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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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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An equation to be solved [closed]
Can anyone solve this ∫∫ ∂/ζℏ_ε^πτ±∞_μ ^λ θ^ηβ+σρ+υ+φ^ψω∅^⊗∀_ΩΓ δπΣΛ°√ÅΨ^ΦΞ+Δ^εζ±∩∉^∞ (∃λμ_ξσ)^ζℏ(p̄) * y''(ṙ ̇)+θ^±∑∏υτ(x)'(γ)^∮δρφ * f(x)^pi * <|X(p̄)Y|>
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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):
...
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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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String theory models with non-compact extra dimensions
In the most known incarnations of string theory, we have to compactify the needed, additional dimensions that are then taken to be a.) periodic and b.) "small" in some sense (most of the ...
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$g$-function and D-brane tension
In https://arxiv.org/abs/hep-th/0009148 page 9 it is said that at the fixed points of the RG-flow of the open bosonic string , the $g$-function has stationary points which are the D-brane tensions. ...
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Are the one-loop beta functions in bosonic string theory written in terms of bare or renormalized background fields?
Given a bosonic string theory defined by the action
$$\tag1 S = \frac{1}{4\pi \alpha'}\int_\Sigma \! \mathrm{d}^2 \sigma \, \sqrt{|g|} \, \left[ G_{\mu\nu} \partial_\alpha X^\mu \partial_\beta X^\nu ...
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Confusing definitions of Modular Group and Teichmüller space [migrated]
Notations
1.$\Sigma_g$ is the Reimann surface with genus $g$
2.$M_g$ is the space of all metrics
3.Diff($\Sigma_g$) is the diffeomorphism on $\Sigma_g$
4.$\text{Diff}_0(\Sigma)$ is the connected ...
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RG equations for renormalized metric in string theory
I'm studying these PDF notes on strings on curved backgrounds and the author introduces the dimensional regularization of the theory by first defining the bare and renormalized target space metric, $...
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Quantization of string via topological twist
Polyakov action of a bosonic string propagating in Minkowskian spacetime is:
$$S[\gamma, X] = \frac{T}{2}\int \mathrm{d}^{2}\sigma{\sqrt{-\gamma}}\gamma^{ab}\partial _{a}X^{\mu}(\sigma)\partial_{b}X^{\...
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How is the dimensionful renornalization scale $\mu$ related to break of scale invariance in String Theory?
In the $7.1.1$ of David Tong's String Theory notes it is said the following about regularization of Polyakov action in a curved target manifold:
$$\tag{7.3} S= \frac{1}{4\pi \alpha'} \int d^2\sigma \ ...
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Confusion about choosing an Euclidean world sheet metric in String Theory path integral
When it comes to construct a well-defined path integral for the Polyakov action in Bosonic String Theory, most authors assume that the world sheet metric $g$ is Riemannian (i.e. it has Euclidean ...
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How do Dedekind's eta function arise while computing the partition function of a compact scalar field over circle?
I am following the book String Theory in a nutshell (From Elias Kiritsis). In chapter 4.18, it takes a theory following the action:
$$S=\frac{1}{4\pi l_s^2}\int X\square X\ d\sigma,\tag{4.18.1}$$
$$ \...
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Does String Theory address the problem of time?
According to the argument in this post, a theory of Quantum Gravity should not be compatible with the notion of time evolution. This is also called "The Problem of time".
However, the target ...
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Proof of energy-momentum tensor is zero in Polyakov action
The polyakov action is defined as
\begin{equation}
S=-\frac{T}{2}\int d\sigma d\tau \sqrt{-h}h^{\alpha \beta} \partial_{\alpha}X^{\mu}\partial_{\beta}X^{\nu}\eta_{\mu \nu}
\end{equation}
by varing ...
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Representation of nonabelian Wilson line in terms of fermionic fields
Context:
The coupling action of a particle of charge $q$ to a $U(1)$ gauge field is given by
\begin{equation}
S = q \int d \tau A_\mu \left( X \right) \frac{dX^\mu(\tau)}{d \tau} = -i \ln W_q,
\tag{...
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Do singular $G_2$-holonomy manifolds in M-theory have stable compactifications?
