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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32 views

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
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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
84 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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101 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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43 views

Is it possible to have an unbroken SUSY and the superpartners are hiding because they travel sometimes to extra dimensions? [closed]

Is it possible to have an unbroken SUSY and the superpartners are hiding because they travel sometimes to extra dimensions? It is hard to lose SUSY so maybe SUSY Particles are just hiding in ...
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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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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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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 ...
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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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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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56 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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Coordinates vs. parametrization of a worldsheet

In introductory string theory, the worldsheet is described (e.g. Tong, Polchinski) as a surface $X^\mu(\tau,\sigma)$ in Minkowski spacetime indexed by two parameters: $(\tau,\sigma)$. Now, I initially ...
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Existence of Weyl invariant regulator for bosonic string theory

In sec $(3.4)$ Polchinksi says It is easy to preserve the diff- and Poincare invariances in the quantum theory. For example, one may define the gauge fixed path integral using a Pauli-Villars ...
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Reason for $r (t)$ as a functional in path integral derivation of state-operator isomorphism in Polchinski

While deriving state-operator isomorphism using path integral Polchinksi introduce us to eq $(2.8.18)$ $$\int_{}\mathcal{D\phi'_b}\mathcal{D}\phi_i \exp(-S[\phi_i])\color{red}{r^{-L_0-\tilde{L_o}}}\...
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Existence of ground states in $bc$ CFT

I am reading Polchinski's Vol. 1 on String Theory, and I have some basic doubts on how he introduces the $bc$ conformal field theory (see section 2.7, page 61). He basically starts from the ...
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General and geometric prescription of Picture-changing operator (PCO), Polchinski Vol.2, section 12.5

In section 12.5, Polchinski tried to give a general description of PCO from a super-riemann surface view. He gave the generalized amplitude, The measure on supermoduli space The expression $(5.4.19)$ ...
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How does string theory explain gravity? [duplicate]

I read once that string theory explains gravitation via invoking quanta of the electromagnetic field to transmit the force of gravity over large distances. Is this the truth? I read somewhere else ...
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1answer
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Do we have an upper bound to the size of the six hypothetical curled up dimensions in string theory?

String theory requires ten (or eleven for M-theory) extra dimensions. These dimensions are not observed at large scales and so it has been hypothesised that they are curled up and invisible at larger ...
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How Randall-Sundrum model has solved the hierarchy problem?

I'm trying to understand how the RS model solved the hierarchy problem from this mass relation $$ M^2_p = \frac{M^3}{k} \Large[1- e^{-2k\pi r} \Large],$$ Equ. 16 in their paper: https://arxiv.org/abs/...
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The hierarchy problem

I recently read a couple of scenarios to solve the hierarchy problem: the huge ratio between the electroweak scale $M_W$ of order $100-1000 $ GeV and the Planck scale $\sim 10^{19}$ GeV I think I ...
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1answer
124 views

How do I decompose an $SO(10)$ antisymmetric tensor in $SO(4) \times SU(3) \times U(1)$?

My guess is that If I denote the $SO(4)$ indices $\mu, \nu = 1,...4$ and the $SU(3)$ indices by $I,J=1,2,3$, I think $N^{mn}$ should decompose as $N^{\mu \nu}, N^{IJ}, N^{I}_J, N_{IJ}$ plus other ...
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Computation of 2pt function of free boson [closed]

It is well known that the 2pt function of 2D free massless boson is given by \begin{equation} \label{s} \langle \phi(z,\bar{z})\phi(y,\bar{y})\rangle=-\frac{1}{4\pi g} \ln |z-y|^2\tag1 \end{equation} ...
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2answers
119 views

Why is string theory considered the best candidate for quantum gravity if it cannot resolve singularities? [closed]

The reason we want a theory of quantum gravity is to be able to understand singularities like the big bang and black holes. However the best candidate so far for such a theory, string theory, does not ...
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1answer
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Deriving an action from a metric

I try to find out how in this paper https://arxiv.org/abs/hep-ph/9905221 the authors derived an effective action from the metric. The paper I study is related to string theory and modified gravity ...
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56 views

Are orbifolded 10d E8 GUTs valid low-energy EQFTs of string theory? Or swampland?

AdAMP recently proposed a string-reminiscent E8 GUT (digest, full) where 6 extra dimensions are compactified on a $\mathbb T^6/(\mathbb Z_3\times\mathbb Z_3)$ orbifold to yield the 4d Standard Model. ...
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82 views

Action in AdS/CFT correspondence

I am a beginner trying to study AdS/CFT correspondence. Could someone please explain, can we connect action in the gravity side to the field theory side by this correspondence? Can we write the ...
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1answer
66 views

Zero modes in bosonic string theory

I recently began studying string interactions, my main references have been David Tong and Kevin Wray lecture notes. While going trough chapter 6 of the former one, I came across with the zero modes ...
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1answer
188 views

String Theory, understading Einstein-Field Equations

Let me give some insight. I was researching about how Einstein-Field Equations arise from String Theory, and I came upon this post. It explains, mathematically, how you can arrive at the corrected ...
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Global and gauge symmetries in AdS/CFT correspondence

Based on the AdS/CFT dictionary, global symmetries of the boundary theory are related to the gauge symmetries in the bulk theory, but I could not find a relation between gauge symmetries of the ...
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The M2 brane of M theory creates the Type IIA string and D2; the M5 brane creates the D4 and NS5. What are the other objects grouped with the D0?

