Higher Spin Operators Research Articles

Two-dimensional coherent spectrum of high-spin models via a quantum computing approach

We present and benchmark a quantum computing approach to calculate the two-dimensional coherent spectrum (2DCS) of high-spin models. Our approach is based on simulating their real-time dynamics in the presence of several magnetic field pulses, which are spaced in time. We utilize the adaptive variational quantum dynamics simulation algorithm for the study due to its compact circuits, which enables simulations over sufficiently long times to achieve the required resolution in frequency space. Specifically, we consider an antiferromagnetic quantum spin model that incorporates Dzyaloshinskii-Moriya interactions and single-ion anisotropy. The obtained 2DCS spectra exhibit distinct peaks at multiples of the magnon frequency, arising from transitions between different eigenstates of the unperturbed Hamiltonian. By comparing the one-dimensional coherent spectrum with 2DCS, we demonstrate that 2DCS provides a higher resolution of the energy spectrum. We further investigate how the quantum resources scale with the magnitude of the spin using two different binary encodings of the high-spin operators: the standard binary encoding and the Gray code. At low magnetic fields both encodings require comparable quantum resources, but at larger field strengths the Gray code is advantageous. Numerical simulations for spin models with increasing number of sites indicate a polynomial system-size scaling for quantum resources. Lastly, we compare the numerical 2DCS with experimental results on a rare-earth orthoferrite system. The observed strength of the magnonic high-harmonic generation signals in the 2DCS of the quantum high-spin model aligns well with the experimental data, showing significant improvement over the corresponding mean-field results.

Anomalous and linear holographic hard wall models for glueballs and the pomeron

In this work we propose improved holographic hard wall (HW) models by the inclusion of anomalous dimensions in the dual operators that describe glueballs inspired by the AdS/CFT correspondence. The anomalous dimensions come from well known semiclassical gauge/string duality analysis showing a dependence with the logarithm of spin S of the boundary states. We show that these logarithm anomalous dimensions of the high spin operators combined with the usual HW model allow us to match the pomeron trajectory and give glueball masses that are better than that of the original HW and soft wall models in comparison with lattice data. We also build up other anomalous HW models considering that the logarithm anomalous dimensions can be approximated by a truncated series of odd powers of the difference S−1/S. These models also fit the pomeron trajectory and produce good glueball masses. Then, we consider an anomalous dimension that is proportional to S, providing reasonable results. Finally, we propose an asymptotic linear anomalous HW model that effective dimensions for high spins operators are of the form Δ=aS+b, where a and b are constants to be fixed by comparison with the soft pomeron trajectory. In this last model, the Regge trajectory is asymptotically linear even for very high spins (J∼100) matching the soft pomeron trajectory accurately and generates glueball masses with deviations with respect to the lattice data better than the original HW and soft wall models. Published by the American Physical Society 2024

Two-point sum-rules in three-dimensional Yang-Mills theory

We compute the stress-tensor two-point function in three-dimensional Yang-Mills theory to three-loops in perturbation theory. Using its calculable shape at high momenta, we test the notion that its Borel transform is saturated at low energies by the lowest glueball state(s). This assumption provides relatively stable estimates for the mass of the lightest glueball that we compare with lattice simulations. We also provide estimates for the coupling of the lightest glueball to the stress tensor. Along the way, we comment on the extent that such estimates are non-rigorous. Lastly, we discuss the possibility of applying the sum-rule analysis to two-point functions of higher-spin operators and obtain a crude approximation for the glueball couplings to these operators.

Higher-Spin Currents, Operator Mixing and UV Asymptotics in Large-N QCD-like Theories

We extend to operator mixing—specifically, to higher-spin twist-2 operators—the asymptotic theorem on the ultraviolet asymptotics of the spectral representation of 2-point correlators of multiplicatively renormalizable operators in large-N confining QCD-like theories. The extension is based on a recent differential geometric approach to operator mixing that involves the Poincaré-Dulac theorem and allows us to reduce generically the operator mixing to the multiplicatively renormalizable case, provided that γ0β0 is diagonalizable and a certain nonresonant condition for its eigenvalues holds according to the Poincaré-Dulac theorem, with γ0 and β0 the one-loop coefficients of the anomalous dimension matrix and beta function respectively. Relatedly, we solve a conundrum about the generic nonconservation of higher-spin currents versus the conservation—up to contact terms—of the corresponding free propagators in the spectral representation of 2-point correlators of higher-spin operators of pure integer spin to the leading large-N order.

