Large Limit Research Articles

Inclusive J/ψ production in forward proton-proton and proton-lead collisions at high energy

We calculate the cross section for forward J/ψ production in proton-proton and minimum bias proton-lead collisions using the color glass condensate (CGC) and nonrelativistic QCD (NRQCD) formalism consistently with deep inelastic scattering data. The cross section for color singlet states is sensitive to a four-point correlator of Wilson lines for which we describe in the Gaussian approximation in the large-Nc limit. Furthermore, we quantify the importance of finite-Nc corrections to have a small ∼12% effect. In contrast with the generic NRQCD expectation, we show that the color singlet contribution is only 15% to the total cross section. We also compare our predictions for J/ψ production as well as for the nuclear modification ratio RpPb to LHCb and ALICE data. We find a good agreement at forward rapidities, except at low transverse momenta where the cross sections are overestimated. Published by the American Physical Society 2024

Electromagnetic duality for line defect correlators in $$ \mathcal{N} $$ = 4 super Yang-Mills theory

Abstract We study particular integrated correlation functions of two superconformal primary operators of the stress tensor multiplet in the presence of a half-BPS line defect labelled by electromagnetic charges (p, q) in $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory (SYM) with gauge group SU(N). An important consequence of SL(2, ℤ) electromagnetic duality in $$ \mathcal{N} $$ N = 4 SYM is that correlators of line defect operators with different charges (p, q) must be related in a non-trivial manner when the complex coupling τ = θ/(2π) + $$ 4\pi i/{g}_{\textrm{YM}}^2 $$ 4 πi / g YM 2 is transformed appropriately. In this work we introduce a novel class of real-analytic functions whose automorphic properties with respect to SL(2, ℤ) match the expected transformations of line defect operators in $$ \mathcal{N} $$ N = 4 SYM under electromagnetic duality. At large N and fixed τ, the correlation functions we consider are related to scattering amplitudes of two gravitons from extended (p, q)-strings in the holographic dual type IIB superstring theory. We show that the large-N expansion coefficients of the integrated two-point line defect correlators are given by finite linear combinations with rational coefficients of elements belonging to this class of automorphic functions. On the other hand, for any fixed value of N we conjecture that the line defect integrated correlators can be expressed as formal infinite series over such automorphic functions. The resummation of this series produces a simple lattice sum representation for the integrated line defect correlator that manifests its automorphic properties. We explicitly demonstrate this construction for the cases with gauge group SU(2) and SU(3). Our results give direct access to non-perturbative integrated correlators in the presence of an ’t Hooft-line defect, observables otherwise very difficult to compute by other means.

Spontaneous symmetry breaking in two dimensions under non-equilibrium laminar flows

Abstract We study the long-range order in two dimensions, where an order parameter is advected by laminar flows such as rotational, shear and elongational flows. Under these flows, we analyze the ordered state of the O(N) scalar model in the large-N limit. We show that the stability of the ordered state depends on the flow pattern; shear and elongational flows stabilize the long-range order but rotational flow does not. We discuss the physical mechanism underlying our results by connecting static correlations between fluctuations and their dynamics based on the interaction representation used in quantum mechanics. We find that advective transport induces superdiffusion under shear and elongational flows, thereby stabilizing the long-range order.

Enhancing Bias Assessment for Complex Term Groups in Language Embedding Models: Quantitative Comparison of Methods.

