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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16 views

Finding the energy-momentum tensor after fixing the gauge in the Polyakov action

Suppose we have the Polyakov action given for a closed string, with the background metric being the Minkowski metric, as $$ S = - \frac{1}{ 4 \pi \alpha } \int d ^2 \sigma \sqrt{-h} h ^{ab} \partial ...
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How do I self-study String Theory? [duplicate]

I am an absolute beginner, with little to no knowledge on the subject but I have somehow developed a strong interest in theories like String theory and M-theory, by reading about them on other forums. ...
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Can a free String Field Theory be described in terms of a “wavefunctional” of classical string field configurations?

A free scalar QFT can be understood as a wavefunctional that maps classical field configurations to complex numbers representing amplitudes.  An eigenstate of this basis is a classical field ...
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What is a NS-2 brane?

This is a question about topological string theory. The existence of a new brane called "an NS-2 brane" is predicted in (the second paragraph in the page 14 of) the paper N=2 strings and the ...
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Why does the perturbative ($\mathcal{N}$=8, d=4) supergravity and type IIB closed string compactified on $T^{6}$ spectrums coincide?

The observation is that the perturbative spectrum of $\mathcal{N}$=8 supergravity in four dimensions is exactly the same as the type IIB closed superstring spectrum after dimensional reduction on $T^{...
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Is there only one “master” field in string theory?

Others have asked how many quantum fields there are according to the Standard model (How many quantum fields are there?). In a comment on that post, it was claimed that in string theory there is only ...
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Free theory in AdS/CFT

In $AdS_5$/$CFT_4$, scalar fields of mass $m$ are mapped to conformal operators of dimension $\Delta$ via the dictionary: $$\frac{m^2}{L^2} = \Delta(\Delta - 4)\tag{$*$}$$ From the string theory ...
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1answer
27 views

Confusion about the mass operator in the RNS superstring

In the RNS formulation of superstring theory we have the action: $$S=-\frac{T}{2}\int d^2\sigma(\partial_\alpha X^\mu \partial^\alpha X_\mu + \bar{\psi}^\mu \rho^\alpha \partial_\alpha \psi_\mu)$$ ...
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Absence of topological phases in quantum gravity and the BFSS matrix model of $M$-theory

McNamara and Vafa have recently conjectured in their paper Cobordism Classes and the Swampland that any vacua in string theory can be reached from any other one (possibly by a process that require an ...
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51 views

Do dark matter and dark energy have different physical laws from ordinary matter and energy? [closed]

What are dark matter and dark energy? Do dark matter and dark energy have different physical laws from ordinary matter and energy? Can string theory explain their mechanisms?
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How does the philosophy of 'Emergent Gravity' differ from that of 'Quantum Gravity'?

How are the two approaches of understanding gravity, the so-called 'Emergent/entropic gravity' and 'Quantum gravity' (String theory, LQG etc) differ from each other? I am very curious and will ...
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Boundary terms for stringy correction to GR

We know that there can be possible higher derivative corrections (stringy corrections) to the Einstein-Hilbert action. In GR, to ensure that we get the Einstein Field equations from varying the E-H ...
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Worldsheet symmetry vs Lorentz symmetry

In string theory, consider the following variation of the worldsheet coordinate $$\delta z = \epsilon(z)$$ This induces the following variation in the target space coordinates $$\delta X^{\mu} = \...
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Alternatives to Calabi-Yau spaces? [duplicate]

Are there alternatives to Calabi-Yau spaces describing dimensions in superstring theory? If yes, what are they? If no, why?
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D-brane analogue in ordinary QFT

I am reading David Tong's lectures on string theory and on the page 180 in chapter 7 of his lecture notes http://www.damtp.cam.ac.uk/user/tong/string.html : he claims that D-branes are something in ...
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65 views

How do branes come into existence according to string theory? [closed]

How do branes come into existence according to string theory? Also what are branes made out of?
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Show $Z_\text{orb}(\sqrt{\alpha'}) = Z_\text{tor}(2\sqrt{\alpha '})$ for string compactification

In Polchinski Eq 8.5.21, it states $Z_\text{orb}(\sqrt{\alpha'}) = Z_\text{tor}(2\sqrt{\alpha '})$, which can be verified by theta function identities. I try to show that. Here Is what I tried. I ...
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Equivalence of the Dirac representation of the Lorentz algebra and its conjugate in even dimensions - Polchinski

In Polchinski's String Theory, Appendix B.1 we look at the smallest irreps of the Clifford algebra in even-dimensional spacetimes $d=2k+2$. In (B.1.16) he defines two operators from the gamma matrices ...
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In string theory path integral, what happens if I fix worldsheet metric?

