N-point Correlation Research Articles

Towards complexity in de Sitter space from the doubled-scaled Sachdev-Ye-Kitaev model

How can we define complexity in dS space from microscopic principles? Based on recent developments pointing towards a correspondence between a pair of double-scaled Sachdev-Ye-Kitaev (DSSYK) models/ 2D Liouville-de Sitter (LdS2) field theory/ 3D Schwarzschild de Sitter (SdS3) space in [1–3], we study concrete complexity proposals in the microscopic models and their dual descriptions. First, we examine the spread complexity of the maximal entropy state of the doubled DSSYK model. We show that it counts the number of entangled chord states in its doubled Hilbert space. We interpret spread complexity in terms of a time difference between antipodal observers in SdS3 space, and a boundary time difference of the dual LdS2 CFTs. This provides a new connection between entanglement and geometry in dS space. Second, Krylov complexity, which describes operator growth, is computed for physical operators on all sides of the correspondence. Their late time evolution behaves as expected for chaotic systems. Later, we define the query complexity in the LdS2 model as the number of steps in an algorithm computing n-point correlation functions of boundary operators of the corresponding antipodal points in SdS3 space. We interpret query complexity as the number of matter operator chord insertions in a cylinder amplitude in the DSSYK, and the number of junctions of Wilson lines between antipodal static patch observers in SdS3 space. Finally, we evaluate a specific proposal of Nielsen complexity for the DSSYK model and comment on its possible dual manifestations.

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.

C3NN: Cosmological Correlator Convolutional Neural Network an Interpretable Machine-learning Framework for Cosmological Analyses

Modern cosmological research in large-scale structure has witnessed an increasing number of machine-learning applications. Among them, convolutional neural networks (CNNs) have received substantial attention due to their outstanding performance in image classification, cosmological parameter inference, and various other tasks. However, many models based on CNNs are criticized as “black boxes” due to the difficulties in relating their outputs intuitively and quantitatively to the cosmological fields under investigation. To overcome this challenge, we present the Cosmological Correlator Convolutional Neural Network (C3NN)—a fusion of CNN architecture and cosmological N-point correlation functions (NPCFs). We demonstrate that its output can be expressed explicitly in terms of the analytically tractable NPCFs. Together with other auxiliary algorithms, we can open the “black box” by quantitatively ranking different orders of the interpretable outputs based on their contribution to classification tasks. As a proof of concept, we demonstrate this by applying our framework to a series of binary classification tasks using Gaussian and log-normal random fields and relating its outputs to the NPCFs describing the two fields. Furthermore, we exhibit the model’s ability to distinguish different dark energy scenarios (w 0 = −0.95 and −1.05) using N-body simulated weak-lensing convergence maps and discuss the physical implications coming from their interpretability. With these tests, we show that C3NN combines advanced aspects of machine learning architectures with the framework of cosmological NPCFs, thereby making it an exciting tool to extract physical insights in a robust and explainable way from observational data.

Full shape cosmology analysis from BOSS in configuration space using neural network acceleration

Recently, a new wave of full modeling analyses have emerged within the Large-Scale Structure community, leading mostly to tighter constraints on the estimation of cosmological parameters, when compared with standard approaches used over the last decade by collaboration analyses of stage III experiments. However, the majority of these full-shape analyses have primarily been conducted in Fourier space, with limited emphasis on exploring the configuration space. Investigating n-point correlations in configuration space demands a higher computational cost compared to Fourier space because it typically requires an additional integration step. This can pose a limitation when using these approaches, especially when considering higher-order statistics. One avenue to mitigate the high computation time is to take advantage of neural network acceleration techniques. In this work, we present a full shape analysis of Sloan Digital Sky Survey III/BOSS in configuration space using a neural network accelerator. We show that the efficacy of the pipeline is enhanced by a time factor 103 without sacrificing precision, making it possible to reduce the error associated with the surrogate modeling to below 10-2 percent which is compatible with the precision required for current stage IV experiments such as DESI. We find Ω m = 0.286±0.009, H 0 = 68.8±1.2 kms-1Mpc-1 and A s × 109 = 2.09 +0.25 -0.29. Our results on public BOSS data are in good agreement with BOSS official results and compatible with other independent full modeling analyses. We explore relaxing the prior on ωb and varying ns , without significant changes in the mean values of the cosmological parameters posterior distributions, but enlarging their widths. Finally, we explore the information content of the multipoles when constraining cosmological parameters.