Artificial intelligence (AI) is rapidly being adopted to build products and aid in the decision-making process across industries. However, AI systems have been shown to exhibit and even amplify biases, causing a growing concern among people worldwide. Thus, investigating methods of measuring and mitigating bias within these AI-powered tools is necessary. In natural language processing applications, the word embedding association test (WEAT) is a popular method of measuring bias in input embeddings, a common area of measure bias in AI. However, certain limitations of the WEAT have been identified (ie, their nonrobust measure of bias and their reliance on predefined and limited groups of words or sentences), which may lead to inadequate measurements and evaluations of bias. Thus, this study takes a new approach at modifying this popular measure of bias, with a focus on making it more robust and applicable in other domains. In this study, we introduce the SD-WEAT, which is a modified version of the WEAT that uses the SD of multiple permutations of the WEATs to calculate bias in input embeddings. With the SD-WEAT, we evaluated the biases and stability of several language embedding models, including Global Vectors for Word Representation (GloVe), Word2Vec, and bidirectional encoder representations from transformers (BERT). This method produces results comparable to those of the WEAT, with strong correlations between the methods' bias scores or effect sizes (r=0.786) and P values (r=0.776), while addressing some of its largest limitations. More specifically, the SD-WEAT is more accessible, as it removes the need to predefine attribute groups, and because the SD-WEAT measures bias over multiple runs rather than one, it reduces the impact of outliers and sample size. Furthermore, the SD-WEAT was found to be more consistent and reliable than its predecessor. Thus, the SD-WEAT shows promise for robustly measuring bias in the input embeddings fed to AI language models.

Worldvolume fermions as baryons in holographic quantum chromodynamics with instantons

In this study, we investigated worldvolume fermions on the flavor brane in the D0–D4/D8 model, which is holographically equivalent to four-dimensional quantum chromodynamics with instantons or equivalently with a theta angle. The action involving the worldvolume fermions was obtained by the T-duality rules in string theory, and we accordingly derived their effective five-dimensional and canonical four-dimensional forms by using the systematic dimensional reduction and decomposition of the spinor. Subsequently, we used the AdS/CFT dictionary to evaluate the two-point correlation function as the spectral function for the worldvolume fermions and interpreted the fermions as baryons by analyzing their quantum number with the baryon vertex in holography. In this sense, the interacted action involving the worldvolume fermions and gauge field on the flavor brane was finally derived in holography, which describes the various interactions of mesons and baryons with instantons in the large-N limit. Therefore, this study provides a holographic picture to describe baryons and their interactions based on string theory, particularly in the presence of instantons or a theta angle.

Characteristics of applicants with a first-time recognition of need for long-term care

Abstract Background The increasing number of care-dependent individuals requires approaches to prevent care dependency or reduce loss of independence. Long-term care assessments can provide valuable insights into this. In Germany, the Medical Service is responsible for the long-term care assessment (care level) that focuses on limitations in independent living. Objectives The aim of this contribution is to describe initial applicants with identified need for long-term care. Materials and methods The nationwide database consists of long-term care assessments conducted by the German Medical Service of health insured people aged 60 and above who received a care level (1=smallest till 5= largest limitations) for the first time in 2021. Long-term care-relevant information is analyzed descriptively. Results 339,486 individuals with an average age of 79.6 years (SD: 8.4) were analyzed. The age distribution shows that the 80-89 age group comprises half of the sample (49.9%), whereas those aged 90+ encompass the smallest proportion of the sample (9.3%). More women than men received a care level (59.0% women vs. 41.0% men), with women predominant in care level 1-2 and men in the higher care level 3-5. Overall, approximately half of the sample received care level 2, 32.4 % received care level 1. Care levels 3-5 were assessed less frequently (16.2 % vs. 4.8 % vs. 1.7 %). The most frequent care-relevant diagnoses were senility (R54), polyarthrosis (M15), and dementia (F03). Conclusions Over three quarters of initial applicants are classified into the lowest care levels (1 and 2). Accordingly, tertiary prevention measures are recommended, as these may delay the further progression into a higher care level. Key messages • Over three quarters of initial applicants for long-term care are classified into the lowest care levels. Accordingly, tertiary prevention measures may recommended to delay further care progression. • The most frequent care-relevant diagnoses were senility (R54), polyarthrosis (M15), and dementia (F03).

Hyperbolic Lattices and Two-Dimensional Yang-Mills Theory.