Machine learning etudes in conformal field theories

We demonstrate that various aspects of Conformal Field Theory are amenable to machine learning. Relatively modest feed-forward neural networks are able to distinguish between scale and conformal invariance of a three-point function and identify a crossing-symmetric four-point function to nearly 100% accuracy. Furthermore, neural networks are also able to identify conformal blocks appearing in a putative CFT four-point function and predict the values of the corresponding operator product expansions (OPE) coefficients. Neural networks also successfully classify primary operators by their quantum numbers under discrete symmetries in the CFT from examining OPE data. We also demonstrate that neural networks are able to learn the available OPE data for scalar correlation function in the 3D Ising model and predict the twists of higher-spin operators that appear in scalar OPE channels by regression.

Scheme-independent series for anomalous dimensions of higher-spin operators at an infrared fixed point in a gauge theory

We consider an asymptotically free vectorial gauge theory, with gauge group $G$ and $N_f$ fermions in a representation $R$ of $G$, having an infrared fixed point of the renormalization group. We calculate scheme-independent series expansions for the anomalous dimensions of higher-spin bilinear fermion operators at this infrared fixed point up to $O(\Delta_f^3)$, where $\Delta_f$ is an $N_f$-dependent expansion variable. Our general results are evaluated for several special cases, including the case $G={\rm SU}(N_c)$ with $R$ equal to the fundamental and adjoint representations.

Einstein gravity from ANEC correlators

We study correlation functions with multiple averaged null energy (ANEC) operators in conformal field theories. For large N CFTs with a large gap to higher spin operators, we show that the OPE between a local operator and the ANEC can be recast as a particularly simple differential operator acting on the local operator. This operator is simple enough that we can resum it and obtain the finite distance OPE. Under the large N - large gap assumptions, the vanishing of the commutator of ANEC operators tightly constrains the OPE coefficients of the theory. An important example of this phenomenon is the conclusion that a = c in d = 4. This implies that the bulk dual of such a CFT is semi-classical Einstein-gravity with minimally coupled matter.

Mathcal{N}=left(0, 2right) SYK, chaos and higher-spins

We study a 2-dimensional SYK-like model with mathcal{N}=left(0, 2right) supersymmetry. The model describes N chiral supermultiplets and M Fermi supermultiplets with a (q + 1)- field interaction. We solve the model analytically and numerically in the N ≫ 1, M ≫ 1 limit with mu equiv frac{M}{N} being a free parameter. Two distinct higher-spin symmetries emerge when the μ parameter approaches the two ends of its range. This is verified by the appearance of conserved higher-spin operators and the vanishing of chaotic behaviors in the two limits. Therefore this model provides a manifest realization of the widely believed connection between SYK-like models and higher-spin theories. In addition, as the parameter μ varies we find the largest Lyapunov exponent of this model to be slightly larger than that in models with non-chiral supersymmetry.

Anomalous dimensions at finite conformal spin from OPE inversion

We compute anomalous dimensions of higher spin operators in Conformal Field Theory at arbitrary space-time dimension by using the OPE inversion formula of [1], both from the position space representation as well as from the integral viz. Mellin representation of the conformal blocks. The Mellin space is advantageous over the position space not only in allowing to write expressions agnostic to the space-time dimension, but also in that it replaces tedious recursion relations in terms of simple sums which are easy to perform. We evaluate the contributions of scalar and spin exchanges in the t-channel exactly, in terms of higher order Hypergeometric functions. These relate to a particular exchange of conformal spin β = Δ + J in the s-channel through the inversion formula. Our results reproduce the special cases for large spin anomalous dimension and OPE coefficients obtained previously in the literature.

