ASU Scholarship Showcase

We present a new approach to computing event shape distributions or, more precisely, charge flow correlations in a generic conformal field theory (CFT). These infrared finite observables are familiar from collider physics studies and describe the angular distribution of global charges in outgoing radiation created from the vacuum by some source. The charge flow correlations can be expressed in terms of Wightman correlation functions in a certain limit. We explain how to compute these quantities starting from their Euclidean analogues by means of a nontrivial analytic continuation which, in the framework of CFT, can be performed elegantly in Mellin space. The relation between the charge flow correlations and Euclidean correlation functions can be reformulated directly in configuration space, bypassing the Mellin representation, as a certain Lorentzian double discontinuity of the correlation function integrated along the cuts. We illustrate the general formalism in N = 4 SYM, making use of the well-known results on the four-point correlation function of half-BPS scalar operators. We compute the double scalar flow correlation in N = 4 SYM, at weak and strong coupling and show that it agrees with known results obtained by different techniques. One of the remarkable features of the N = 4 theory is that the scalar and energy flow correlations are proportional to each other. Imposing natural physical conditions on the energy flow correlations (finiteness, positivity and regularity), we formulate additional constraints on the four-point correlation functions in N = 4SYM that should be valid at any coupling and away from the planar limit.

The Operator Product Expansion for null polygonal Wilson loop in planar maximally supersymmetric Yang–Mills theory runs systematically in terms of multi-particle pentagon transitions which encode the physics of excitations propagating on the color flux tube ending on the sides of the four-dimensional contour. Their dynamics was unraveled in the past several years and culminated in a complete description of pentagons as an exact function of the 't Hooft coupling. In this paper we provide a solution for the last building block in this program, the SU(4) matrix structure arising from internal symmetry indices of scalars and fermions. This is achieved by a recursive solution of the Mirror and Watson equations obeyed by the so-called singlet pentagons and fixing the form of the twisted component in their tensor decomposition. The non-singlet, or charged, pentagons are deduced from these by a limiting procedure.

We address the near-collinear expansion of NMHV six-particle scattering amplitudes at strong value of the 't Hooft coupling in planar maximally supersymmetric Yang–Mills theory. We complement recent studies of this observable within the context of the Pentagon Operator Product Expansion, via the dual superWilson loop description, by studying effects of multiple scalar exchanges that accompany (or not) massive flux-tube excitations. Due to the fact that holes have a very small, nonperturbatively generated mass m_h which is exponentially suppressed in the 't Hooft coupling, their exchanges must be resummed in the ultraviolet limit, T <<1/m_h. This procedure yields a contribution to the expectation value of the superloop which enters on equal footing with the classical area — a phenomenon which was earlier observed for MHV amplitudes. In all components, the near-massless scalar exchanges factorize from the ones of massive particles, at leading order in strong coupling.

Scattering amplitudes in maximally supersymmetric gauge theory receive a dual description in terms of the expectation value of the super Wilson loop stretched on a null polygonal contour. This makes the analysis amenable to nonperturbative techniques. Presently, we elaborate on a refined form of the operator product expansion in terms of pentagon transitions to compute twist-two contributions to NMHV amplitudes. To start with, we provide a novel derivation of scattering matrices starting from Baxter equations for flux-tube excitations propagating on magnon background. We propose bootstrap equations obeyed by pentagon form factors with nonsinglet quantum numbers with respect to the R-symmetry group and provide solutions to them to all orders in 't Hooft coupling. These are then successfully confronted against available perturbative calculations for NMHV amplitudes to four-loop order.

We address the near-collinear expansion of multiparticle NMHV amplitudes, namely, the heptagon and octagons in the dual language of null polygonal super Wilson loops. In particular, we verify multiparticle factorization of charged pentagon transitions in terms of pentagons for single flux-tube excitations within the framework of refined operator product expansion. We find a perfect agreement with available tree and one-loop data.

Scattering amplitudes in maximally supersymmetric gauge theory are dual to super-Wilson loops on null polygonal contours. The operator product expansion for the latter revealed that their dynamics is governed by the evolution of multiparticle GKP excitations. They were shown to emerge from the spectral problem of an underlying open spin chain. In this work we solve this model with the help of the Baxter Q-operator and Sklyanin's Separation of Variables methods. We provide an explicit construction for eigenfunctions and eigenvalues of GKP excitations. We demonstrate how the former define the so-called multiparticle hexagon transitions in super-Wilson loops and prove their factorized form at leading order of 't Hooft coupling for particle number-preserving transitions that were suggested earlier in a generic case.

