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A Twistorial Description of the IKKT-Matrix Model
High Energy Physics - Theory · Submitted 10 Mar 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The higher-spin (HS) gauge theory emerging in this limit from the IKKT model, denoted as HS-IKKT, on fuzzy twistor space is shown to be a higher-spin extension of $\mathcal{N}=4$ SYM, with vertices that have more than two derivatives.
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The abstract, sentence by sentence
We consider the fuzzy 4-sphere $S_N^4$ as a background in the IKKT matrix model and explore the relation between $S_N^4$ and fuzzy twistor space in the semi-classical limit. A novel description for the IKKT-matrix model in terms of spinorial indices is given, which is reminiscent of $\mathcal{N}=4$ super-symmetric Yang-Mills (SYM) in $4d$. On fuzzy twistor space, the interactions of the IKKT model are of gravitational type. The higher-spin (HS) gauge theory emerging in this limit from the IKKT model, denoted as HS-IKKT, on fuzzy twistor space is shown to be a higher-spin extension of $\mathcal{N}=4$ SYM, with vertices that have more than two derivatives. We obtain its (Euclidean) spacetime action using the Penrose transform. Although this is a gravitational theory, it shares many features with the higher-spin extensions of Yang-Mills in $4d$ flat space obtained in arXiv:2105.12782, arXiv:2107.04500. The tree-level amplitudes of the HS-IKKT are studied in the semi-classical flat limit. The self-dual sector of the IKKT model is obtained by dropping some parts of the cubic- and the quartic interactions, which is shown to reduce to a BF-type action on commutative deformed projective twistor space.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider the fuzzy 4-sphere $S_N^4$ as a background in the IKKT matrix model and explore the relation between $S_N^4$ and fuzzy twistor space in the semi-classical limit. | contribution 0.77 | 0.86 | 0.08 | asserted 0.73 |
| s1 | A novel description for the IKKT-matrix model in terms of spinorial indices is given, which is reminiscent of $\mathcal{N}=4$ super-symmetric Yang-Mills (SYM) in $4d$. | contribution 0.91 | 0.93 | 0.11 | asserted 0.99 |
| s2 | On fuzzy twistor space, the interactions of the IKKT model are of gravitational type. | result 0.88 | 0.74 | 0.17 | asserted 1.00 |
| s3 | The higher-spin (HS) gauge theory emerging in this limit from the IKKT model, denoted as HS-IKKT, on fuzzy twistor space is shown to be a higher-spin extension of $\mathcal{N}=4$ SYM, with vertices that have more than two derivatives. | result 0.83 | 0.91 | 0.41 | asserted 1.00 |
| s4 | We obtain its (Euclidean) spacetime action using the Penrose transform. | method 0.59 | 0.94 | 0.08 | asserted 1.00 |
| s5 | Although this is a gravitational theory, it shares many features with the higher-spin extensions of Yang-Mills in $4d$ flat space obtained in arXiv:2105.12782, arXiv:2107.04500. | interpretation 0.85 | 0.43 | 0.12 | asserted 0.91 |
| s6 | The tree-level amplitudes of the HS-IKKT are studied in the semi-classical flat limit. | contribution 0.98 | 0.91 | 0.07 | asserted 0.96 |
| s7 | The self-dual sector of the IKKT model is obtained by dropping some parts of the cubic- and the quartic interactions, which is shown to reduce to a BF-type action on commutative deformed projective twistor space. | result 0.72 | 0.93 | 0.13 | asserted 1.00 |
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The paper
Original abstract
We consider the fuzzy 4-sphere $S_N^4$ as a background in the IKKT matrix model and explore the relation between $S_N^4$ and fuzzy twistor space in the semi-classical limit. A novel description for the IKKT-matrix model in terms of spinorial indices is given, which is reminiscent of $\mathcal{N}=4$ super-symmetric Yang-Mills (SYM) in $4d$. On fuzzy twistor space, the interactions of the IKKT model are of gravitational type. The higher-spin (HS) gauge theory emerging in this limit from the IKKT model, denoted as HS-IKKT, on fuzzy twistor space is shown to be a higher-spin extension of $\mathcal{N}=4$ SYM, with vertices that have more than two derivatives. We obtain its (Euclidean) spacetime action using the Penrose transform. Although this is a gravitational theory, it shares many features with the higher-spin extensions of Yang-Mills in $4d$ flat space obtained in arXiv:2105.12782, arXiv:2107.04500. The tree-level amplitudes of the HS-IKKT are studied in the semi-classical flat limit. The self-dual sector of the IKKT model is obtained by dropping some parts of the cubic- and the quartic interactions, which is shown to reduce to a BF-type action on commutative deformed projective twistor space.