In string theory worldsheet path integral, integral is done over all possible topologies, metric and coordinates. And I was wondering if there is something in string theory similar to quantum field ...
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Why is the Nambu-Goto path-integral ill-defined?

I have found a lot of places saying that the Nambu-Goto action is ill-defined, that the squareroot exponential is a complicated thing to make sense of in a path-integral and so on. Then people go on ...
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How far can one continue to use the Polyakov formalism in string theory?

Polyakov action is often used to introduce string theory. But many introductory texts do not make clear when one should stop using the Polyakov formalism. It seems reasonable to think that the ...
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1answer
66 views

Difference between TCFTs and 2D TQFTs

I have been reading a lot lately on Topological String Theory and general TQFTs and as I noticed, in most contexts the terms "2-dimensional TQFT" and "Topological Conformal Field Theory" (TCFT) seem ...
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A theory for calculating mass and charge of electron

I wonder if we have such a fundamental theory in which we could calculate mass and charge of electron? And if string theory could do this then why it is said we have no practical experiment for ...
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CFT has no massive particles. How does string theory then work?

This is rather an elementary conceptual question to check whether I am getting things right. String theory essentially builds a conformal field theory. And in a conformal field theory, there cannot be ...
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Higher-order Weyl dependence of geodesic distance [duplicate]

This is a screenshot from Polchinski String Theory Vol 1. Can anyone please explain how to derive these identities ?
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120 views

What is the obstacle to writing down a String Theory that describes our universe?

It seems like, at this point, string theory is a reasonably well-developed mathematical framework. Tools from string theory are being used to understand things in QCD and condensed matter with no ...
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38 views

Virasoro modes commutation calculation

Given the commutation relations: $$ [\alpha_m,\alpha_n]=m\delta_{m+n,0} $$ and $$ L_m=\frac{1}{2}\sum_\rho\alpha_{m+\rho}\alpha_{-\rho} $$ I am trying to calculate the commutator between $L_m$ and $...
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Are there versions of String Theory formulated in $D$ spacetime dimensions or even in infinitely many dimensions?

There are a lot of different versions of string theory, and almost all of them differ in the number of dimensions. The most famous ones are formulated in 10, 11 or 26 dimensions. But are there any ...
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Understanding the gauge condition in light-cone gauge

When going over Cambridge String Theory Notes (page 38) I came across the following gauge conditions: $$X^+ (t, \sigma) = x^+(t)\hspace{5mm}, \hspace{5mm} P_−(t, \sigma) = p_−(t) \tag{1} $$ which is ...
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Gauge invariance of Faddeev-Popov determinant in bosonic string theory

I am, once again, going through an introduction to (bosonic) string theory, following the lecture notes by David Tong on the subject, and once again I am stumbling on technicalities around the ...
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1answer
59 views

Does $\partial^\mu X^\nu = \partial_\mu X_\nu$ (Neumann Boundary Conditions)?

Problem I am trying to prove that the Neumann boundary condition , $\partial_\sigma X_\mu=0$ , implies that no momentum flows out of the end of an open string. I'm told that the associated conserved ...
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47 views

(Almost homework question) Three gauge-boson amplitude in open string theory

I'm working through Polchinski's little book, in which he describes how to get string amplitudes in a somewhat heuristic manner, without the machinery introduced in the big book. These lectures are ...
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Why is the worldvolume theory a $U(1)$ gauge theory?

So in string theory a Dp-brane can be described by a $(p+1)$ dimensional QFT living in its worldvolume. For a string, this is similar to the description of the string as a twodimensional QFT living ...
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Why does a square root term make the quantisation of action difficult?