Hyperbolic lattices are a new type of synthetic quantum matter emulated in circuit quantum electrodynamics and electric-circuit networks, where particles coherently hop on a discrete tessellation of two-dimensional negatively curved space. While real-space methods and a reciprocal-space hyperbolic band theory have been recently proposed to analyze the energy spectra of those systems, discrepancies between the two sets of approaches remain. In this work, we reconcile those approaches by first establishing an equivalence between hyperbolic band theory and U(N) topological Yang-Mills theory on higher-genus Riemann surfaces. We then show that moments of the density of states of hyperbolic tight-binding models correspond to expectation values of Wilson loops in the quantum gauge theory and become exact in the large-N limit.

Dimer piling problems and interacting field theory

The dimer tiling problem asks in how many ways can the edges of a graph be covered by dimers so that each site is covered once. In the special case of a planar graph, this problem has a solution in terms of a free fermionic field theory. We rediscover and explore an expression for the number of coverings of an arbitrary graph by arbitrary objects in terms of an interacting fermionic field theory first proposed by Samuel. Generalizations of the dimer tiling problem, which we call “dimer piling problems,” demand that each site be covered N times by indistinguishable dimers. Our field theory provides a solution of these problems in the large-N limit. We give a similar path integral representation for certain lattice coloring problems. Published by the American Physical Society 2024

Spin-orbit correlations in the nucleon in the large- Nc limit

We study the twist-3 spin-orbit correlations of quarks described by the nucleon matrix elements of the parity-odd rank-2 tensor QCD operator (the parity-odd partner of the QCD energy-momentum tensor). Our treatment is based on the effective dynamics emerging from the spontaneous breaking of chiral symmetry and the mean-field picture of the nucleon in the large-Nc limit. The twist-3 QCD operators are converted to effective operators, in which the QCD interactions are replaced by spin-flavor-dependent chiral interactions of the quarks with the pion field. We compute the nucleon matrix elements of the twist-3 effective operators and discuss the role of the chiral interactions in the spin-orbit correlations. We derive the first-quantized representation in the mean-field picture and develop a quantum-mechanical interpretation. The chiral interactions give rise to new spin-orbit couplings and qualitatively change the correlations compared to the quark model picture. We also derive the twist-3 matrix elements in the topological soliton picture where the quarks are integrated out (skyrmion). The methods used here can be extended to other QCD operators describing higher-twist nucleon structure and generalized parton distributions. Published by the American Physical Society 2024

Chiral-odd GPDs in the bag model

A study of chiral-odd generalized parton distributions (GPDs) of the nucleon is presented in the bag model demonstrating that in this model all four chiral-odd GPDs are nonzero contrary to other claims in literature. The bag model results for the GPDs HTq(x,ξ,t), ETq(x,ξ,t), H˜Tq(x,ξ,t) agree with other models within a typical quark model accuracy. We present one of the few quark model calculations where polynomiality is satisfied and the sum rule ∫dxE˜Tq(x,ξ,t)=0 holds. We confront our results with predictions from the large-Nc limit, and with lattice QCD calculations. We conclude that the bag model successfully catches the main features of chiral-odd GPDs. Published by the American Physical Society 2024

Non-invertible symmetries in SN orbifold CFTs and holography

We study non-invertible defects in two-dimensional SN orbifold CFTs. We construct universal defects which do not depend on the details of the seed CFT and hence exist in any orbifold CFT. Additionally, we investigate non-universal defects arising from the topological defects of the seed CFT. We argue that there exist universal defects that are non-trivial in the large-N limit, making them relevant for the AdS3/CFT2 correspondence. We then focus on AdS3×S3 × M4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{M}}_4 $$\\end{document} with one unit of NS-NS flux and propose an explicit realization of these defects on the worldsheet.

An intriguing connection between Pisarski's fixed point and (2 + 3)-spin glasses

This paper aims to establish a connection between Pisarski's fixed point and a (2+3)-spin-glass model with sextic confinement potential. This is made possible by the unconventional power-counting induced by the effective kinetics provided by the disorder coupling in the large N-limit. Because of the absence of epsilon expansion, our approach is more attractive than the previous one. It may be relevant to the signal detection issue in nearly continuous spectra.

