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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46 views

What are linking diagrams in string theory like $SO(6)$?

https://youtu.be/5rB1YKjEwco (51:33) A toy model is presented but I want to know the name of this toy model as well as $\phi^4$ in QFT what is that called? What is it doing with the $SO(6)$ group?
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Question about Kaluza-Klein excitations

In Randall Sundrum (RS) model-type 1 : A Large Mass Hierarchy from a Small Extra Dimension, it’s mentioned that: This result contrasts sharply with the scenario of large extra dimensions for solving ...
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Gauge invariance / charge conservation on string ending on brane

Consider a fundamental string charged under the Kalb-Ramond 2-form $B$ and ending on a D5-brane. Charge conservation implies the existence of a 1-form gauge field $A$ with field strength $F$ living on ...
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Should I capitalize the term 'superstring revolution'? [closed]

I'm writing an essay in physics and will include the word 'superstring revolution'. There have been two superstring revolutions before. In my understanding, such revolutions changed people's views ...
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Mathematical prerequisites for M-theory [duplicate]

I am interested in learning M-theory; however I have no Idea as to what mathematics is required for it. Are the prerequisites the same as string theory? Is there more mathematical knowledge needed for ...
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String length $\gg$ Planck length?

The potential energy of a string $E_{pot}$ is given by $$E_{pot}=T \times L\tag{1}$$ where $T$ is the string tension and $L$ is the length of the string. The internal kinetic energy $E_{kin}$ of a ...
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1answer
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Neumann vs Dirichlet boundary conditions for vector fields

From hep-th/9611230, A vector field $A_\mu$ in $3 + 1$ dimensions may obey either Dirichlet boundary conditions, in which the components of $F_{\mu\nu}$ with $\mu$ and $\nu$ tangent to the boundary ...
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Moduli space for Riemann surfaces with boundaries and open string loop diagrams

I'm searching for information on the moduli space for Riemann surfaces with boundaries, like the ones used to compute open string loop diagrams. I found a huge lot of info for the case without ...
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Amount of SUSY preseved by branes

Consider 10d superstring theory, a D5 brane extended in the 012789 directions, and an NS5 brane extended in the 012345 directions. I have read that this configuration preserves 1/4 of the ...
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What does cohomology of $Q_B$ mean in BRST quantization in Polchinski?

While proving no-ghost theorem ($4.4$ Polchinski) the term cohomology of $Q_B$ is used quite a lot of time. From what I understand this has to be a set since "cohomology of $Q_B$" is ...
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Confusion about Generating Functionals in AdS/CFT

I have a question regarding an equation in the book "Gauge/Gravity Duality" by Martin Ammon and Johanna Erdmenger which however can also be found in other AdS/CFT books or lecture notes. The ...
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In what sense does a pure spinor represent the orientation of a unique spacelike codimension-2 plane?

References 1 and 2 define a pure spinor $\psi$ to be a solution of the Cartan-Penrose equation $$ \newcommand{\opsi}{{\overline\psi}} v^\mu\gamma_\mu\psi=0 \hspace{1cm} \text{with} \hspace{1cm} v^\mu\...
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Why is high energy required if we want to send a message in a short amount of time?

I am somewhat puzzled by the following statement "If Alice, after crossing the horizon, has less than a Planck time to communicate with Bob about the status of her qubits, then she is required to ...
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1answer
76 views

Dimensional Reduction and Supersymmetry

I am working my way through "Basic Concepts of String Theory", by Blumenhagen, Lüst and Theisen. Currently I am working on the compactifications of string theories on Calabi-Yau manifolds. ...
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Idea/Intuition behind using commutator of light cone number operator and BRST generator

In ch-$4$ of Polchinksi while proving no-ghost theorem we are introduced to number operator of light cone oscillators $$N^{lc}=\sum_m{\frac{1}{m}:\alpha^+_{-m}\alpha^-_m:}\tag{4.4.6}$$ $$\alpha^{\pm}...
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How does commutator of $Q_B$ with change in $H$ results in moving around in gauge space

In ch-$4$ Polchinksi states following: In order to move around in space of gauge choices, the BRST charge must remain conserved. Thus it must commute with change in the Hamiltonian. Commutation with ...
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Counting sign definiteness in BRST cohomology of string

In Polchinksi ch-$4$ following manipulation is done: $$|\psi_1\rangle=(e\cdot\alpha_{-1}+\beta b_{-1}+\gamma c_{-1})|0,\textbf{k}\rangle .\tag{4.3.25}$$ $$\langle\psi_1|\psi_1\rangle=\Big(e^*\cdot e+(\...
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1answer
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What is "bulk" in brane cosmology?

