Questions tagged [higher-spin]

A theory of interacting fields of arbitrary spin. Generalizes Yang-Mills as a theory of spin-one, gravity as a theory of spin-two to fields of any spin.

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No-go theorem evasion for higher spin (super)string theory

The inclusion of (conventional) SUSY truncates spin states in (super)string theory and M-theory. My question here is the following: could a non-standard SUSY algebra be constructed in such a way (...
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Is superstring (M-theory) an effective theory from higher spin theory?

In the proceedings of the 2003 conference to celebrate Stephen Hawking's 60th birthday Hawking writes: String theorists have long used the term, effective theory, as a pejorative description of ...
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Well-posed classical field equations for spin $s>1$ fields

Wald Section $13.2$ states that the initial value formulation of the minimally coupled Dirac equation on curved spacetime is not well posed for spin $s>1$ spinor fields. However, it does not state ...
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Initial value formulation of Dirac equation for spin $>1$ - modern resources?

At the end of Wald Section 13.2, he mentions that the natural generalization of Dirac equation to curved spacetime does not have a well-posed initial value formulation for $s>1$ , and refers to ...
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How many field components are there in vector-spinor field?

I am trying to find out the degrees of freedom of the vector-spinor field ($s=3/2$). The degrees of freedom are given by $N=\frac{1}{2}\left(N_{F}-N_{C}\right)$ for this spin where $N_F$ is the number ...
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Does Higher spinor field bend Space-time?

Consider the free massless spin-$n/2$ field in a general curved space-time ($M$, $g$): \begin{equation} \nabla^{AA'}\phi_{\underbrace{AB\cdots L}_n} =0\end{equation}If $\phi_{AB\cdots L}$ has charge $...
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Are interactions mediated by spin 3 or higher bosons allowed in mainstream QFT? [duplicate]

Electromagnetism, the strong interaction, and the weak interaction are mediated by spin 1 particles, and in Quantum Gravity spin 2. I saw in this question that the answers pointed out how ...
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The linearized solution for the Vasiliev scalar field in stereographic coordinates [arXiv:1712.02401]

I am reading [arXiv:1712.02401] and struggling to reproduce equation (5.3), using iso(3) invariance. My goal is to write a similar so(1,3) invariant solution in using (3.12a). The equation I am trying ...
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Why can't we define mathematical observables in asymptotic $dS$ or flat space for gravitational theories?

In higher spin currents, the boundary CFT is dual to an asymptotic $AdS$. I have heard that $dS$ is not quantizable. But I don't understand why we want it to be in the first place. Isn't Chern-Simons ...
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What does it mean for correlation functions to be dominated by the vacuum block for a 2D CFT?

In a 2D CFT, correlation functions dominated by the vacuum block have no conical defects. You can calculate the OPE and determine the correlation function using the D-S equations and cancel out UV ...
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Equations of motion for higher spin quantum fields

In the canonical quantization of a massive Lagrangian, we obtain equations of motion via the Euler-Lagrange formalism. As I have read, these can become rather long but decouple into the Klein-Gordon (...
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Relation between the spin of a field and the way charges interact

When solving the problems of V. Rubakov's "Classical Theory of Gauge fields" book, I encountered the following phenomenon: For a real scalar fields (spin 0) $\phi$, if we consider the ...
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Can a wave function that represents a particle of spin that is not 1/2 be a solution of the Dirac equation?

During a QFT course, we were deriving the Dirac equation using the relativistic quantum mechanics' approach. Dirac was well aware of the Klein-Gordon $$\frac{1}{c^2}\frac{\partial^2}{\partial t^2}\psi-...
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Actions for relativistic point-particles of higher spin

To describe the behavior of a relativistic point-particle, we have the standard action $$S=\int d\tau \bigg[\frac{1}{e} \dot X^\mu\dot X_\mu +m^2 e\bigg], $$ where $e$ is the worldline einbein. Then, ...
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Spin 3 vs spin 2 vs spin 1

I wanna to understand, why when one gonna to construct interacting theory of spin 3, one need also include infinite tower of spins 4, 5, 6 , ... As I know, this statement correct even in classical ...
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Combinatorics identity for arbitrary value of Spin

