On non-planar ABJM anomalous dimensions from M2 branes in AdS4 × S7/ℤk

The partition function of N=6 supersymmetric Chern-Simons-matter theory (known as ABJM theory) on S^3, as well as certain Wilson loop observables, are captured by a zero dimensional super-matrix model. This super-matrix model is closely related to a matrix model describing topological Chern-Simons theory on a lens space. We explore further these recent observations and extract more exact results in ABJM theory from the matrix model. In particular we calculate the planar free energy, which matches at strong coupling the classical IIA supergravity action on AdS_4 x CP^3 and gives the correct N^{3/2} scaling for the number of degrees of freedom of the M2 brane theory. Furthermore we find contributions coming from world-sheet instanton corrections in CP^3. We also calculate non-planar corrections, both to the free energy and to the Wilson loop expectation values. This matrix model appears also in the study of topological strings on a toric Calabi-Yau manifold, and an intriguing connection arises between the space of couplings of the planar ABJM theory and the moduli space of this Calabi-Yau. In particular it suggests that, in addition to the usual perturbative and strong coupling (AdS) expansions, a third natural expansion locus is the line where one of the two 't Hooft couplings vanishes and the other is finite. This is the conifold locus of the Calabi-Yau, and leads to an expansion around topological Chern-Simons theory. We present some explicit results for the partition function and Wilson loop observables around this locus.

We include vortices in the superfluid EFT for four dimensional CFTs at large global charge. Using the state-operator correspondence, vortices are mapped to charged operators with large spin and we compute their scaling dimensions. Different regimes are identified: phonons, vortex rings, Kelvin waves, and vortex crystals. We also compute correlators with a Noether current insertion in between vortex states. Results for the scaling dimensions of traceless symmetric operators are given in arbitrary spacetime dimensions.

The holographic configurations dual to Wilson loops in higher rank representations in the ABJM theory are described by branes with electric flux along their world volumes. In particular, D2 and D6 branes with electric flux play a central role as potential dual to totally symmetric and totally antisymmetric representations, respectively. We compute the spectra of excitations of these brane configurations in both, the bosonic and fermionic sectors. We highlight a number of aspects that distinguish these configurations from their D3 and D5 cousins including new peculiar mixing terms in the fluctuations. We neatly organize the spectrum of fluctuations into the corresponding supermultiplets.

In this note we summarize some of the properties found in [1–3]. We characterize spectral properties of the quantum mechanical hamiltonian of theories with fermionic degrees of freedom beyond semiclassical approximation. We obtain a general class of bosonic polynomial potentials for which the Schröedinger operator has a discrete spectrum. This class includes all the scalar potentials in membrane, 5‐brane, p‐branes, multiple M2 branes, BLG and ABJM theories. We also give a sufficient condition for discreteness of the spectrum for supersymmmetric and non supersymmetric theories with a fermionic contribution. We characterize then the spectral properties of different theories: the BMN matrix model, the supermembrane with central charges and a bound state of N D2 with m D0. We show that, while the first two models have a purely discrete spectrum with finite multiplicity, the latter has a continuous spectrum starting from a constant given in terms of the monopole charge.

We explore the idea that large N, non-supersymmetric conformal field theories with a parametrically large gap to higher spin single-trace operators may be obtained as infrared fixed points of relevant double-trace deformations of superconformal field theories. After recalling the AdS interpretation and some potential pathologies of such flows, we introduce a concrete example that appears to avoid them: the ABJM theory at finite k, deformed by {displaystyle int {mathcal{O}}^2} , where mathcal{O} is the superconformal primary in the stress-tensor multiplet. We address its relation to recent conjectures based on weak gravity bounds, and discuss the prospects for a wider class of similarly viable flows. Next, we proceed to analyze the spectrum and correlation functions of the putative IR CFT, to leading non-trivial order in 1/N. This includes analytic computations of the change under double-trace flow of connected four-point functions of ABJM superconformal primaries; and of the IR anomalous dimensions of infinite classes of double-trace composite operators. These would be the first analytic results for anomalous dimensions of finite-spin composite operators in any large N CFT3 with an Einstein gravity dual.

We study the spectrum of local operators living on a defect in a generic conformal field theory, and their coupling to the local bulk operators. We establish the existence of universal accumulation points in the spectrum at large s, s being the charge of the operators under rotations in the space transverse to the defect. Our tools include a formula that inverts the bulk to defect OPE, analogous to the Caron-Huot formula for the four-point function [1]. Analyticity of the formula in s implies that the scaling dimensions of the defect operators are aligned in Regge trajectories widehat{Delta}(s) . These results require the correlator of two local operators and the defect to be bounded in a certain region, a condition that we do not prove in general. We check our conclusions against examples in perturbation theory and holography, and we make specific predictions concerning the spectrum of defect operators on Wilson lines. We also give an interpretation of the large s spectrum in the spirit of the work of Alday and Maldacena [2].

We study (near-)circular orbits of charged particles in the background of charged black holes in asymptotically anti–de Sitter (AdS) spacetimes of arbitrary dimensionality. We calculate the energy and angular momentum of such particles in a large-radius limit. This allows us to compute the anomalous dimension of the dual charged double-twist operators in a large-spin expansion, making a prediction for the bootstrap analysis at large charge and spin. We relate our result to the weak gravity conjecture (WGC) for AdS black holes of all sizes. We also discuss the relation of WGC with the existence of the innermost stable circular orbit (ISCO) in any dimension. Published by the American Physical Society 2024

We construct an analytical solution to the integral equation which is believed to describe logarithmic growth of the anomalous dimensions of high-spin operators in planar N=4 super Yang-Mills theory and use it to determine the strong coupling expansion of the cusp anomalous dimension.