The central idea of brane cosmology is that the visible, three-dimensional universe is restricted to a brane inside a higher-dimensional space, called the "bulk". What is "bulk"? ...
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Why not one fundamental quantum field instead of several?

Why in the physics of elementary particles is not considered the option of the existence of not several separate, but only one single fundamental quantum field? Like string theory. One fundamental ...
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Why open strings must all end on same D brane?

Consider 10-d open string theory with a D9 brane (i.e. an open string), and $X^9$ compactified on a circle. T-dualising, we find a D8 brane. Why is it that the endpoints of all open strings in this ...
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Residual symmetry of Polyakov action in general backgrounds

In Becker & Becker, Schwarz book String Theory and M-Theory, page $40$ is stated that after choose the conformal gauge $h_{ab} = \eta_{ab}$ in the Polyakov action with background field $G_{\mu \nu}...
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184 views

Dilaton field causes universe expansion?

In string theory low-energy $n$-dimensional gravity is described by an action of the following form: $$S^{(n)}=\frac{1}{2\kappa^{(n)}}\int d^nx\sqrt{-G}e^{-2\Phi}\Big(\mathcal{R}+4\partial_\mu\Phi\...
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About the use of static gauge in string theory

In the paragraph before equation (2.1.44) of GSW 1st Volume, 25th anniversary edition, it's said that after fix the choice of conformal gauge $h_{\alpha \beta} = \eta_{\alpha \beta}$, there still a ...
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1answer
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BRST variation of $\delta_{\alpha}F^A$ in $S_3$ in BRST section of Polchinski

The Faddeev-Popov action reads $$S_3=b_Ac^{\alpha}\delta_{\alpha}F^A(\phi).\tag{4.2.5}$$ I want to find the BRST variation of the gauge variation of $F^A$ in $S_3$ i.e. $$b_Ac^{\alpha}\color{red}{\...
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Do Universal Spacetimes have Non-perturbative quantum corrections?

Universal spacetimes have the interesting property that their quantum corrections vanish to all loop orders, and can be viewed as classical solutions to speculative theories of quantum gravity like ...
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Can the spatial structure of a string theory string be observed?

I understand that, today, the length of a string is too small to be observable. But if technology were not a problem, would we be able to observe the shape of the string, the motion of its ends, its ...
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1answer
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The volume of infinitly large extra dimension

What I understand is that, according to the string theory our universe is a membrane parallel to several other membranes or (universes). These parallel universes are separated by the bulk or extra ...
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Branes with any number $n$ of dimensions and their relation to the laws of physics?

I had a few questions about this paper by Nima Arkani-Hamed, Georgi Dvali and Savas Dimopoulos (https://arxiv.org/abs/hep-th/9907209) which is closely related to the concept of branes (https://en....
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Constraints on non-compactified extra dimensions

I'm reading this paper An introduction to extra dimensions and string phenomenology Which according to it, in string theory the 4-dimensional Plank scale is related to the Planck scale of ...
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Solving the hierarchy problem by large extra dimensions

I'm asking about the model of Arkani-Hamed-Dimopoulos-Dvali ( ADD ) to solve the hierarchy problem. https://arxiv.org/abs/hep-ph/9803315 According to this model, the 4- dimensional Planck scale $M_{pl}...
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1answer
81 views

Sign Wrong in Effective Action of Bosonic String?

In David Tong's Lectures in String Theory Chapter 7 he sketches a derivation of the low-energy effective action of the bosonic string $(7.16)$: $$S=\frac{1}{2k_0^2}\int d^{26}X\sqrt{-G}e^{-2\Phi}\Big(\...
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How do I understand this conformal transformation?

I am learning conformal transformation, and this is by far the most confusing transformation for me. For the 2D bc system $$S=\frac{1}{2\pi}\int d^2 z b\overline{\partial}c,$$ we have the ghost ...
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How many different vacua really are there in the string theory landscape?

How many different vacua are there in the string theory landscape? Different sources give different estimates: some sources talk about the number $10^{500}$, others $10^{272\ 000}$, still others say ...
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Why integrand of $V_1$ is constructed as a scalar $(3.6.14)$ for $\mu,\nu$ indicies in Polchinski

When doing Polyakov treatment of vertex operator of first excited state using diff-invariance symmetry Polchinski comes with following: $$V_1=\frac{g_c}{\alpha'}\int d^2\sigma \hspace{2pt}g^{1/2}\bigg\...
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The Hubble parameter of Randall-Sundrum model

It’s mentioned in this paper On the cosmological constant problem and brane-world geometry that the Hubble parameter of the Randall-Sundram model is given by: $$ H^2 = \frac{8\pi}{3m_{pl}^2} \rho + \...
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1answer
71 views

What does Polchinki mean when he says identifying under involution?