I wanted to prove this identity for the general value of $\lambda$ $$ \sum_{n=0}^{\lambda-1} (-1)^n{\lambda-1 \choose n} {\partial^{\left(\lambda-1-n \right)}{\partial_-}^{\left(n \right)}}\left( \...
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Appearence of higher spin algebra

I start from massles & free scalar field theory in $d$-dimenisonal space. It is clear that this theory has conformal symmetry. My question is devoted to derivation of conserved current $$J_{\mu_1\...
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Gamma traceless

I read this Under what conditions is a vector-spinor gamma trace free. And also read many papers about higher spin, but no one explains why irreducible spinor is gamma traceless spinor? Can anyone ...
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Field degrees of freedom from equations of motion and higher spin

It is my understanding that we compute the number of degrees of freedom of a quantum field as the number of its components minus the number of non trivial equations we get by taking the divergence of ...
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Why does the renormalizable theory have only those particles with helicity less than or equal to 1?

Let the helicity operator be $$\frac{P \cdot J}{P^0}$$ with an eigenvalue $\lambda$. Then why do renormalizable theories have $|\lambda| \le 1?$ (in general dimensions or in 4D?) Also, what is the ...
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Are there supersymmetry algebras with higher spinor representations?

The super-Poincare algebra contains supersymmetry generators $Q^I$ which satisfy fermionic anticommutation relations. By the higher-dimensional analogue of the spin-statistics theorem, they must ...
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Help with understanding the imposition of gauge conditions

Let $s$ be a positive integer and $h_{a_1\dots a_s}$ be a traceless and totally symmetric (real) field which is defined modulo gauge transformations of the form $$\delta_{\xi}h_{a_1\dots a_s}=\...
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Is Quantum spin greater than $1$ possible? [duplicate]

I know that fermions have a spin of half of and bosons have a spin of 1 but at many places I have seen that their is written that spin for a boson can be 0,1,2.... Is there any physical meaning of ...
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Conserved current of $O(N)$ vector model

I was reading a paper by Klebanov and Polyakov, Phys.Lett. B550 (2002) 213, (hep-th/0210114). In the paper, where they are discussing free O(N) vector models, they state that the theory has a class of ...
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Supersymmetry beyond $D=11$ spacetime dimensions

Taking into account the higher spin theories, from which string theory is an effective field theory, I just wondering if there is something to do to extend supersymmetry to any dimension without any ...
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What is the spin of stringy excitations?

In bosonic string theory, excitations of open strings obey the mass relation $$ M^2 = \frac{N-1}{\alpha'} \,$$ and this seems to imply that such a theory has an infinite tower of massive excitations ...
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What is the proper method to obtain the Equations of motion from this higher spin action?

The results I am trying to derive can be found in this paper, appendix B. In class I have only ever dealt with actions that involve a single scalar field so dealing with actions of this form is quite ...
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2 votes
1 answer
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Massive spin-$s$ representations of the Poincare group on the space of spin tensor fields

Context The following is from the book "Ideas and methods in supersymmetry and supergravity" by I.L. Buchbinder and S.M Kuzenko, pg 56-60. It is about realizing the irreducible massive ...
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Analogue of helicity in higher dimensions and concrete formula

Consider Poincare group $ISO(1,d-1)$ in some dimension $d>4$. There are two Casimirs. Let's look at massless one-particle states: the little group is $ISO(d-2)$, and if we restrict to finite ...
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Spins corresponding to anti-symmetric Ramond-Ramond gauge potentials

In string theory there are many anti-symmetric higher rank gauge potentials like $B_{\mu \nu}$ or the Ramond-Ramond potentials (e.g. $C_{\mu \nu \lambda}, C_{\mu \nu \lambda \sigma}$). Since they are ...
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2 answers
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A spin zero graviton?

Why can the graviton not be a spin 0 particle? On a similar note why can it not be a spin 4, spin 6 particle?
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1 answer
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How does higher spin theory evade Weinberg's and the Coleman-Mandula no-go theorem?

Recently I heard some seminar on higher spin gauge theory, and got some interest. I know there are some no-go theorems in quantum field theories: Weinberg: Massless higher spin amplitudes are ...
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Dirac or Schrödinger equation for higher spin?