Human review
References
How the literature uses it
18 arXiv papers cite this in 51 sentences
Papers citing it · 30 sentences without a confident label
Builds on it 2 papers
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To overcome that limitation, we generalize in the present paper the analysis in [ref] to backgrounds defined using $H_N^4$.
Spinorial higher-spin gauge theory from IKKT in Euclidean and Minkowski signatures · Introduction · 0.97
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First, we will consider Yang–Mills interactions for partially-massless fields, which are straightforward generalization of the higher spin extension of self-dual Yang–Mills theory introduced in [ref] , and recently revisited in [ref] , see also [ref] .
Chiral approach to partially-massless fields · Yang–Mills interactions · 0.94
Uses its method or tool 2 papers
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Using [ref], we obtain the spinorial form of the effective vielbein in analogous to [ref] :
Spinorial higher-spin gauge theory from IKKT in Euclidean and Minkowski signatures · The stereographic projection to H4 · 0.85
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This situation can be circumvented by using a more practical approach known as fuzzy twistor construction [ref] .
Twistor approach to higher-spin theories and matrix model · Constructing chiral HSGRA from twistor space · 0.93
Compares with it 2 papers
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In the first case, we essentially recover the same results of [ref] (up to signs) for the spinorial formulation of the IKKT-matrix model on $H^4$.
Spinorial higher-spin gauge theory from IKKT in Euclidean and Minkowski signatures · Introduction · 0.96
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Let us also point out that the way CHS gravity emerges in the Segal construction is somewhat similar to the IKKT model based on a higher spin algebra studied e.g. in [ref] .
Covariant action for conformal higher spin gravity · Conclusions and Discussion · 0.95
Cites it as support 2 papers
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Intriguingly, in the flat limit, all higher-spin fields in the self-dual sector of HS-IKKT theory are effectively massless since there is an `emergent' shift symmetry which can be used to gauge away the higher-spin modes $$ in $$ [ref] .
Spinorial higher-spin gauge theory from IKKT in Euclidean and Minkowski signatures · Reduced Euclidean action on H4 · 0.96
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It can be checked that all contributions related to the background $_5$ vanish in this limit [ref] .
Twistor approach to higher-spin theories and matrix model · HS-IKKT from fuzzy twistor space · 0.96
Cites it as background 9 papers
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Free differential algebra approach to the construction of equations of motion for chiral higher-spin gravity (HSGRA) [ref] , and the twistor construction in [ref] are important results of the covariantization program for chiral HSGRA and its contractions from their light-cone descriptions [ref] .[See also [ref] for supersymmetric version of chiral HSGRA.] In this note, we want to convey a formula for: (i) constructing the dual twistor actions of various 4-dimensional local higher-spin theories, (ii) obtaining their covariant spacetime actions from (non-commutative) twistor space [ref] .
Twistor approach to higher-spin theories and matrix model · Introduction · 0.84
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As a result, all concrete HiSGRA's available at the moment are quite peculiar: topological models $3d$ with (partially)-massless and conformal fields [ref] ; $4d$ conformal HiSGRA [ref] that is a higher spin extension of Weyl gravity; Chiral HiSGRA [ref] and its truncations [ref] .[There are also other interesting recent ideas, e.g. [ref] and [ref] .] In this paper we covariantize the interactions of Chiral HiSGRA.
