau +d}$ in type IIB SUGRA?
Becker-Becker-Schwarz (BBS) on page 316 in the book "String theory and M-theory" state that the complex scalar field $$\tau =C_0 +ie^{-\Phi}\tag{8.64}$$ in type IIB SUGRA transforms ...
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How to prove $16\pi G_{11}=2\kappa^2_{11}=\frac{1}{2\pi}(2\pi \ell_p)^9$?
By comparing the Einstein-Hilbert action
$$S=\frac{1}{16\pi G_D}\int \sqrt{-g}R d^D x\tag{8.5}$$ with bosonic part of the 11-dimensional supergravity action in 11-dimensional supergravity
$$2\kappa^2_{...
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Non-Abelian $T$-duality
I am looking at a $\mathbb{R}^3$ section of the $10d$ flat spacetime, in spherical coordinates
\begin{equation}
\mathrm{d}s^2_3 = \mathrm{d}r^2 + r^2 (\mathrm{d}\theta^2 + \sin^2\theta \; \mathrm{...
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Normal ordering of string in vertex operator
I am following Blumenhagen & Plauschinn, “Introduction to Conformal Field Theory,” §2.9. For the holomorphic piece of the vertex operator
$$
V_{\alpha}(z,\bar z)=:\!\exp\!\bigl(i\alpha\,X(z,\bar ...
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Can negative dimensions have a physical meaning? (e.g., in string theory) [duplicate]
I was playing around with the formula for the volume of an $n$-dimensional sphere, and out of curiosity, I tried plugging in negative values for the dimension $ n $. Surprisingly, the math still works ...
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Should the Brans-Dicke scalar field couple to the matter Lagrangian?
The Brans-Dicke action is generally given by:
$$S = \frac{1}{16 \pi}\int d^4x\sqrt{-g}
\left(\phi R - \frac{\omega}{\phi}\partial_a\phi\partial^a\phi\right) + \int d^4 x \sqrt{-g} \,\mathcal{L}_\...
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How to rewrite $\exp(-\sum_{n=1}^\infty \frac{\alpha_{-n}\tilde{\alpha}_{-n}}{n})|0\rangle$?
This concerned the Ishibashi's famous 1989 paper Eq. 2.21.
It's been a while and I'm not sure how to resolve the calculation.
Consider
$$\exp(-\sum_{n=1}^\infty \frac{\alpha_{-n}\tilde{\alpha}_{-n}}{n}...
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Sign issue in the Nambu-Goto constraint algebra
When trying to show that the momentum constraint in the Nambu-Goto string actually generates world-sheet spatial diffeomorphisms, I encountered the following sign issue which I was not able to resolve:...
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What exactly is the $N$-point correlation function (convention) in 2D CFT?
I had some conflicted results from the $N$-point correlation function in 2D CFTs.
Convention 1
The first set of convention is from A.A. Belavin, A.M. Polyakov, A.B. Zamolodchikov's Infinite conformal ...
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How to define expectation value when operators are inserted at the same point?
Conventions:
$\bullet\ $ Everything is expressed in lightcone coordinates defined as
$$\sigma_{\pm}=\frac{1}{\sqrt{2}}(\sigma_{1}\pm\sigma_{2})$$
$\bullet\ |\sigma_{12}|$ is the distance between two ...
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What's the state operator correspondence of the boundary states in boundary conformal field theory?
The state operator correspondence in the bulk of 2D CFT are explained in various places. However, the state operator correspondence of the boundary field $\phi^{\alpha \beta}$ in BCFT were not common. ...
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What is the meaning of moduli space? [duplicate]
The authors (Becker-Becker-Schwarz) in the book "String theory and M-theory" on pages 268-270 prove that the mass spectrum of the closed bosonic strings on a toroidally (torus $T^n$) ...
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Polyakov action for relativistic point particle and 1D quantum gravity
In most textbooks on string theory, and also Witten's beautiful article "What every physicist should know about string theory", one quantizes the relativistic point particle and shows that ...
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Suggested reading for String Theory [duplicate]
TLDR: I know the basics of QFT and GR and looking to read IAS series on QFT and strings. I'm specifically looking for math or math for physicists books with exercises to study beforehand, the ...
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Compactifying mismatched dimensions between asymmetric WZW primaries
In Di Francesco's Conformal Field Theory, Chapter 15, it is stated that any field $\phi_{\lambda,\mu}$ transforming covariantly with respect to some representation specified by $\lambda$ in the ...