A conformal collider for holographic CFTs

We develop a formalism to study the implications of causality on OPE coefficients in conformal field theories with large central charge and a sparse spectrum of higher spin operators. The formalism has the interpretation of a new conformal collider-type experiment for these class of CFTs and hence it has the advantage of requiring knowledge only about CFT three-point functions. This is accomplished by considering the holographic null energy operator which was introduced in [1] as a generalization of the averaged null energy operator. Analyticity properties of correlators in the Regge limit imply that the holographic null energy operator is a positive operator in a subspace of the total CFT Hilbert space. Utilizing this positivity condition, we derive bounds on three-point functions 〈TO1O2〉 of the stress tensor with various operators for CFTs with large central charge and a sparse spectrum. After imposing these constraints, we also find that the operator product expansions of all primary operators in the Regge limit have certain universal properties. All of these results are consistent with the expectation that CFTs in this class, irrespective of their microscopic details, admit universal gravity-like holographic dual descriptions. Furthermore, this connection enables us to constrain various inflationary observables such as the amplitude of chiral gravity waves, non-gaussanity of gravity waves and tensor-to-scalar ratio.

Beyond a = c : gravitational couplings to matter and the stress tensor OPE

We derive constraints on the operator product expansion of two stress tensors in conformal field theories (CFTs), both generic and holographic. We point out that in large N CFTs with a large gap to single-trace higher spin operators, the stress tensor sector is not only universal, but isolated: that is, leftlangle TTmathcal{O}rightrangle =0 , where mathcal{O}ne T is a single-trace primary. We show that this follows from a suppression of leftlangle TTmathcal{O}rightrangle by powers of the higher spin gap, Δgap, dual to the bulk mass scale of higher spin particles, and explain why leftlangle TTmathcal{O}rightrangle is a more sensitive probe of Δgap than a − c in 4d CFTs. This result implies that, on the level of cubic couplings, the existence of a consistent truncation to Einstein gravity is a direct consequence of the absence of higher spins. By proving similar behavior for other couplings leftlangle T{mathcal{O}}_1{mathcal{O}}_2rightrangle where {mathcal{O}}_i have spin si ≤ 2, we are led to propose that 1/Δgap is the CFT “dual” of an AdS derivative in a classical action. These results are derived by imposing unitarity on mixed systems of spinning four-point functions in the Regge limit. Using the same method, but without imposing a large gap, we derive new inequalities on these three-point couplings that are valid in any CFT. These are generalizations of the Hofman-Maldacena conformal collider bounds. By combining the collider bound on TT couplings to spin-2 operators with analyticity properties of CFT data, we argue that all three tensor structures of 〈TTT〉 in the free-field basis are nonzero in interacting CFTs.

Taming the \u03f5-expansion with large spin perturbation theory

We apply analytic bootstrap techniques to the four-point correlator of fundamental fields in the Wilson-Fisher model. In an ϵ-expansion crossing symmetry fixes the double discontinuity of the correlator in terms of CFT data at lower orders. Large spin perturbation theory, or equivalently the recently proposed Froissart-Gribov inversion integral, then allows one to reconstruct the CFT data of intermediate operators of any spin. We use this method to compute the anomalous dimensions and OPE coefficients of leading twist operators. To cubic order in ϵ the double discontinuity arises solely from the identity operator and the scalar bilinear operator, making the computation straightforward. At higher orders the double discontinuity receives contributions from infinite towers of higher spin operators. At fourth order, the structure of perturbation theory leads to a proposal in terms of functions of certain degree of transcendentality, which can then be fixed by symmetries. This leads to the full determination of the CFT data for leading twist operators to fourth order.

Towards a bootstrap approach to higher orders of epsilon expansion

We employ a hybrid approach in determining the anomalous dimension and OPE coefficient of higher spin operators in the Wilson-Fisher theory. First we do a large spin analysis for CFT data where we use results obtained from the usual and the Mellin bootstrap and also from Feynman diagram literature. This gives new predictions at O(ϵ4) and O(ϵ5) for anomalous dimensions and OPE coefficients, and also provides a cross-check for the results from Mellin bootstrap. These higher orders get contributions from all higher spin operators in the crossed channel. We also use the bootstrap in Mellin space method for ϕ3 in d = 6 − ϵ CFT where we calculate general higher spin OPE data. We demonstrate a higher loop order calculation in this approach by summing over contributions from higher spin operators of the crossed channel in the same spirit as before.