Minimal models of field theories: Chiral Higher Spin Gravity · Introduction · 0.98
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Very close to them is the higher spin IKKT-model, see e.g. [ref] , which is also a noncommutative field theory.[Another direction in the context of holographic theories is to derive the bulk dual by massaging the CFT partition function, see e.g. [ref] , which, however, leads to higher derivative free equations, has a slightly different spectrum and nonlocal interactions, the strong point being in that it does reproduce the CFT correlation functions by construction.] There are also incomplete (formal) theories [ref] that can only be constructed at the formal level of $L_∞$-algebras with the associated field equations suffering from nonlocality [ref] .[It should be noted that while every classical field theory (PDE) is defined by some $L_∞$-algebra, e.g. [ref] , not every $L_∞$-algebra leads to a well-defined theory.
Strong Homotopy Algebras for Chiral Higher Spin Gravity via Stokes Theorem · Introduction and summary · 0.91
What it cites · 129 sentences without a confident label
Builds on 1 paper
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This theory is can be thought of as the higher-derivative extension version of the HS-YM in [ref] .
Twistor Constructions for Higher-spin Extensions of (Self-dual) Yang-Mills · Twistor construction for gravHS-SDYM · 0.94
Uses the method or tool of 8 papers
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We will propose how this can be achieved using the twistor construction for higher-spin fields in [ref] .
Twistor Constructions for Higher-spin Extensions of (Self-dual) Yang-Mills · Twistor construction for gravHS-SDYM · 0.99
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We will propose how this can be achieved using the twistor construction for higher-spin fields in [ref] .
Conformal Higher Spin Theory and Twistor Space Actions · Twistor construction for gravHS-SDYM · 0.99
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We will propose how this can be achieved using the twistor construction for higher-spin fields in [ref] .
Conformal higher spin scattering amplitudes from twistor space · Twistor construction for gravHS-SDYM · 0.99
Compares with 15 papers
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The action for this sector is [equation] where [equation] The above action is closely related to the action of HS-SDGRA in [ref] .
Actions for Self-dual Higher Spin Gravities · Scattering of the HS-IKKT in the flat limit · 0.99
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Then [equation] Due to symmetrization, the above includes terms of the form [equation] etc. which is in complete analogy to the field strength in non-commutative gauge theory, cf. [ref] .
On the 1-loop effective action for the IKKT model and non-commutative branes · Spinorial representation for the action of the IKKT model · 0.88
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Hence, the [ref] action reduces to [equation] which is reminiscent of self-dual $=4$ SYM in $4d$ [ref] .
The self-dual sector of QCD amplitudes · Spinorial representation for the action of the IKKT model · 0.88
Cites as support 3 papers
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Hence, the HS-IKKT is a gravitational higher-spin theory as pointed out previously in [ref] .
Higher-spin kinematics & no ghosts on quantum space-time in Yang-Mills matrix models · Spacetime actions for the (self-dual) HS-IKKT model · 0.98
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Hence, the HS-IKKT is a gravitational higher-spin theory as pointed out previously in [ref] .
Cosmological space-times with resolved Big Bang in Yang-Mills matrix models · Spacetime actions for the (self-dual) HS-IKKT model · 0.98
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Hence, the HS-IKKT is a gravitational higher-spin theory as pointed out previously in [ref] .
The fuzzy 4-hyperboloid $H^4_n$ and higher-spin in Yang-Mills matrix models · Spacetime actions for the (self-dual) HS-IKKT model · 0.98
Cites as background 22 papers
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The rotational symmetry is recovered through the extra structure of covariant background geometries which induces a higher-spin theory, see [ref] for a review.
On the quantum structure of space-time, gravity, and higher spin in matrix models · Introduction · 0.82
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The higher-spin extensions of (self-dual) Yang-Mills (HS-(SD)YM) [ref] and self-dual gravity (HS-SDGRA) [ref] were obtained recently, using also some methods with deep roots in twistor theory.
Twistor Constructions for Higher-spin Extensions of (Self-dual) Yang-Mills · Introduction · 0.81
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The higher-spin extensions of (self-dual) Yang-Mills (HS-(SD)YM) [ref] and self-dual gravity (HS-SDGRA) [ref] were obtained recently, using also some methods with deep roots in twistor theory.
Actions for Self-dual Higher Spin Gravities · Introduction · 0.81
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