Simplifying large spin bootstrap in Mellin space

We compute numerically the dimensions and OPE coefficients of several operators in the 3d Ising CFT, and then try to reverse-engineer the solution to crossing symmetry analytically. Our key tool is a set of new techniques for computing infinite sums of SL(2, mathrm{mathbb{R}} ) conformal blocks. Using these techniques, we solve the lightcone bootstrap to all orders in an asymptotic expansion in large spin, and suggest a strategy for going beyond the large spin limit. We carry out the first steps of this strategy for the 3d Ising CFT, deriving analytic approximations for the dimensions and OPE coefficients of several infinite families of operators in terms of the initial data {Δσ, Δϵ, fσσϵ, fϵϵϵ, cT}. The analytic results agree with numerics to high precision for about 100 low-twist operators (correctly accounting for O(1) mixing effects between large-spin families). Plugging these results back into the crossing equations, we obtain approximate analytic constraints on the initial data.

We study conformal partial waves (CPWs) in Mellin space with totally symmetric external operators of arbitrary integer spin. The exchanged spin is arbitrary, and includes mixed symmetry and (partially)‐conserved representations. In a basis of CPWs recently introduced in arXiv:1702.08619, we find a remarkable factorisation of the external spin dependence in their Mellin representation. This property allows a relatively straightforward study of inversion formulae to extract OPE data from the Mellin representation of spinning 4pt correlators and in particular, to extract closed‐form expressions for crossing kernels of spinning CPWs in terms of the hypergeometric function 4F3. We consider numerous examples involving both arbitrary internal and external spins, and for both leading and sub‐leading twist operators. As an application, working in general d we extract new results for anomalous dimensions of double‐trace operators induced by double‐trace deformations constructed from single‐trace operators of generic twist and integer spin. In particular, we extract the anomalous dimensions of double‐trace operators with a single‐trace operator of integer spin J.

The anomalous dimensions of planar N = 4 SYM theory operators like tr ( Φ D + S Φ ) expanded in large spin S have the asymptotics γ = f ln S + f c + 1 S ( f 11 ln S + f 10 ) + ⋯ , where f (the universal scaling function or cusp anomaly), f c and f m n are given by power series in the 't Hooft coupling λ. The subleading coefficients appear to be related by the so-called functional relation and parity (reciprocity) property of the function expressing γ in terms of the conformal spin of the collinear group. Here we study the structure of such large spin expansion at strong coupling via AdS/CFT, i.e. by using the dual description in terms of folded spinning string in AdS 5 . The large spin expansion of the classical string energy happens to have exactly the same structure as that of γ in the perturbative gauge theory. Moreover, the functional relation and the reciprocity constraints on the coefficients are also satisfied. We compute the leading string 1-loop corrections to the coefficients f c , f 11 , f 10 and verify the functional/reciprocity relations at subleading 1 λ order. This provides a strong indication that these relations hold not only in weak coupling (gauge-theory) but also in strong coupling (string-theory) perturbative expansions.

Planar parts of conformal dimensions of primary operators in Uk(N) × U−k(N) ABJM theory are controlled by integrability. Strong coupling asymptotics of planar dimensions of operators with large spins can be found from the energy of semiclassical strings in AdS4 × CP3 but computing non-planar corrections requires understanding higher genus string corrections. As was pointed out in arXiv:2408.10070, there is an alternative way to find the non-planar corrections by quantizing M2 branes in AdS4 × S7/ℤk which are wrapped around the 11d circle of radius 1/k = λ/N and generalize spinning strings in AdS4 × CP3. Computing the 1-loop correction to the energy of M2 brane that corresponds to the long folded string with large spin S in AdS4 allowed to obtain a prediction for the large λ limit of non-planar corrections to the cusp anomalous dimension. Similar predictions were found for non-planar dimensions of operators dual to M2 branes that generalize the “short” and “long” circular strings with two equal spins J1 = J2 in CP3. Here we consider two more non-trivial examples of 1-loop M2 brane computations that correspond to: (i) long folded string with large spin S in AdS4 and orbital momentum J in CP3 whose energy determines the generalized cusp anomalous dimension, and (ii) circular string with spin S in AdS4 and spin J in CP3. We find the leading terms of the expansion of the corresponding 1-loop M2 brane energies in 1/k. We also discuss similar semiclassical 1-loop M2 brane computation in flat 11d background and comment on possible relation to higher genus corrections to energies in 10d string theory.