In this paper: Chiral Fermions from Manifolds of G2 Holonomy it is shown that compactifications of M-theory on a $7d$ $G_2$-holonomy manifold $X$, generate chiral fermions, if only $X$ is singular.
I ...
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Relativistic string tension vs non-relativistic Hooke's Law tension
I don't have a specific question, I am just confused about what I have read and would like an explanation of it. On pages 118 and 119 of "A First Course in String Theory", professor Zwiebach ...
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Is there a clean mathematical way to deduce grand unification from string theory?
The question says it all. Simply stated:
Can one prove grand unification from string theory?
What is the argument chain of such a proof?
The textbooks I read so far only appear to give hand-waving
...
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Schreiber/Sati Hypothesis H and emergence of spacetime
Good day,
I am a lay person in this field So i am very sorry if my question Is dumb.
I am wondering whether the Hypothesis H formulated by Schreiber and Sati stating that C-field is charge quantized ...
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"Polyakov trick" for general relativity
In introductory String Theory textbooks, one typically starts with the Nambu-Goto action
\begin{equation}
S_{NG} \sim \int d^2 \sigma \sqrt{\dot{X}^2 - X'^2}
\end{equation}
and then arrive later at ...
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Decomposition of vector bundle in $M$-theory
I was studying this paper where the authors construct some field theory solutions by wrapping M5-branes on holomorphic curves on Calabi-Yau. I have some questions about their construction.
What they ...
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Must open string endpoints lie on a D-brane?
In the second edition of professor Zwiebach's book "A First Course in String Theory", on page 331, on the 3rd line of section 15.1, it says
"In the presence of a D-brane, the endpoints ...
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Precise use of Neumann B.C.s in the Nambu-Goto action
Sometime ago I posted this: Logical consistence in Neumann BC in the Nambu-Goto action, whose answer was not helpful to me. Basically in classical string theory with the Nambu-Goto action, we have ...
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Question about the breaking and closing of string in string theory
I was watching Susskind lectures in string theory. There he explains that open strings can both, split at any point, and also join at the ends when the ends touch at a single point. I have one ...
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Unitarity of Effective String Theory away from critical dimesions ($D=26$) , in the static gauge
Starting from compete UV description of QCD (in the confined phase), if we integrate out the quarks and Glueballs, in principle, we will get an effective theory of strings (QCD flux tube and not ...
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Why did Polyakov choose the particular expression for "distance" between metrics in the space of parametrized curves? (Eq. 9.23)
In Chapter 9 of Polyakov's book Gauge Fields and Strings, 1987 , he studies measures in the space of metrics and diffeomorphisms. My question is - how does one come up with Eq. 9.23?
For some context: ...
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The BRST variation of the gauge fixing condition
Following Polchinski volume I, p 126 onwards, The BRST variation of fields $\phi^{i}$ is given by
$$\delta_{B} \phi_{i} = - i \epsilon c^{\alpha} {\delta}_{\alpha}\phi_{i} \; .\tag{4.2.6a}$$
My ...
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Strange Wick rotation in the computation of string partition function
In order to compute the one-loop vacuum-to-vacuum amplitude for the bosonic string, one runs into
\begin{equation}
Z(\tau) = V_D (q \bar{q})^{-D/24} \int \frac{d^Dk}{(2 \pi)^D} \exp({- \pi \alpha^\...
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How can simple classicall things be described with string theory?
It is of course overkill to use string theory for this, but I am still interested in how, for example, the trajectory of a horizontal throw of a mass point could be derived from string theory, after ...
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Can open Strings interact and lead to a String which is not fixed to a Brane?
Would it be possible that two open Strings interacted with each other and could they theoretically then leave their Brane?
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What is a Majorana spinor-vector gravitino?
I started to read about superstring theory, I do not have a good basis on SUGRA but I got asked to directly jump into superstrings.
Following ``Basic concepts of String Theory'' (Springer), I have two ...
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Binding energy in lorentz boost
In the first lecture here- M theory and string theory lecture 1, Leonard Susskind
The lecturer gives a heuristic as to why a string of length $L$ has mass $L$.
Set all $h=c=1$.
His explanation is that ...