We compute one-loop renormalization group equations for non-singlet twist-four operators in QCD. The calculation heavily relies on the light-cone gauge formalism in the momentum fraction space that essentially rephrases the analysis of all two-to-two and two-to-three transition kernels to purely algebraic manipulations both for non- and quasipartonic operators. This is the first brute force calculation of this sector available in the literature. Fourier transforming our findings to the coordinate space, we checked them against available results obtained within a conformal symmetry-based formalism that bypasses explicit diagrammatic calculations and confirmed agreement with the latter.

Chronic manganese (Mn) exposure is associated with neuromotor and neurocognitive deficits, but the exact mechanism of Mn neurotoxicity is still unclear. With the advent of magnetic resonance imaging (MRI), in-vivo analysis of brain structures has become possible. Among different sub-cortical structures, the basal ganglia (BG) has been investigated as a putative anatomical biomarker in MR-based studies of Mn toxicity. However, previous investigations have yielded inconsistent results in terms of regional MR signal intensity changes. These discrepancies may be due to the subtlety of brain alterations caused by Mn toxicity, coupled to analysis techniques that lack the requisite detection power. Here, based on brain MRI, we apply a 3D surface-based morphometry method on 3 bilateral basal ganglia structures in school-age children chronically exposed to Mn through drinking water to investigate the effect of Mn exposure on brain anatomy. Our method successfully pinpointed significant enlargement of many areas of the basal ganglia structures, preferentially affecting the putamen. Moreover, these areas showed significant correlations with fine motor performance, indicating a possible link between altered basal ganglia neurodevelopment and declined motor performance in high Mn exposed children.

The apolipoprotein E (APOE) e4 allele is the most prevalent genetic risk factor for Alzheimer's disease (AD). Hippocampal volumes are generally smaller in AD patients carrying the e4 allele compared to e4 noncarriers. Here we examined the effect of APOE e4 on hippocampal morphometry in a large imaging database—the Alzheimer's Disease Neuroimaging Initiative (ADNI). We automatically segmented and constructed hippocampal surfaces from the baseline MR images of 725 subjects with known APOE genotype information including 167 with AD, 354 with mild cognitive impairment (MCI), and 204 normal controls. High-order correspondences between hippocampal surfaces were enforced across subjects with a novel inverse consistent surface fluid registration method. Multivariate statistics consisting of multivariate tensor-based morphometry (mTBM) and radial distance were computed for surface deformation analysis. Using Hotelling's T2 test, we found significant morphological deformation in APOE e4 carriers relative to noncarriers in the entire cohort as well as in the nondemented (pooled MCI and control) subjects, affecting the left hippocampus more than the right, and this effect was more pronounced in e4 homozygotes than heterozygotes. Our findings are consistent with previous studies that showed e4 carriers exhibit accelerated hippocampal atrophy; we extend these findings to a novel measure of hippocampal morphometry. Hippocampal morphometry has significant potential as an imaging biomarker of early stage AD.

The apolipoprotein E (APOE) e4 genotype is a powerful risk factor for late-onset Alzheimer’s disease (AD). In the Alzheimer’s Disease Neuroimaging Initiative (ADNI) cohort, we previously reported significant baseline structural differences in APOE e4 carriers relative to non-carriers, involving the left hippocampus more than the right—a difference more pronounced in e4 homozygotes than heterozygotes. We now examine the longitudinal effects of APOE genotype on hippocampal morphometry at 6-, 12- and 24-months, in the ADNI cohort. We employed a new automated surface registration system based on conformal geometry and tensor-based morphometry. Among different hippocampal surfaces, we computed high-order correspondences, using a novel inverse-consistent surface-based fluid registration method and multivariate statistics consisting of multivariate tensor-based morphometry (mTBM) and radial distance. At each time point, using Hotelling’s T² test, we found significant morphological deformation in APOE e4 carriers relative to non-carriers in the full cohort as well as in the non-demented (pooled MCI and control) subjects at each follow-up interval. In the complete ADNI cohort, we found greater atrophy of the left hippocampus than the right, and this asymmetry was more pronounced in e4 homozygotes than heterozygotes. These findings, combined with our earlier investigations, demonstrate an e4 dose effect on accelerated hippocampal atrophy, and support the enrichment of prevention trial cohorts with e4 carriers.