MIT Center for Theoretical Physics – a Leinweber Institute

We study two-point functions of half-BPS operators in maximally supersymmetric Yang-Mills theory continued to $d=4-2\,\varepsilon$ dimensions. Using supersymmetric localization on $S^d$, we derive perturbative matrix-model expressions for the $\varepsilon$-expansion of these correlators and obtain all-loop results at leading order in $\varepsilon$ in the planar limit, with extensions to finite-$N$ corrections and higher-charge operators. We compare the localization results with direct perturbative computations in flat space. At order $\varepsilon$ the two descriptions agree perfectly, while at higher orders our construction fails to reproduce the perturbative data due to the breaking of conformal symmetry away from four dimensions. Nevertheless, in the case of the dimension-two operator we conjecture an all-loop formula at order $\varepsilon^2$ by exploiting the precise form of the mismatch.

A principal lesson from recreating droplets of quark-gluon plasma (QGP) in heavy ion collisions is that it is a strongly coupled liquid, not a plasma of partons. The energy density and pressure of quarks and gluons confined within a proton are comparable to those of QGP at or just above the QCD transition temperature. Given this similarity between protons and QGP, we propose that the investigation of correlations between nearby partons within a proton must be a central goal for the future Electron-Ion Collider (EIC). Here, we ask how EIC measurements can discern such short-range correlations (SRCs) of quark pairs. Doing so would characterize the strongly coupled interior of a proton, augmenting the one-parton-at-a-time understanding of protons via (generalized) parton distribution functions, and could at the same time yield a key ingredient for the microscopic understanding of the liquid nature of QGP. Motivated by the experiments that have been used to demonstrate the existence of SRCs between nucleon pairs within a nucleus, we propose using EIC observables involving measurements of a jet and a pion, together with the scattered electron, to seek and quantify the possible existence of SRCs between quark pairs within a nucleon. The pronounced isospin dependence observed in the dominance of $np$ SRCs over $pp$ or $nn$ SRCs has played a central role in establishing the importance of SRCs among nucleons in nuclei. Analogously, the QCD attraction in the $ud$ diquark channel can make the $ud$ SRC stronger than the $uu$ and $dd$ SRCs, allowing a first observation of partonic SRCs.

Coulomb-gauge quasi-parton distributions can be computed directly in momentum space on a finite lattice, enabled by the commutativity of their renormalization and Fourier transform. This approach removes the formal inverse problem in coordinate-space methods. Our momentum-space pion quasi-distributions agree with coordinate-space results Fourier transformed with asymptotic extrapolation, indicating that the formal inverse problem in the latter is not a concern at this volume. We further extend the framework to higher dimensions and obtain the first 3D image of the pion directly from lattice QCD.

The generating functional in quantum field theory provides the natural framework for constructing correlation functions as derivatives with respect to source operators. We present a methodology that leverages machine-learned normalizing flows to reduce the variance of arbitrary $N$-point correlation functions of bosonic operators in lattice gauge field theory calculations by encoding a representation of the generating functional. We show that it is possible to systematically approach noiseless estimators of correlation functions in this framework. We demonstrate this methodology with applications to calculations of glueball correlation functions and Wilson loops in Quantum Chromodynamics and Yang-Mills theory. The results show up to three orders of magnitude variance reduction.