We describe a systematic approach for the evaluation of Witten diagrams for multi-loop scattering amplitudes of a conformally coupled scalar ϕ4-theory in Euclidean AdS4, by recasting the Witten diagrams as flat space Feynman integrals. We derive closed form expressions for the anomalous dimensions for all double-trace operators up to the second order in the coupling constant. We explain the relation between the flat space unitarity methods and the discontinuities of the short distance expansion on the boundary of Witten diagrams.

The spin Hall effect (SHE) is closely related to the spin-orbit coupling. Therefore, heavy metals are usually considered as materials of choice to obtain large spin Hall angles. Among these materials, some 5d transition metals such as Pt, Ta or W offer the largest spin-charge interconversion efficiency for spin current detections through the inverse spin Hall effect or to obtain efficient current induced magnetization switching in SOT-MRAM devices [1].Despite a weaker spin orbit coupling, spin Hall angles comparable to that of the best 5d materials has also been obtained in 3d ferromagnetic metals such as Co [2] or Ni [3]. More recently nonmagnetic alloys containing Nickel atoms such as NiCu [4] and CoNiB [5] attracted great interest for their large spin Hall angles and their potential for spintronic applications. Using the spin pumping by ferromagnetic resonance technique we could compare the spin to charge current conversion in Ni60Cu40 to the one of Pt. As can be seen in figure 1 a) the normalized spin pumping signal obtained in CFB/NiCu is comparable to that of CFB/Pt. We performed a thickness dependence shown in figure 1 b) to extract the spin Hall angle (θSHE) and spin diffusion length (λs) and obtained results comparable to the one of 5d metals using similar method with λs = 2.4 ± 0.3 nm and θSHE = 4.1 ± 0.5 % [6].Keller and coworkers [4] noticed similarities in the bandstructure of paramagnetic Nickel and Platinum possibly explaining the origin of the effect. The calculated band structure of ferromagnetic Nickel does not resemble that of Platinum and the origin of the large spin Hall effect observed in ferromagnetic Ni [3] could thus be different. The interplay between the spin-orbit coupling and magnetism is known to be at the origin of specific transport properties such as the anomalous magnetoresistance and the anomalous Hall effect. However, the link between the SHE and the magnetic order is complex and still unexplored [7].In order to study the effect of the phase transition we performed spin pumping as a function of temperature in Ni60Cu40 and Ni50Cu50 alloys above and below the Curie temperature. To avoid direct contact between the ferromagnetic spin injector CFB and the magnetic NiCu alloy that would modify CFB resonance properties due to the direct coupling [8] we used a 5 nm thick Cu interlayer. The spin pumping measurements performed in CFB\Cu\ Ni60Cu40 and CFB\Cu\ Ni50Cu50 shown in figure 2 indicate that in NiCu the SHE is insensitive to the magnetic order [6].A large variety of alloys composed of Ni, Co or Fe in the ferromagnetic or paramagnetic phase could be explored as spin current generators and detectors, extending the number of possible light metal systems with a large SHE. In particular, the large spin Hall effect in NiCu shows that it is a promising alternative to obtain large spin orbit torque without heavy metals. **

Chromium is a $3d$ spin-density wave antiferromagnetic (AF) metal with a N\'eel temperature of 311 K. By using the thermal spin injection method, we have observed a large inverse spin Hall voltage in Cr. With a negligible magnetic proximity effect and a large spin Hall angle, Cr is an intrinsic pure spin current detector that is superior to many $5d$ metals. Even more strikingly, the temperature dependent thermal spin injection measurements show that the large spin Hall angle in Cr is independent of the AF ordering, and indicating that the inverse spin Hall effect is unrelated to AF ordering in Cr.

Manipulation of the magnetization in heavy-metal/ferromagnetic bilayers via the spin-orbit torque requires high spin Hall conductivity of the heavy metal. We measure inverse spin Hall voltage using a co-planar wave-guide based broadband ferromagnetic resonance set-up in Py/Ta system with varying crystalline phase of Ta. We demonstrate a strong correlation between the measured spin mixing conductance and spin Hall conductivity with the crystalline phase of Ta thin films. We found a large spin Hall conductivity of $-2439~(\hbar/e)~\Omega^{-1}$cm$^{-1}$ for low-resistivity (68 $\mu\Omega-$cm) Ta film having mixed crystalline phase, which we attribute to an extrinsic mechanism of the spin Hall effect.