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Duality between M-theory and type IIB superstring and relation $T_{M2}=2\pi R_B \beta^3 T_{D3}$
In M-theory/type IIB superstring duality in the Becker-Becker-Schwarz book on page 342 the aunthors mention: "Including the metric conversion factor, the matching gives $$T_{M2}=2\pi R_B \beta^3 ...
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How to get $T_{M2}=2\pi (2\pi \ell_p)^{-3}$?
The Einstein-Hilbert action in $D$ dimensions takes the form:
$$S=\frac{1}{16\pi G_D}\int \sqrt{-g}R d^D x.\tag{8.5}$$ Also, the bosonic part of the 11-dimwnsional supergravity action
$$2\kappa^2_{11} ...
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How to obtain the Virasoro decendent $\alpha_{-1}^2|0\rangle$?
It was known that $$[L_m,\alpha_n]=-n \alpha_{m+n}$$
For a virasoro primary states $|\alpha\rangle$, one could act on the $L_{-n}$ raising operator to obtain the decendents $L_{-n} |\alpha \rangle$.
...
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Motion integrals of string theory
My advisor has told me about a problem that has been present for the past 40 years, yet, unfortunately, I can't find anything specific on it neither had he provided any source.
Introduction
Define ...
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What is the difference between these two vector supermultiplets?
The authors (Becker-Becker-Schwarz) in the book "String theory and M-theory" say on page 257 (and some other pages) that $D=10$ vector supermultiplet (in the light-cone gauge notation) is $...
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Some details concerning Kaluza-Klein number
Consider bosonic string theory compactified on a circle of radius $R$ so that the coordinate $X^{25}$ is compact and the remaining coordinates are noncompact. The spectrum is described by the mass ...
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When was the Regge trajectories first proven with $J\sim M^2$?
In Regge's original papers in 1959 and 1960, the function between spin and energy was shown, however, the inequality was proven for a bound of $\frac{1}{\sqrt{E}}\sim \frac{1}{M}$, which is also what'...
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Question on basic strings in curved spaces
Recently when studying strings on curved spaces I arrived at a question that I wasn't able to answer myself. In the particular setup I'm using, I'm considering the Polyakov action $$S = - \frac{T}{2}\...
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SUSY QM as point-particle limit of Superstrings
There is a pretty clear resemblance between the Lagrangians for SUSY QM (1-dim susy sigma model) and various superstring theories (2-dim susy sigma models).
Again intuitively, one should expect the ...
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Global conformal gauge
I'm reading the Blumenhagen-Lust-Theisen book on string theory. On page 18, They want to discuss whether a global conformal flat metric can exist, namely
$$
h_{\alpha\beta}=e^{2\phi}\eta_{\alpha\beta}
...
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What is the relationship between $g_s$ and $\alpha'$?
On page 300 in the book "string theory and M-theory" by M. Becker-Becker-Schwarz, the author mentions
"we have described in previous chapters that how various superstring theories ...
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Magnetic dual of M2 branes and M5 branes? [closed]
Why do we say: the M2 branes and M branes are magnetic dual?
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Field redefinition to absorb counter term
Consider the following string action
$$S = \frac{1}{4\pi\alpha'} \int d^2\xi \bigg[\alpha'\eta_{\mu\nu}\partial_\alpha Y^\mu\partial^\alpha Y^\nu - \frac{(\alpha')^2}{3}R_{\mu\alpha\nu\beta}(X_0) Y^\...
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String theory suppose world-sheet is globally conformally flat?
It is known that every 2-dimensinal Lorentzian manifold is conformally flat and in general it's not globally conformally flat.
(Here, globally conformally flat means there are a global coordinates ...
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String theory without coordinates
I'm sorry but I'm not good at English. If you find any sentence or word doesn't make sense, please comment.
Is there any string theory's book or review reference that doesn't use coordinate-depending ...
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Dine-Seiberg moduli
The Dine-Seiberg problem requires $\lim _{\Phi \to \infty } V(\Phi )=0$ where $V$ is the scalar superpotential. And in type IIB SUGRA, your moduli are essentially the axiodilaton, Kahler moduli and ...
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How much do we know about Yukawa couplings?
Wikipedia says that
"The Yukawa coupling for any given fermion in the Standard Model is an input to the theory. The ultimate reason for these couplings is not known: it would be something that a ...