Effective potential in finite formulation of QFT

In recent works [1,2], we have shown how n-point correlation functions in perturbative QFT can be computed without running into intermediate divergences. Here we want to illustrate explicitly that one can calculate the quantum effective potential by the same method. As a main example, we consider a theory with two fields having large and small vacuum expectation values (vev). We show that no fine-tuning between the physical quantities is needed to keep the hierarchy between the vevs of different fields.

Algorithm to Produce a Density Field with Given Two, Three, and Four-Point Correlation Functions

Abstract Here we show how to produce a 3D density field with a given set of higher-order correlation functions. Our algorithm enables producing any desired two-point, three-point, and four-point functions, including odd-parity for the latter. We note that this algorithm produces the desired correlations about a set of “primary” points, matched to how the spherical-harmonic-based algorithms ENCORE and CADENZA measure them. These “primary points” must be used as those around which the correlation functions are measured. We also generalize the algorithm to i) N-point correlations with N > 4, ii) dimensions other than 3, and iii) beyond scalar quantities. This algorithm should find use in verifying analysis pipelines for higher-order statistics in upcoming galaxy redshift surveys such as DESI, Euclid, Roman, and Spherex, as well as intensity mapping. In particular it may be helpful in searches for parity violation in the 4PCF of these samples, for which producing initial conditions for N-body simulations is both costly and highly model-dependent at present, and so alternative methods such as that developed here are desirable.

Exact evaluation of large-charge correlation functions in nonrelativistic conformal field theory

The large-charge master field which generates all n-point correlation functions with an insertion of large charge Q in nonrelativistic conformal field theory is obtained. This field is used to compute Schrödinger-invariant n-point correlation functions of large-charge operators via a direct evaluation of the path integral. Conformal dimensions are found to agree with calculations based on the state-operator correspondence. The master field solution exhibits an emergent harmonic trap whose frequency is a function of the Euclidean time. The large-charge effective action with operator insertions describes a droplet of superfluid matter whose spatial size scales with the time separation of sources. The solution is used to compute Schrödinger symmetry breaking corrections in the large-charge effective field theory (EFT) due to a finite scattering length in the fundamental theory of fermions near unitarity. The scaling of these effects in the large-charge power counting scheme is established, and the size of the effects is quantified using input from quantum Monte Carlo simulations of the near-unitary gas, as well as from the large-N expansion at large charge. Published by the American Physical Society 2024

Polyakov loop models in the large N limit: Correlation function and screening masses

We explore the ’t Hooft-Veneziano limit of the Polyakov loop models at finite baryon chemical potential. Using methods developed by us earlier we calculate the two- and N-point correlation functions of the Polyakov loops. This gives a possibility to compute the various potentials in the confinement phase and to derive the screening masses outside the confinement region. In particular, we establish the existence of complex masses and an oscillating decay of correlations in a certain range of parameters. Furthermore, it is shown that the calculation of the N-point correlation function in the confinement phase reduces to the geometric median problem. This leads to a large N analog of the Y law for the baryon potential. Published by the American Physical Society 2024

Robust Measurements of n-Point Correlation Functions of Driven-Dissipative Quantum Systems on a Digital Quantum Computer.

We propose and demonstrate a unified hierarchical method to measure n-point correlation functions that can be applied to driven, dissipative, or otherwise open or nonequilibrium quantum systems. In this method, the time evolution of the system is repeatedly interrupted by interacting an ancilla qubit with the system through a controlled operation, and measuring the ancilla immediately afterward. We discuss the robustness of this method as compared to other ancilla-based interferometric techniques (such as the Hadamard test), and highlight its advantages for near-term quantum simulations of open quantum systems. We implement the method on a quantum computer in order to measure single-particle Green's functions of a driven-dissipative fermionic system. This Letter shows that dynamical correlation functions for driven-dissipative systems can be robustly measured with near-term quantum computers.

Exploring the non-Gaussianity of the cosmic infrared background and its weak gravitational lensing

ABSTRACT Gravitational lensing deflects the paths of photons, altering the statistics of cosmic backgrounds and distorting their information content. We take the cosmic infrared background (CIB), which provides plentiful information about galaxy formation and evolution, as an example to probe the effect of lensing on non-Gaussian statistics. Using the Websky simulations, we first quantify the non-Gaussianity of the CIB, revealing additional detail on top of its well-measured power spectrum. To achieve this, we use needlet-like multipole-band filters to calculate the variance and higher-point correlations. Using our simulations, we show the two-, three- and four-point spectra, and compare our calculated power spectra and bispectra to Planck values. We then lens the CIB, shell-by-shell with corresponding convergence maps, to capture the broad redshift extent of both the CIB and its lensing convergence. The lensing of the CIB changes the three- and four-point functions by a few tens of per cent at large scales, unlike with the power spectrum, which changes by less than two per cent. We expand our analyses to encompass the full intensity probability distribution functions (PDFs) involving all n-point correlations as a function of scale. In particular, we use the relative entropy between lensed and unlensed PDFs to create a spectrum of templates that can allow estimation of lensing. The underlying CIB model is missing the important role of star bursting, which we test by adding a stochastic lognormal term to the intensity distributions. The novel aspects of our filtering and lensing pipeline should prove useful for any radiant background, including line intensity maps.