On Dunkl-Bose-Einstein Condensation in Harmonic Traps

The use of the Dunkl derivative, defined by a combination of the difference-differential and reflection operators, allows the classification of the solutions according to even and odd solutions. Recently, we considered the Dunkl formalism to investigate the Bose-Einstein condensation of an ideal Bose gas confined in a gravitational field. In this work, we address another essential problem and examine an ideal Bose gas trapped by a three-dimensional harmonic oscillator within the Dunkl formalism. To this end, we derive an analytic expression for the critical temperature of the N particle system, discuss its value at large-N limit andfinally derive and compare the ground state population with the usual case result. In addition, we explore two thermal quantities, namely the Dunkl-internal energy and the Dunkl-heat capacity functions.

Three Cases of Complex Eigenvalue/Vector Distributions of Symmetric Order-Three Random Tensors

Abstract Random tensor models have applications in a variety of fields, such as quantum gravity, quantum information theory, mathematics of modern technologies, etc., and studying their statistical properties, e.g. tensor eigenvalue/vector distributions, is interesting and useful. Recently some tensor eigenvalue/vector distributions have been computed by expressing them as partition functions of 0D quantum field theories. In this paper, using this method, we compute three cases of complex eigenvalue/vector distributions of symmetric order-three random tensors, where the three cases can be characterized by the Lie-group invariances, $O(N,\mathbb {R})$, $O(N,\mathbb {C})$, and $U(N,\mathbb {C})$, respectively. Exact closed-form expressions of the distributions are obtained by computing partition functions of four-fermi theories, where the last case is of the “signed” distribution, which counts the distribution with a sign factor coming from a Hessian matrix. As an application, we compute the injective norm of the complex symmetric order-three random tensor in the large-N limit by computing the edge of the last signed distribution, obtaining agreement with an earlier numerical result in the literature.

Celestial Dual for Maximal Helicity Violating Amplitudes.

It is shown that a 2D conformal field theory consisting of a central charge c Liouville theory, a chiral level one, rank N Kac-Moody algebra, and a weight -3/2 free fermion holographically generate 4D maximal helicity violating tree-level scattering amplitudes. The correlators of this 2D conformal field theory give directly the 4D leaf amplitudes associated to a single hyperbolic slice of flat space. The 4D celestial amplitudes arise in a large-N and semiclassical large-c limit, according to the holographic dictionary, as a translationally invariant combination of leaf amplitudes. A step in the demonstration is showing that the semiclassical limit of Liouville correlators are given by contact 3D anti-de Sitter Witten diagrams.

Confining strings in three-dimensional gauge theories beyond the Nambu-Gotō approximation

We carry out a systematic study of the effective bosonic string describing confining flux tubes in SU(N) Yang-Mills theories in three spacetime dimensions. While their low-energy properties are known to be universal and are described well by the Nambu-Gotō action, a non-trivial dependence on the gauge group is encoded in a series of undetermined subleading corrections in an expansion around the limit of an arbitrarily long string. We quantify the first two of these corrections by means of high-precision Monte Carlo simulations of Polyakov-loop correlators in the lattice regularization. We compare the results of novel lattice simulations for theories with N = 3 and 6 color charges, and report an improved estimate for the N = 2 case, discussing the approach to the large-N limit. Our results are compatible with analytical bounds derived from the S-matrix bootstrap approach. In addition, we also present a new test of the Svetitsky-Yaffe conjecture for the SU(3) theory in three dimensions, finding that the lattice results for the Polyakov-loop correlation function are in excellent agreement with the predictions of the Svetitsky-Yaffe mapping, which are worked out quantitatively applying conformal perturbation theory to the three-state Potts model in two dimensions. The implications of these results are discussed.