We analytically study the lightcone limit of the conformal bootstrap for 4-point functions containing scalars charged under global symmetries. We show the existence of large spin double-twist operators in various representations of the global symmetry group. We then compute their anomalous dimensions in terms of the central charge $C_T$, current central charge $C_J$, and the OPE coefficients of low dimension scalars. In AdS, these results correspond to the binding energy of two-particle states arising from the exchange of gravitons, gauge bosons, and light scalar fields. Using unitarity and crossing symmetry, we show that gravity is universal and attractive among different types of two-particle states, while the gauge binding energy can have either sign as determined by the representation of the two-particle state, with universal ratios fixed by the symmetry group. We apply our results to 4D $\mathcal{N}=1$ SQCD and the 3D O(N) vector models. We also show that in a unitary CFT, if the current central charge $C_J$ stays finite when the global symmetry group becomes infinitely large, such as the $N\rightarrow\infty$ limit of the O(N) vector model, then the theory must contain an infinite number of higher spin currents.

Using conformal field theory (CFT) arguments we derive an infinite number of constraints on the large spin expansion of the anomalous dimensions and structure constants of higher spin operators. These arguments rely only on analiticity, unitarity, crossing-symmetry and the structure of the conformal partial wave expansion. We obtain results for both, perturbative CFT to all order in the perturbation parameter, as well as non-perturbatively. For the case of conformal gauge theories this provides a proof of the reciprocity principle to all orders in perturbation theory and provides a new "reciprocity" principle for structure constants. We argue that these results extend also to non-conformal theories.

In this paper, an adaptive controller for a class of uncertain nonlinear systems is presented using a combination of Legendre polynomials and brain emotional learning-based intelligent controller (BELBIC). Recently, some versions of BELBIC have been presented with the aim of satisfying the universal approximation property using Gaussian basis function. However, the size of regressor vector is too large that imposes a heavy computational load to the processor. The novelty of this paper is presenting a new version of BELBIC with less computational burden using Legendre polynomials. Moreover, there are very few tuning parameters in Legendre polynomials. Another contribution of this paper is editing the stability analysis presented in recent related works. Due to the intrinsic non-differentiability of the adaptation rules of BELBIC, the second time derivative of Lyapunov function is undefined and thus, the Barbalat’s lemma cannot be applied to verify the asymptotic convergence of the error function. Therefore, bounded-input-bounded-output (BIBO) stability can only be claimed for this controller. Simulation results on different case studies show that Legendre polynomials can improve the universal approximation property of BELBIC with less tuning parameters. Moreover, in the absence of the robust control term in the control law, the performance Legendre polynomials will not deteriorate, while the performance degrade in Gaussian basis function is quite considerable.

The generalized function is an indispensable tool in the study of complex physical processes. Owing to its universal property it encompasses a wide range of mathematical functions and can be used for modelling complex physical processes. In this paper the authors demonstrate some special cases of generalized functions. The application of such special cases forms a subject of further study.

We study conformal blocks for thermal one-point-functions on the sphere in conformal field theories of general dimension. These thermal conformal blocks satisfy second-order Casimir differential equations and have integral representations related to AdS Witten diagrams. We give an analytic formula for the scalar conformal block in terms of generalized hypergeometric functions. As an application, we deduce an asymptotic formula for the three-point coefficients of primary operators in the limit where two of the operators are heavy.

An exact expression for the probability of inversion of a large spin is established in the form of an asymptotic expansion in the series of Bessel functions with orders belonging to an arithmetic progression. Based on the new asymptotic expansion, a formula for the inversion time of the spin is derived.

A low energy action for double-layer quantum Hall systems at filling fractions $\nu = 2/m$ ($m$ an odd integer) is introduced. Interlayer antiferromagnetic exchange induces a phase with canted spin order, and also a spin-singlet phase. Universal properties of zero and finite temperature transitions are obtained. We compute the critical temperature at which the canted order vanishes in a Kosterlitz-Thouless transition. Implications for recent light scattering experiments at $\nu = 2$ are noted.