We present the first calculations of next-to-next-to-next-to-next-to-leading order (N4LO) contributions to anomalous dimensions of spin-N twist-2 operators in perturbative QCD. Specifically, we have obtained the respective non-singlet quark–quark anomalous dimensions at N=2 and N=3 to the fifth order in the strong coupling αs. These results set the scale for the N4LO contributions to the evolution of the non-singlet quark distributions of hadrons outside the small-x region, and facilitate a first approximate determination of the five-loop cusp anomalous dimension. While the N4LO coefficients are larger than expected from the lower-order results, their inclusion stabilizes the perturbative expansions for three or more light flavours at a sub-percent accuracy for αs<0.3.

We consider a circular string with spin S in AdS5 wrapped around big circle of S 5 and carrying also momentum J. The corresponding N = 4 SYM operator belongs to the SL(2) sector, i.e. has tr(D S Z J) +... structure. The leading large J term in its 1-loop anomalous dimension can be computed using Bethe ansatz for the SL(2) spin chain and was previously found to match the leading term in the classical string energy. The string solution is stable at large J, and the Lagrangian for string fluctuations has constant coefficients, so that the 1-loop string correction to the energy E1 is given simply by the sum of characteristic frequencies. Curiously, we find that the leading term in the zero-mode part of E1 is the same as a 1/J correction to the one-loop anomalous dimension on the gauge theory (spin chain) side that was found in hep-th/0410105. However, the contribution of non-zero string modes does not vanish. We also discuss the “fast string ” expansion of the classical string action which coincides with the coherent state action of the SL(2) spin chain at the first order in λ, and extend this expansion to higher orders clarifying the role of the S 5 winding number.

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.

3-point correlators in AdS_5xS^5 string theory in which two states are "heavy" (have large quantum numbers) and the third is "light" (here chosen as chiral primary scalar) can be computed semiclassically in terms of the "light" vertex operator evaluated on the classical string solution sourced by the two "heavy" operators. We observe that in the case when the "heavy" operators represent BPS states there is an ambiguity in the computation depending on whether the mass shell (or marginality) condition is imposed before or after integration over the world sheet. We show that this ambiguity is resolved in a universal way by defining the BPS correlator as a limit of the one with non-BPS "heavy" states. We consider several examples with "heavy" states represented by folded or circular spinning strings in AdS_5xS^5 that admit a point-like BMN-type limit when one S^5 spin J is much larger than the others. Remarkably, in all of these cases the large J expansion of the 3-point correlator has the same structure as expected in perturbative (tree-level and one-loop) dual gauge theory. We conjecture that, like the leading chiral primary correlator term, the coefficients of the first few subleading terms are also protected, i.e. should be the same at strong and weak coupling.

Temperature and field dependent electronic structure and magnetic properties of LaCoO3 and GdCoO3

A theoretical model for drying of a thin gel film is presented. The model is based upon the premise that as solvent is removed from any portion of a gel structure which is permeable by the solvent, the structure shrinks locally to fill the voids left by the solvent. The diffusion coefficient of solvent through the gel film is assumed to be an exponential function of concentration and temperature. The governing equations for the model indicate that for nonisothermal drying, the results of drying and shrinkage rates are functions of 13 independent dimensionless system variables. These results are obtained with the help of a computer solution of the proposed model. The computer results indicate that, except under extreme temperature conditions, the drying and shrinkage rates are most influenced by dimensionless groups M, P, and P̄, defined by eq. (9) of the paper. Furthermore, the drying and shrinkage rates are essentially independent of groups M and P for the values of M and P greater than approximately 100 and 10, respectively. The effect of variable solvent diffusivity on approximate time to achieve the steady‐state drying and shrinkage rates is approximately handled by defining a dimensionless time variable τ in terms of average solvent diffusivity. Finally, some experimental data on drying and shrinkage rates of isothermal drying of lyphogel film under natural convection condition are obtained. These data are found to be in qualitative agreement with similar computer predictions by the proposed model.

The observable gravitational and electromagnetic parameters of an electron: mass m, spin J = ℏ/2, charge e and magnetic moment ea = eℏ/(2m) indicate unambiguously that the electron should had the Kerr-Newman background geometry – exact solution of the Einstein-Maxwell gravity for a charged and rotating black hole. Contrary to the widespread opinion that gravity plays essential role only on the Planck scales, the Kerr-Newman gravity displays a new dimensional parameter a = ℏ/(2m), which for parameters of an electron corresponds to the Compton wavelength and turns out to be very far from the Planck scale. Extremely large spin of the electron with respect to its mass produces the Kerr geometry without horizon, which displays very essential topological changes at the Compton distance resulting in a two-fold structure of the electron background. The corresponding gravitational and electromagnetic fields of the electron are concentrated near the Kerr ring, forming a sort of a closed string, structure of which is close to the described by Sen heterotic string. The indicated by Gravity stringlike structure of the electron contradicts to the statements of Quantum theory that electron is pointlike and structureless. However, it confirms the peculiar role of the Compton zone of the "dressed" electron and matches with the known limit of the localization of the Dirac electron. We discuss the relation of the Kerr string with the low energy string theory and with the Dirac theory of electron and suggest that the predicted by the Kerr-Newman gravity closed string in the core of the electron, should be experimentally observable by the novel regime of the high energy scattering - the Deeply Virtual (or "nonforward") Compton Scattering".