MIT Center for Theoretical Physics – a Leinweber Institute

We introduce a procedure called random dimension reduction that simultaneously reduces the dimensions of many, potentially distinct quantum states while preserving properties invariant under the tensor power action of an isometry. This provides a black-box method to replace the dimension with the maximum rank in the sample complexity of learning symmetric properties, even those depending on multiple input states. We show that dimension reduction followed by full state tomography yields improved upper bounds for estimating distances, fidelities, and relative entropies between pairs of states. We also give an efficient quantum circuit implementation of the procedure using the Schur transform. Expressing the action of our procedure through the Choi-Jamiolkowski isomorphism reveals an intimate connection with the recently introduced random purification channel by Tang, Wright, and Zhandry. This perspective also completes an end-to-end analysis of sample-optimal tomography without requiring a reference to the Schur transform or Schur polynomials. Finally, we prove that there does not exist a random purification channel that simultaneously purifies copies of multiple, potentially different input states. Hence, random dimension reduction is related to, but distinct from, random purification.

We introduce the \emph{Centauric 1-jettiness}, $τ_1^C$, a generalized event shape for Deep Inelastic Scattering (DIS) with adjustable beam and jet reference vectors and thus beam and jet regions. We demonstrate that a specific choice of weights allows this observable to exactly reproduce the geometric boundaries of the Centauro jet algorithm in the Breit frame. Within the framework of Soft-Collinear Effective Theory (SCET), we derive a factorized cross section in the small-$τ_1^C$ region in terms of known perturbative ingredients. This allows the resummation of large logarithms to N$^3$LL accuracy, which we then match to fixed-order NLO QCD ($\mathcal{O}(α_s^2)$) predictions from \texttt{NLOJet++}. We establish that the soft measurement reduces to a rescaled hemisphere measurement, placing Centauric 1-jettiness in the same universality class, for the leading non-perturbative corrections, as DIS thrust and jet mass. As a consequence, the leading non-perturbative shift depends on the same universal first-moment-shift parameter $Ω_1$ and scales exactly as $1/R$ with the jet radius, thanks to the boost invariance of the Centauro algorithm along the photon axis in the Breit frame, a scaling that we test using \textsc{Pythia} simulations. These results open new strategies for determining the strong coupling from DIS event shapes, with $R$ providing a handle to break the degeneracy between $α_s$ and the universal non-perturbative shift parameter $Ω_1$.

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.