Low-energy theorem revisited and OPE in massless QCD

We revisit a low-energy theorem (LET) of NSVZ type in SU(N) QCD with Nf massless quarks derived in [1] by implementing it in dimensional regularization. The LET relates n-point correlators in the l.h.s. to n + 1-point correlators with the extra insertion of TrF2 at zero momentum in the r.h.s. We demonstrate that, for 2-point correlators of an operator O in the l.h.s., the LET implies that, in general, the integrated 3-point correlator in the r.h.s. needs in perturbation theory an infinite additive renormalization in addition to the multiplicative one. We relate the above counterterm to a corresponding divergent contact term in a certain coefficient of the OPE of TrF2 with O in the momentum representation, thus extending to any operator O an independent argument that first appeared for O = TrF2 in [2]. Finally, we demonstrate that in the asymptotically free phase of QCD the aforementioned counterterm in the LET is actually finite nonperturbatively after resummation to all perturbative orders. We also briefly recall the implications of the LET in the gauge-invariant framework of dimensional regularization for the perturbative and nonperturbative renormalization in large-N QCD. The implications of the LET inside and above the conformal window of SU(N) QCD with Nf massless quarks will appear in a forthcoming paper.

A Scaling Relation, Zm-Type Deconfinement Phases, and Imaginary Chemical Potentials in Finite Temperature Large-N Gauge Theories

Abstract We show that the effective potentials for the Polyakov loops in finite temperature SU$(N)$ gauge theories obey a certain scaling relation with respect to temperature in the large-N limit. This scaling relation strongly constrains the possible terms in the Polyakov loop effective potentials. Moreover, by using the effective potentials in the presence of imaginary chemical potentials or imaginary angular velocities in several models, we find that phase transitions to $Z_m$-type deconfinement phases ($Z_m$ phase) occur, where the eigenvalues of the Polyakov loop are distributed $Z_m$ symmetrically. Physical quantities in the $Z_m$ phase obey the scaling properties of the effective potential. The models include Yang–Mills (YM) theories, the bosonic BFSS matrix model, and ${\mathcal {N}}=4$ supersymmetric YM theory on $S^3$. Thus, the phase diagrams of large-N gauge theories with imaginary chemical potentials are very rich and the stable $Z_m$ phase would be ubiquitous. Monte-Carlo calculations also support this. As a related topic, we discuss the phase diagrams of large-N YM theories with real angular velocities in finite volume spaces.

Coupling renormalization flow in the strongly interacting regime of an asymptotically free quantum field theory in four dimensions

We consider a scalar quantum field theory with global O(N)3 symmetry in four Euclidean dimensions and solve it numerically in closed form in the large-N limit. For imaginary tetrahedral coupling the theory is asymptotically free, with stable and real quantum effective action. We demonstrate the dynamical build-up of a strong interaction as the correlation length increases in a regime where the coupling renormalization flow remains well defined in the infrared. This is in contrast to perturbative results of asymptotically free theories, which predict that the coupling becomes ill defined in the infrared, like in quantum chromodynamics. These properties make the model an important laboratory for the study of strong-coupling phenomena in quantum field theory from first principles. Published by the American Physical Society 2024

Large-N integrated correlators in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM: when resurgence meets modularity

Exact expressions for certain integrated correlators of four half-BPS operators in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 supersymmetric Yang-Mills theory with gauge group SU(N) have been recently obtained thanks to a beautiful interplay between supersymmetric localisation and modular invariance. The large-N expansion at fixed Yang-Mills coupling of such integrated correlators produces an asymptotic series of perturbative terms, holographically related to higher derivative interactions in the low energy expansion of the type IIB effective action, as well as exponentially suppressed corrections at large N, interpreted as contributions from coincident (p, q)-string world-sheet instantons. In this work we define a manifestly modular invariant Borel resummation of the perturbative large-N expansion of these integrated correlators, from which we extract the exact non-perturbative large-N sectors via resurgence analysis. Furthermore, we show that in the ’t Hooft limit such modular invariant non-perturbative completions reduce to known resurgent genus expansions. Finally, we clarify how the same non-perturbative data is encoded in the decomposition of the integrated correlators based on SL(2, ℤ) spectral theory.