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Ground state vertex operator in superstring theory
In Tongs' "String Theory" lectures chapters 5.4.1-5.4.2 Tong referred to alternative way to find the mass of the different string states using suitable operators, and then integrating the ...
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What would the universe look like if it had undergone a false vacuum decay in the past?
Inspired by "if a metastable de Sitter space lasting for cosmological durations really is impossible in string theory, then dark energy needs to be explained in some other way, e.g. via ...
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Why there is only one modulus for a Klein bottle?
In Polchinski Page 207, there is a claim that only one modulus for a Klein bottle, I tried to understand this claim, Here's what I have tried:
As I understand, modulus means the geometries that are ...
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Strange definition of the fermion number operator in Polchinski
In Polchinski's exposition of the RNS formalism for the superstring (String Theory: Volume II, chapter 10), in page 8, he mentions the worldsheet fermion number operator, which he calls $F$. He then ...
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Momentum Space Propagator from Path Integral Formulation of “Polyakov-style” action for a massive relativistic point particle
I have the derived the following expression for the propagator of a “Polyakov-style” action for a massive relativistic point particle:
\begin{equation*}
G(X_2 - X_1) = \mathcal{N}'\int_{0}^{\infty}...
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The string spectrum with several compactified dimensions
In his String Theory Vol. I book, Polchinski wants to compute the string spectrum when $k$ of the 26 dimensions are compactified $$X^m \sim X^m + 2 \pi R, \quad 26 - k \leq m \leq 25 \, . \tag{8.4.1}$...
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Can we compute tree-level amplitudes in string theory using the fundamental domain of $SL(2; \mathbb{C})$?
I am not a specialist in string theory. I understand the computation of tree-level string amplitudes (Veneziano or Virasoro-Shapiro), where three variables are fixed using the symmetry $SL(2;\mathbb{C}...
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What is the mass dimension of scattering amplitudes in string and membrane theories?
It's all in the title: I am interested in the mass dimension (in natural units) of scattering amplitudes in string and membrane theories. For particles in $d=4$, it seems to be
$$[ \mathcal{A}^{(n)} ] ...
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Hagedorn Temperature of Type I Superstring
In many sources, the Hagedorn temperature of different string theories is given using the high temperature (or high-level limit) $N\gg1$ in the calculation of the string entropy such that:
$$T_H=\left(...
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OPE of Energy-Momentum Tensor in Polchinski
I am learning Polchinski's textbook on string theory. In section 2.6 I get confused when Polchinski introduce two natural choices of complex coordinates of closed strings
$$w=\sigma^1+i\sigma^2,\tag{2....
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How can strings be more fundamental than quantum fields?
I had the feeling that physics has moved on from the idea that spacially bounded objects located in spacetime (such as particles) can be fundamental. Instead, QFT describes everything by quantum ...
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Are branes topological defects? How else could they be physical?
As far as I understand, the branes of brane cosmology are lower-dimensional "sub-manifolds" of some space. It was hard to imagine for me how such structure could exist and be physical. But ...
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Do matrix models capture the string landscape?
Essentially what the title asks-- are matrix models, such as BFSS, believed to capture in any way the large possible space of false string vacua, for instance as saddles in the action with nonminimal ...
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Lorentz transformation relations (in AdS space) between coordinates of observers derived from the generators of symmetries in the AdS space
I have a question related to the Anti de Sitter Space in General Relativity. Please help me understand it:
In Anti de Sitter (AdS) spacetime, the symmetry generator operators are associated with ...
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Could the universe be a topological defect in a higher space?
I am a mathematician with an undergrad understanding of physics. I recently learned of topological defects in quantum fields. It is an intriguing idea that there could be regions in our universe that, ...
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What does the WZ term in a WZW action means for string theory on group manifolds?
Let $G$ be a semi-simple Lie group. By Cartan's criterion its Killing form $B(X,Y)$ on $\frak g$ is non-degenerate. We can use it to define an inner product on the whole group by left translation
$${\...
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Knowledge pre-requisite on mathematics and physics in order to study string theory [closed]
I would like to study string-theory on my own and would like to know the knowledge pre-requisite on mathematics and physics I should master before embarking on my journey to study string theory.
...