Crossing symmetry and Higher spin towers

We consider higher spin operators in weakly coupled gauge conformal field theories. Crossing symmetry of mixed scalar correlators relates different higher spin towers and we study the consequences for the spectrum and structure constants of higher spin operators of different twists. Constraints are obtained to all loops in perturbation theory. The large spin contributions to the structure constants can be resummed into a theory-dependent prefactor times a universal factor, whose structure of poles agrees with the one that would be obtained from a Witten diagram supergravity computation, although only crossing symmetry is assumed. Finally, our results provide an all loop expression for the double null limit of mixed correlators, which is in perfect agreement with the correlator/Wilson loop correspondence.

Einstein gravity 3-point functions from conformal field theory

We study stress tensor correlation functions in four-dimensional conformal field theories with large N and a sparse spectrum. Theories in this class are expected to have local holographic duals, so effective field theory in anti-de Sitter suggests that the stress tensor sector should exhibit universal, gravity-like behavior. At the linearized level, the hallmark of locality in the emergent geometry is that stress tensor three-point functions 〈T T T 〉, normally specified by three constants, should approach a universal structure controlled by a single parameter as the gap to higher spin operators is increased. We demonstrate this phenomenon by a direct CFT calculation. Stress tensor exchange, by itself, violates causality and unitarity unless the three-point functions are carefully tuned, and the unique consistent choice exactly matches the prediction of Einstein gravity. Under some assumptions about the other potential contributions, we conclude that this structure is universal, and in particular, that the anomaly coefficients satisfy a ≈ c as conjectured by Camanho et al. The argument is based on causality of a four-point function, with kinematics designed to probe bulk locality, and invokes the chaos bound of Maldacena, Shenker, and Stanford.

Averaged null energy condition from causality

Unitary, Lorentz-invariant quantum field theories in flat spacetime obey mi-crocausality: commutators vanish at spacelike separation. For interacting theories in more than two dimensions, we show that this implies that the averaged null energy, ∫ duTuu, must be non-negative. This non-local operator appears in the operator product expansion of local operators in the lightcone limit, and therefore contributes to n-point functions. We derive a sum rule that isolates this contribution and is manifestly positive. The argument also applies to certain higher spin operators other than the stress tensor, generating an infinite family of new constraints of the form ∫ duXuuu···u ≥ 0. These lead to new inequalities for the coupling constants of spinning operators in conformal field theory, which include as special cases (but are generally stronger than) the existing constraints from the lightcone bootstrap, deep inelastic scattering, conformal collider methods, and relative entropy. We also comment on the relation to the recent derivation of the averaged null energy condition from relative entropy, and suggest a more general connection between causality and information-theoretic inequalities in QFT.

On the higher-spin spectrum in large N Chern-Simons vector models

Chern-Simons gauge theories coupled to massless fundamental scalars or fermions define interesting non-supersymmetric 3d CFTs that possess approximate higher-spin symmetries at large N . In this paper, we compute the scaling dimensions of the higher-spin operators in these models, to leading order in the 1/N expansion and exactly in the ’t Hooft coupling. We obtain these results in two independent ways: by using conformal symmetry and the classical equations of motion to fix the structure of the current non-conservation, and by a direct Feynman diagram calculation. The full dependence on the ’t Hooft coupling can be restored by using results that follow from the weakly broken higher-spin symmetry. This analysis also allows us to obtain some explicit results for the non-conserved, parity-breaking structures that appear in planar three-point functions of the higher-spin operators. At large spin, we find that the anomalous dimensions grow logarithmically with the spin, in agreement with general expectations. This logarithmic behavior disappears in the strong coupling limit, where the anomalous dimensions turn into those of the critical O(N ) or Gross-Neveu models, in agreement with the conjectured 3d bosonization duality.