I am reading chapter 7 of Polchinki's String Theory vol. 1 textbook and I am trying to understand why one obtains the cylinder (annulus) from the torus by identifying points under involution. To be ...
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Open-closed amplitude in bosonic string theory

I want to know the scattering amplitude involving both open and closed string, more specifically, the amplitude between two gluons and one graviton in open closed set up. Is there a reference where ...
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To what degree have Calabi-Yau manifolds been shown to be all linked by conifold transitions?

Originally, the number of Calabi-Yau manifolds (these are special vacuum solutions of Einsteins GR) was estimated by Yau to be a small finite number, later he revised it to be a large finite number - ...
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How to read of the conformal dimension of $bc$ CFT to be $(2,-1)$ from the action $S_g$?

Quote Polchinski String Theory volume 1 page 89. $$S_f=\frac{1}{2\pi} \int d^2 z(b_{zz}\partial_{\bar z} c^z+b_{\bar z \bar z }\partial_zc^{\bar z})$$ Since the action... is weyl invariant, $b_{ab},c^...
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Why are vertex operators integrated over the worldsheet?

In chapter $3$ of Polchinski after discussing why vertex operators are used for preparing states in S-matrix. We are given the vertex operator for closed string tachyon is $$V_0=2g_c\int d^2\sigma\...
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2answers
73 views

Problems to understand closed string BCs in Polyakov action

I apologize if this is an odd question. In the derivation of equations of motion in the Polyakov action $$S_P = -\frac{T}{2}\int d^2\sigma \sqrt{-h} h^{ab}\partial_a X^\mu\partial_bX^\nu \eta_{\mu \nu}...
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1answer
94 views

Area element with worldsheet metric in Polyakov action

I became confused while reading this article for the following reason: For $p=1$ we have strings such that the Nambu-Goto action is proportional to the area of the worldsheet embedded by the maps $X^\...
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Number of unbroken supersymmetries in compactifications

In type II compactifications, we take a 10/11-d spinor $\epsilon$ to decompose into internal $\eta$ and external $\zeta$ pieces, $$\epsilon^1=\zeta^1\otimes\eta^1\ \ (+c.c.)$$ $$\epsilon^2=\zeta^2\...
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1answer
127 views

Polchinski's first derivation of the Weyl anomaly

So, i've been reading volume 1 of Polchinski's String Theory text book and have a doubt. His first derivation of the Weyl anomaly goes as follows: From dimensional analysis, we know that: $$\begin{...
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1answer
49 views

Polchinski OPE of spacetime translation current

I am trying to derive $$ j^\mu(z):e^{ik\cdot X(0,0)}: \;\sim \frac{k^\mu}{2z}:e^{ik\cdot X(0,0)} \tag{2.3.14a} $$ from Polchinski's String Theory vol.1 equation (2.3.14a). using $j^{\mu}=\frac{i}{\...
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1answer
40 views

Functional and total variations in einbein action [duplicate]

I'm currently studying String theory by Becker& Becker, Schwarz textbook. The exercise 2.3 consists in verifying diffeomorphism invariance of einbein action wich is given by $$ S_0 = \frac{1}{2} \...
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41 views

Normal ordering constant value in String Theory and Old Covariant Quantization

Suppose you are approaching the quantization of the closed bosonic string for the first time (so we are in the so called Old Covariant Quantization (OCQ), and by now we know nothing about Lightcone ...
3
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1answer
116 views

Witt algebra, $\mathfrak{sl}(2,\mathbb{R})$, $\mathfrak{sl}(2,\mathbb{C})$ and Bosonic String Theory

Suppose you know nothing about CFT, and suppose you have found in (closed bosonic) String Theory that \begin{equation} [L_n , L_m ]=(n-m) L_{n+m} \;\;\;\;(\mathrm{"right"\;Witt\;Algebra}\; \mathfrak{w}...
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1answer
56 views

How this limiting procedure defines an operator in the state-operator map?

I'm confused about one aspect of Polchinski's discussion of the state-operator map. He starts with an operator ${\mathscr{A}}(0)$ at the origin and then defines $$\Psi[\phi_b]=\int[d\phi_i]_{\phi_b}\...
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57 views

What would physics look like if light were not constant in all reference frames? [closed]

Is there a more fundamental theory that explains why speed of light must be constant in all reference frames? This seems like such a huge premise but I've never heard why it must be true, only that it ...

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