Schwinger-Keldysh effective field theory for stable and causal relativistic hydrodynamics

We construct stable and causal effective field theories (EFTs) for describing statistical fluctuations in relativistic diffusion and relativistic hydrodynamics. These EFTs are fully non-linear, including couplings to background sources, and enable us to compute n-point time-ordered correlation functions including the effects of statistical fluctuations. The EFTs we construct are inspired by the Maxwell-Cattaneo model of relativistic diffusion and Müller-Israel-Stewart model of relativistic hydrodynamics respectively, and have been derived using both the Martin-Siggia-Rose and Schwinger-Keldysh formalisms. The EFTs non-linearly realise the dynamical Kubo-Martin-Schwinger (KMS) symmetry, which ensures that n-point correlation functions and interactions in the theory satisfy the appropriate fluctuation-dissipation theorems. Since these EFTs typically admit ultraviolet sectors that are not fixed by the low-energy infrared symmetries, we find that they simultaneously admit multiple realisations of the dynamical KMS symmetry. We also comment on certain obstructions to including statistical fluctuations in the recently-proposed stable and causal Bemfica-Disconzi-Noronha-Kovtun model of relativistic hydrodynamics.

Hypergraphs in LHC phenomenology — the next frontier of IRC-safe feature extraction

In this study, we critically evaluate the approximation capabilities of existing infra-red and collinear (IRC) safe feature extraction algorithms, namely Energy Flow Networks (EFNs) and Energy-weighted Message Passing Networks (EMPNs). Our analysis reveals that these algorithms fall short in extracting features from any N-point correlation that isn’t a power of two, based on the complete basis of IRC safe observables, specifically C-correlators. To address this limitation, we introduce the Hypergraph Energy-weighted Message Passing Networks (H-EMPNs), designed to capture any N-point correlation among particles efficiently. Using the case study of top vs. QCD jets, which holds significant information in its 3-point correlations, we demonstrate that H-EMPNs targeting up to N=3 correlations exhibit superior performance compared to EMPNs focusing on up to N=4 correlations within jet constituents.

Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to free theory correlators

We develop a systematic method to constrain any n-point correlation function of spinning operators in Large N Slightly Broken Higher Spin (SBHS) theories. As an illustration of the methodology, we work out the three point functions which reproduce the previously known results. We then work out the four point functions of spinning operators. We show that the correlation functions of spinning operators in the interacting SBHS theory take a remarkably simple form and that they can be written just in terms of the free fermionic and critical bosonic theory correlators. They also interpolate nicely between the results in these two theories. When expressed in spinor-helicity variables we obtain an anyonic phase which nicely interpolates between the free fermionic and critical bosonic results which makes 3D bosonization manifest. Further, we also obtain a form for five and higher point functions as well by performing a similar analysis.

Determinants in self-dual mathcal{N} = 4 SYM and twistor space

We consider correlation functions of supersymmetrized determinant operators in self-dual super Yang-Mills (SYM). These provide a generating function for correlators of arbitrary single-trace half-BPS operators, including, for appropriate Grassmann components, the so-called loop integrand of the non-self-dual theory. We introduce a novel twistor space representation for determinant operators which makes contact with the recently studied m = 2 amplituhedron. By using matrix duality we rewrite the n-point determinant correlator as a n × n matrix integral where the gauge group rank Nc is turned into a coupling. The correlators are rational functions whose denominators, in the planar limit, contain only ten-dimensional distances. Using this formulation, we verify a recent conjecture regarding the ten-dimensional symmetry of the components with maximal Grassmann degree and we obtain new formulas for correlators of Grassmann degree four.

Triple-spherical Bessel function integrals with exponential and Gaussian damping: towards an analytic N-point correlation function covariance model

Spherical Bessel functions (sBFs) appear commonly in many areas of physics wherein there is both translation and rotation invariance, and often integrals over products of several arise. Thus, analytic evaluation of such integrals with different weighting functions (which appear as toy models of a given physical observable, such as the galaxy power spectrum) is useful. Here, we present a generalization of a recursion-based method for evaluating such integrals. It gives relatively simple closed-form results in terms of Legendre functions (for the exponentially damped case) and Gamma, incomplete Gamma, and hypergeometric functions (for the Gaussian-damped case). We also present a new, non-recursive method to evaluate integrals of products of sBFs with Gaussian damping in terms of incomplete Gamma functions and hypergeometric functions.

