Theory of higher spin tensor currents and central charges

D. Anselmi

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Theory of higher spin tensor currents and central charges

D. Anselmi

High Energy Physics - Theory · Submitted 2 Aug 1998

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Higher spin central charges c_(s,I) with arbitrary s are defined by higher spin channels of the many-point T-correlators and central functions interpolating between the UV and IR limits are constructed.

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.49 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.16 · compares with prior results 0.10 · mentions code or data availability 0.02.

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arXiv listing abstract v4. Results and the main claim are underlined; show every role.

We study higher spin tensor currents in quantum field theory. Scalar, spinor and vector fields admit unique "improved" currents of arbitrary spin, traceless and conserved. Off-criticality as well as at interacting fixed points conservation is violated and the dimension of the current is anomalous. In particular, currents J^(s,I) with spin s between 0 and 5 (and a second label I) appear in the operator product expansion of the stress tensor. The TT OPE is worked out in detail for free fields; projectors and invariants encoding the space-time structure are classified. The result is used to write and discuss the most general OPE for interacting conformal field theories and off-criticality. Higher spin central charges c_(s,I) with arbitrary s are defined by higher spin channels of the many-point T-correlators and central functions interpolating between the UV and IR limits are constructed. We compute the one-loop values of all c_(s,I) and investigate the RG trajectories of quantum field theories in the conformal window following our approach. In particular, we discuss certain phenomena (perturbative and nonperturbative) that appear to be of interest, like the dynamical removal of the I-degeneracy. Finally, we address the problem of formulating an action principle for the RG trajectory connecting pairs of CFT's as a way to go beyond perturbation theory.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study higher spin tensor currents in quantum field theory.	contribution 0.80	0.88	0.03	asserted 0.87
s1	Scalar, spinor and vector fields admit unique "improved" currents of arbitrary spin, traceless and conserved.	background 0.72	0.24	0.08	asserted 1.00
s2	Off-criticality as well as at interacting fixed points conservation is violated and the dimension of the current is anomalous.	background 0.79	0.26	0.07	asserted 1.00
s3	In particular, currents J^(s,I) with spin s between 0 and 5 (and a second label I) appear in the operator product expansion of the stress tensor.	result 0.63	0.38	0.07	asserted 0.99
s4	The TT OPE is worked out in detail for free fields; projectors and invariants encoding the space-time structure are classified.	contribution 0.61	0.91	0.05	asserted 1.00
s5	The result is used to write and discuss the most general OPE for interacting conformal field theories and off-criticality.	contribution 0.61	0.91	0.10	asserted 1.00
s6	Higher spin central charges c_(s,I) with arbitrary s are defined by higher spin channels of the many-point T-correlators and central functions interpolating between the UV and IR limits are constructed.	contribution 0.93	0.90	0.26	asserted 1.00
s7	We compute the one-loop values of all c_(s,I) and investigate the RG trajectories of quantum field theories in the conformal window following our approach.	contribution 0.66	0.96	0.17	asserted 1.00
s8	In particular, we discuss certain phenomena (perturbative and nonperturbative) that appear to be of interest, like the dynamical removal of the I-degeneracy.	result 0.61	0.67	0.10	hedged possibility 0.89
s9	Finally, we address the problem of formulating an action principle for the RG trajectory connecting pairs of CFT's as a way to go beyond perturbation theory.	contribution 0.78	0.80	0.11	asserted 0.71

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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arXiv listing abstract v4

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The paper

Original abstract

We study higher spin tensor currents in quantum field theory. Scalar, spinor and vector fields admit unique "improved" currents of arbitrary spin, traceless and conserved. Off-criticality as well as at interacting fixed points conservation is violated and the dimension of the current is anomalous. In particular, currents J^(s,I) with spin s between 0 and 5 (and a second label I) appear in the operator product expansion of the stress tensor. The TT OPE is worked out in detail for free fields; projectors and invariants encoding the space-time structure are classified. The result is used to write and discuss the most general OPE for interacting conformal field theories and off-criticality. Higher spin central charges c_(s,I) with arbitrary s are defined by higher spin channels of the many-point T-correlators and central functions interpolating between the UV and IR limits are constructed. We compute the one-loop values of all c_(s,I) and investigate the RG trajectories of quantum field theories in the conformal window following our approach. In particular, we discuss certain phenomena (perturbative and nonperturbative) that appear to be of interest, like the dynamical removal of the I-degeneracy. Finally, we address the problem of formulating an action principle for the RG trajectory connecting pairs of CFT's as a way to go beyond perturbation theory.

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References

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Cited by 13 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Cubic Vertices for Symmetric Higher-Spin Gauge Fields in $(A)dS_d$
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Positivity of forward scattering amplitudes forces the cutoff of a massive higher-spin effective theory down to the particle mass, and the leading quartic potentials for spin-3 fail the bounds outright.
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Free scalar CFTs built from k powers of the Laplacian contain, for k=2 in d=3 and d=6, zero-norm operators that are both primary and descendant, together with partner operators that are neither.

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The one-loop effective action of a free massless scalar in a higher-spin background is computed perturbatively, with its divergent and finite parts expressed in terms of higher-spin curvatures and linked to conformal ...
Holography of the N=1 Higher-Spin Theory on AdS4
hep-th 2003-04 conditional novelty 6.0 of 10

The minimal N=1 higher-spin theory on AdS4 is proposed to be holographically dual to the singlet sector of the N=1 supersymmetric O(N) vector model in three dimensions, with parity assignments selecting between the fr...
On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry
hep-th 2002-09 accept novelty 6.0 of 10

At the unitarity threshold a long superconformal multiplet decomposes into four semi-short multiplets, and only the 1/2-BPS [0,p,0] and 1/4-BPS [1,p,1] multiplets are guaranteed to have protected scale dimensions.
Massless Higher Spins and Holography
hep-th 2002-05 conditional novelty 6.0 of 10

The paper argues that free large-N superconformal field theories are holographically dual to massless higher-spin gauge theories in AdS, and constructs the 7D supersymmetric higher-spin algebra plus a rotating membran...
Partition Functions and Casimir Energies in Higher Spin AdS_{d+1}/CFT_d
hep-th 2014-02 conditional novelty 5.0 of 10

The one-loop free energy and Casimir energy of higher-spin gravity in AdS_{d+1} match the order-N^0 terms of large-N singlet-sector free scalar and fermion CFTs on S^1 x S^{d-1} in all dimensions.
Higher Spin Gauge Theories: Star-Product and AdS Space
hep-th 1999-10 conditional novelty 5.0 of 10

A d=3 integrating flow for higher spin equations is generalized to d=4, where it is argued to generate perturbative solutions of the nonlinear higher spin system.
On (Un)Broken Higher-Spin Symmetry in Vector Models
hep-th 2015-12 conditional novelty 4.0 of 10

One-loop anomalous dimensions of higher-spin currents in Wilson-Fisher CFTs are re-derived via multiplet recombination, matching known results, and part of the dual AdS higher-spin cubic action is reconstructed.
Stringy gravity, interacting tensionless strings and massless higher spins
hep-th 2001-03 conditional novelty 4.0 of 10

At zero string tension the AdS/CFT correspondence identifies free N=4 super Yang-Mills with an interacting theory of massless higher-spin fields, and its thermodynamics shows a black-hole-like phase transition.

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