Given a fermion or boson with an arbitrary integer or half integer spin, then what would be its Dirac or Klein-Gordon equation? Dirac equation for an equation with arbitrary spin 0, 1/2 , 1 , 2 , 3/2 ...
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1 answer
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Review of Higher Spin Theory

What is the most comprehensive and up-to-date review of Higher Spin Theory (in particular, in AdS space)?
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"No-go" theorems and goldstone bosons

There are "no-go" theorems who forbid interaction through soft helicity 3 and higher massless particles and soft interaction between massless fermions with spin more than $\frac{3}{2}$. But if ...
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Higher spins elementary particles

Lorentz invariance requirement of theory imposes the absense of interactions between spin 3 and higher spins bosons and arbitrary field (like spin $\frac{1}{2}$ fermions etc) at least in infrared ...
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2 votes
1 answer
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Generalized spin connection and dreibein in higher spin gravity

I am studying 3D higher spin gravity and I would like to know the mathematical and physical meaning of generalized spin connection and generalized dreibein that appear in this theory. It is well known ...
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1 answer
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Gauge invariance of Rarita-Schwinger action in curved spacetime

The Rarita-Schwinger action in curved $n$-dimensional spacetime is $$ \int \sqrt{g} \overline{\psi}_a \gamma^{abc} D_b \psi_c $$ Here $g = \det(g_{\mu \nu})$, and the indices $a, b \dots$ are '...
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Green Function for Proca Equation

I have tried to find a retarded and advanced Green function for Proca field equation. $(\Box - \mu^2)A^{\mu}=J^{\mu}$ where $\mu$ is the mass term. How I did it: first: I made Fourier ...
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7 votes
1 answer
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Connection beween infinite gauge symmetries and UV finiteness

In e.g., http://arxiv.org/abs/arXiv:0712.3526 the author claims: Since the massless higher-spin field theories involve infinite-dimensional gauge symmetries, one expects that such theories may be ...
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Anomalous dimensions in the $O(N)$ model

Is there any statement known about the anomalous dimensions of the $O(N)$ model in various dimensions and/or in the large-N limit? If a $\phi^4$ ("double-trace") term is coupled to an $O(N)$ model ...
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5 votes
1 answer
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Some questions about the paper, "AdS description of induced higher spin gauge theory"

I am referring to this paper. I guess that in this paper one is trying to relate the massless spin $s$ gauge fields in $AdS_4$ to conformal spin $s$ theory on $S^3$. So am I right that the ...
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4 votes
2 answers
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Star product of two commuting spinors

Ok so this might be a very stupid and trivial question but I have spent a couple of hours on this little problem. I am trying to derive a simple formula in a paper. We have a real commuting spinorial ...
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3 votes
1 answer
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Symmetric transverse traceless tensors of rank $s$ and $(s,0,0,..,0)$ representations of $SO(n)$

Can someone help see this connection as to why a spin $s$ (an Integer) particle is to be thought of as a symmetric transverse traceless tensor of rank $s$ and that they lie in the $(s,0,0,..,0)$ ...
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5 votes
1 answer
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Conserved currents in higher-spin theories

After the proposal of Maldacena (AdS/CFT), there have been numerous attempts to find out gravity duals of various kinds of CFT. Klebanov and Polyakov gave one such correspondence here. The claim is ...
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1 vote
1 answer
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About higher spin gauge theory

I'm going to listen to a talk about Vasiliev's higher spin gauge theory. Before that I want to know more about the background.This is an introduction. Could anybody give a more detailed introduction ...
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An use of the Schwinger-Dyson equation

I was confused as to how the equation 10 on page 7 or equation 21 on page 8 of this paper http://arxiv.org/abs/1211.1866 was derived. Can someone explain from where does this come and what do the "...
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2 votes
1 answer
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't Hooft limit of coupling fundamental fermions to Chern-Simons theory

This question is in reference to this paper: arXiv:1110.4386 [hep-th]. I would like to know what is the derivation or a reference to the proof of their crucial equation 2.3 (page 12). In their ...
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178 votes
2 answers
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Why do we not have spin greater than 2?

It is commonly asserted that no consistent, interacting quantum field theory can be constructed with fields that have spin greater than 2 (possibly with some allusion to renormalization). I've also ...
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24 votes
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Vasiliev Higher Spin Theory and Supersymmetry

Recently there is renewed interest in the ideas of Vasiliev, Fradkin and others on generalizing gravity theories on deSitter or Anti-deSitter spaces to include higher spin fields (utilizing known ...
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