When going over my lecturer's notes on String Theory and trying to understand a particle as a theory of gravity in 1D, it is mentioned that the action $(1)$ is regularisation invariant, $$S=-m\...
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The value of Gravitational Chern Simons theory integration on some three manifolds

Consider the 3d gravitational Chern Simons theory $$S= \frac{k}{192 \pi} \int_{M_3} \mathrm{Tr}\left(\omega\; \mathrm{d} \omega + \frac{2}{3}\omega^3\right)$$ where $\omega$ is the spin-connection on ...
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What is NS5 brane?

NS5 brane can be considered as 1/2 BPS solution in supergravity (with other solutions to compare): This branes of Type IIA/B supergravity are expected to extend to solutions of the full Type IIA/B ...
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62 views

Why do we not try to describe $4$d quantum gravity with a $3$d CFT?

In AdS/CFT correspondence, one mostly studies the case with AdS$_5 \times$ S$_5$ on the string side and $4$d $\mathcal{N}=4$ Super Yang-Mills on the gauge field theory side. Real-world observations ...
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62 views

SUGRA & consistent field theories

Why must a consistent theory with a rarita schwinger field (i.e. massless gravitino in the spectrum) be supersymmetric? I was reviewing the GSO projection, Spin Structure, etc. & wasn’t able to ...
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String in arbitrary dilaton background

I have only seen literature string theory with linear dilaton i.e. $\Phi(X) = V.X $. What if I consider something like $\Phi(X) = X^2$ ?
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95 views

Lorentz rotations Noether current

I want to derive the conserved charge for Lorentz rotations in the target space of the following action. $$ \mathscr{S}_p=-\frac{T}{2}\int{d^2\sigma\;\eta^{\alpha\beta}\partial_\alpha X^\mu\partial_\...
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75 views

Four dimensional massless spectra of type IIA/B compactified on $\mathcal{M}_{4} \times {\rm CY}_3$

I am following “String Theory and M-Theory” by Becker, Becker, and Schwarz and I am currently studying chapter 9. I have a question - or better yet a point of confusion - regarding the derivation of ...
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46 views

Sign of effective action of bosonic string?

I've been looking at David Tong's Lectures on String Theory. He states that the low-energy effective action of the bosonic string is given by $$S=\frac{1}{2k_0^2}\int d^{26}X\sqrt{-G}e^{-2\Phi}\Big(\...
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49 views

Physical significance of the string anti-symmetric tensor field?

I've been looking at David Tong's Lectures on String Theory. Is the anti-symmetric tensor field $B_{\mu\nu}$ (Eqn. 2.29) of string theory related to the electromagnetic field? Also I've seen $B_{\mu\...
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52 views

Metric on a punctured riemann surface

In string theory, it is often said that the scattering amplitudes of $n$-particles are related to Riemann surface with $n$-punctures. How literal is this statement? And what does a metric on a Riemann ...
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de Sitter vacua in String Theory

I don't quite understand what goes wrong with the de Sitter vacua in string theory. Firstly, how are the vacua calculated (I'm given to understand there is no standard method, so what are the efforts ...
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1answer
75 views

Equation of motion of Nambu-Goto action with respect to $X^\mu$

I'm trying to derive the following equation of motion: $$ \partial_\alpha(\sqrt{-h}h^{\alpha\beta}\partial_\beta X^\mu)=0 $$ from the Nambu-Goto action: $$ \mathcal{S}_{NG}=-\frac{1}{2\alpha}\...
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53 views

Vertex operators in string theory

It is well known that operators in string theory are inserted at the origin. So, for example, the vertex operator for tachyon looks like $$:e^{ik.X(0, 0)}:$$ However, while computing the string ...
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Picture Number Operator in String Theory

My question concerns the ghost picture charge/picture number operator in the RNS formalism of Superstring theory. In particular I refer to page 403 of "Basic Concepts of String Theory" by R. ...
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What is the difference between type IIA and type 0A string theory?

When people study string theory the most useful models are IIA and IIB. I'm not quite sure I understand what is the difference between 0A and IIA string theory. In the type 0 case we only have bosons ...
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Bosonic string spectrum

How can we derive in a systematic way the spectrum of a given string theory? For example if we assume a bosonic string theory how can we derive the types of fields that our states are representations ...

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