Anomalous dimensions in CFT with weakly broken higher spin symmetry

In a conformal field theory with weakly broken higher spin symmetry, the leading order anomalous dimensions of the broken currents can be efficiently determined from the structure of the classical non-conservation equations. We apply this method to the explicit example of $O(N)$ invariant scalar field theories in various dimensions, including the large $N$ critical $O(N)$ model in general $d$, the Wilson-Fisher fixed point in $d=4-\epsilon$, cubic scalar models in $d=6-\epsilon$ and the nonlinear sigma model in $d=2+\epsilon$. Using information from the $d=4-\epsilon$ and $d=2+\epsilon$ expansions, we obtain some estimates for the dimensions of the higher spin operators in the critical 3d $O(N)$ models for a few low values of $N$ and spin.

Generalized helicity formalism, higher moments, and theB→KJK(→Kπ)ℓ1¯ℓ2angular distributions

We generalise the Jacob-Wick helicity formalism, which applies to sequential decays, to effective field theories of rare decays of the type $B \to K_{J_K}(\to K \pi) \bar{\ell}_1 \ell_2$. This is achieved by reinterpreting local interaction vertices $\bar b \Gamma'_{\mu_1 ..\mu_n} s \bar \ell \Gamma^{\mu_1 ..\mu_n} \ell$ as a coherent sum of $1 \to 2$ processes mediated by particles whose spin ranges between zero and $n$. We illustrate the framework by deriving the full angular distributions for $B \to K\bar{\ell}_1 \ell_2$ and $B \to K^*(\to K \pi) \bar{\ell}_1 \ell_2$ for the complete dimension-six effective Hamiltonian for non-equal lepton masses. Amplitudes and decay rates are expressed in terms of Wigner rotation matrices, leading naturally to the method of moments in various forms. We discuss how higher-spin operators and QED corrections alter the standard angular distribution used throughout the literature, potentially leading to differences between the method of moments and the likelihood fits. We propose to diagnose these effects by assessing higher angular moments. These could be relevant in investigating the nature of the current LHCb anomalies in $R_K = {\cal B}( B \to K \mu^+\mu^-) /{\cal B}( B \to K e^+e^-)$ as well as angular observables in $B \to K^* \mu^+\mu^-$.

Supersymmetry, Supergravity, and Superstring Phenomenology

Supersymmetry, supergravity, and superstring are amongst the most popular research topics in particle physics. Supersymmetry is a generalization of the space-time symmetries of quantum field theory that links the matter particles with the force-carrying particles and implies that there are additional superparticles necessary to complete the symmetry. Supergravity is the theory that combines the principles of supersymmetry and general relativity. It naturally includes gravity along with the other fundamental forces (the electromagnetic force, the weak nuclear force, in turn already unified in the electroweak interactions, and the strong nuclear force). String theory is the leading candidate for a theory that unifies all fundamental forces in nature in a consistent scheme. It also provides a consistent framework for the theory of quantum gravity. Compactified string/M-theories make testable predictions about our four-dimensional world. The phenomenology of supersymmetry, supergravity, and superstring is thus very rich and covers many topics: flavour physics and CP violation, Higgs and collider physics, model building beyond the Standard Model, and astroparticle physics and cosmology. Some recent developments in these theories, each with important applications to particle physics and/or cosmology, are the main theme of this special issue. One of the papers of this special issue discusses the constrained generalized Killing spinors, which characterize supersymmetric flux compactifications of supergravity theories, using geometric algebra techniques. Another paper presents a study on what are called Adinkras, which are combinatorial objects developed to study (1-dimensional) supersymmetry representations. Another paper reviews moduli stabilization in type IIB string theory compactification with fluxes. Another paper in this special issue describes supermultiplets wherein a continuously variable “tuning parameter” modifies the supersymmetry transformations. Another paper studies the constraints imposed on the Minimal Supersymmetric Standard Model (MSSM) parameter space by the Large Hadron Collider (LHC) Higgs mass measurements and gluino mass lower bound. Another paper studies helical phase inflation which realizes “monodromy inflation” in supergravity theory. Another paper considers scalar Wilson operators of Supersymmetric Yang-Mills (SYM) theories at high spin and generic twist operators in the multicolor limit. Another paper author gives an overview about the features that the Mathematica package SARAH provides to study new supersymmetric models. Another paper reviews a possible mechanism for the spontaneous breaking of supersymmetry, based on the presence of vacuum condensates. Another paper constructs and studies a formulation of a chargeless complex vector matter field in a supersymmetric framework.