Type IIA string theory is related to M theory with the 10th spatial dimension compactified on a circle.  The origin of the F1 string, D2 brane, D4 brane and NS5 branes is simple: they come from the M2 ...
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Boundary in AdS / CFT correspondence

In AdS / CFT correspondence, the boundary with 2D conformal field theory refers to the observer who is at the center of the 3D AdS space. What will happen when the coordinates of the observer change? ...
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Question about canonical quantization of the open string ghost system

In section 3.1.3 of Green, Schwarz and Witten book on superstrings, it is stated that the canonical anti commutation relations for the fermionic ghosts are $$ \{ b_{++}(\sigma, \tau), c^+(\sigma', \...
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76 views

Conformal blocks in AdS/CFT

In a CFT one can expand correlation functions in conformal blocks, for example the four-point function can be written (schematically) as: $$\langle \mathcal{O}_1 (x_1) \mathcal{O}_2 (x_2) \mathcal{O}...
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Kalb-Ramond vs electromagnetic field

As I understand it string theory says that charged particles like electrons and quarks are actually open strings whose endpoints interact with the electromagnetic field $A_\mu$. String theory also ...
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1answer
63 views

Spin structures and boundary conditions for worldsheet fermions

The definition I'm aware of a spin structure is the following one: Definition: Let $(M,g)$ be a semi-Riemannian manifold with signature $(p,q)$. Let ${\cal F}M$ be the principal ${\rm SO}(p,q)$-...
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Why do we consider the Witt algebra to be the symmetry algebra of a classical conformal field theory?

In standard physics textbooks, it is usually stated that the Witt algebra is the symmetry algebra of classical conformal field theories in two dimensions. Following M. Schottenloher, A Mathematical ...
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431 views

Why do string theorists seem to ignore cosmology?

Related and sort of a follow-up question to: If string theory is inconsistent with observations, why hasn't it been rejected yet? From the answer to that question, string theorists are aware the ...
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260 views

Realistic String Theories without Supersymmetry

In a podcast with Cumrun Vafa (https://www.youtube.com/watch?v=yppqz12ngbM&t=654s with the relevant part from 35:30 to 35:50), Vafa mentioned that there exists string theories that can describe ...
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Are "Selective Extra Dimensions" possible?

The large extra dimensions model also known as the ADD model proposes that the six hidden dimensions implied by string theory are not rolled up to the Planck length and some (or all) of them are ...
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Vertex operator change from conformal normal ordering to operator normal ordering

Boundary Conformal Field Theory and the Worldsheet Approach to D-Branes by Andreas Recknagel and Volker Schomerus. The "tachyon vertex operators" defined by $$\phi_{k,k}(z,\bar z) = :e^{ikX(...
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Why are there only two 496-dim. gauge groups $E_8\times E_8$ and $SO(32)$ allowed in string theory? Why not $E_8\times U(1)^{248}$ or $U(1)^{496}$?

While constructing anomaly-free string theories with $\mathcal N=1$ supersymmetry (16 supercharges constituting a Majorana-Weyl spinor), we learn that the gauge group must be 496-dimensional in order ...
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1answer
93 views

Partition function in SYK Model

In SYK model, we have the partition function for $N$-interacting fermions as \begin{equation} z=\int d^{N} \psi \exp \left(\imath^{q / 2} \sum J_{a_{1} a_{2} \ldots a_{q}} \psi_{a_{1} a_{2} \ldots a_{...
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How does one show that the free compact boson CFT is rational when the radius squared is a rational number?

In Rational Conformal Field Theories and Complex Multiplication by Gukov and Vafa, they briefly mention that the conformal field theory (CFT) describing a free bosonic field on a circle of radius $R$ ...
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Show that $\chi=\frac{1}{4\pi}\int _M d^2 \sigma g^{1/2} R +\frac{1}{2\pi}\int_{\partial M}ds k$ is locally a total derivative in 2D [closed]

In Polchinski Page 83 mentioned that $$\chi=\frac{1}{4\pi}\int _M d^2 \sigma g^{1/2} R +\frac{1}{2\pi}\int_{\partial M}ds k$$ is locally a total derivative in two dimension $R$ was the Ricci scalar ...
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56 views

Boundary conditions for the $bc$ system

In this question, I will be referring to chapter 2 of Polchinski String Theory vol. 1. In equation (2.7.29), he states that the boundary conditions for the $bc$ system of the open string are \begin{...
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316 views

How is spacetime curvature generated in string field theory?

In String Theory, the graviton originates from a mode of vibration of the fundamental strings and spacetime curvature itself is somehow generated by the strings themselves. In String Field Theory, ...
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1answer
125 views

Structure of Planck volumes in String theory

This question (as the previous one) is mostly arose from such pictures: As explained by Brian Greene, this is something what our Universe should look like at a Planck scales in superstring theories. ...
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169 views

Quiver Mechanics

What do you suggest as an essential and introductory set of references in Physics literature for learning quivers? Any textbook?

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