Spacetime topology from holographic entanglement

An asymptotically AdS geometry connecting two or more boundaries is given by a entangled state, that can be expanded in the product basis of the Hilbert spaces of each CFT living on the boundaries. We derive a prescription to compute this expansion for states describing spacetimes with general spatial topology in arbitrary dimension. To large N, the expansion coincides with the Schmidt decomposition and the coefficients are given by n-point correlation functions on a particular Euclidean geometry.We show that this applies to all spacetime that admits a Hartle-Hawking type of wave functional, which via a standard hypothesis on the spatial topology, can be (one to one) mapped to CFT states defined on the asymptotic boundary. It is also observed that these states are endowed with quantum coherence properties.Applying this as holographic engineering, one can to construct an emergent space geometry with certain predetermined topology by preparing an entangled state of the dual quantum system. As an example, we apply the method to calculate the expansion and characterize a spacetime whose initial spatial topology is a (genus one) handlebody.

Counterflow-induced clustering: Exact results.

We analyze the cluster formation in a nonergodic stochastic system as a result of counterflow, with the aid of an exactly solvable model. To illustrate the clustering, a two species asymmetric simple exclusion process with impurities on a periodic lattice is considered, where the impurity can activate flips between the two nonconserved species. Exact analytical results, supported by Monte Carlo simulations, show two distinct phases, free-flowing phase and clustering phase. The clustering phase is characterized by constant density and vanishing current of the nonconserved species, whereas the free-flowing phase is identified with nonmonotonic density and nonmonotonic finite current of the same. The n-point spatial correlation between n consecutive vacancies grows with increasing n in the clustering phase, indicating the formation of two macroscopic clusters in this phase, one of the vacancies and the other consisting of all the particles. We define a rearrangement parameter that permutes the ordering of particles in the initial configuration, keeping all the input parameters fixed. This rearrangement parameter reveals the significant effect of nonergodicity on the onset of clustering. For a special choice of the microscopic dynamics, we connect the present model to a system of run-and-tumble particles used to model active matter, where the two species having opposite net bias manifest the two possible run directions of the run-and-tumble particles, and the impurities act as tumbling reagents that enable the tumbling process.

Test for Cosmological Parity Violation Using the 3D Distribution of Galaxies.

We show how the galaxy four-point correlation function can test for cosmological parity violation. The detection of cosmological parity violation would reflect previously unknown forces present at the earliest moments of the Universe. Recent developments both in rapidly evaluating galaxy N-point correlation functions and in determining the corresponding covariance matrices make the search for parity violation in the four-point correlation function possible in current and upcoming surveys such as those undertaken by Dark Energy Spectroscopic Instrument, the Euclid satellite, and the Vera C. Rubin Observatory. We estimate the limits on cosmic parity violation that could be set with these data.

On Correlation Functions as Higher-Spin Invariants

(Chern–Simons) vector models exhibit an infinite-dimensional symmetry, the slightly-broken higher-spin symmetry with the unbroken higher-spin symmetry being the first approximation. In this note, we compute the n-point correlation functions of the higher-spin currents as higher-spin invariants directly on the CFT side, which complements earlier results that have a holographic perspective.

DRalgo: A package for effective field theory approach for thermal phase transitions

DRalgo is an algorithmic implementation that constructs an effective, dimensionally reduced, high-temperature field theory for generic models. The corresponding Mathematica package automatically performs the matching to next-to-leading order. This includes two-loop thermal corrections to scalar and Debye masses as well as one-loop thermal corrections to couplings. DRalgo also allows for integrating out additional heavy scalars. Along the way, the package provides leading-order beta functions for general gauge-charges and fermion-families; both in the fundamental and in the effective theory. Finally, the package computes the finite-temperature effective potential within the effective theory. The article explains the theory of the underlying algorithm while introducing the software on a pedagogical level. Program summaryProgram title: Dimensional Reduction algorithm (DRalgo) 1.0CPC Library link to program files:https://doi.org/10.17632/k66j9vmh9r.1Developer's repository link:https://github.com/DR-algo/DRalgoLicensing provisions: GNU General Public License 3Programming language:MathematicaExternal routines/libraries:GroupMath [1]Nature of problem: Construction of high-temperature effective field theories for beyond the Standard Model physics.Solution method: Matching of n-point correlation functions using tensor-notation of couplings [2–6]Additional comments including restrictions and unusual features:Mathematica version 12 or above.