Two-point Function Research Articles

De Sitter at all loops: the story of the Schwinger model

We consider the two-dimensional Schwinger model of a massless charged fermion coupled to an Abelian gauge field on a fixed de Sitter background. The theory admits an exact solution, first examined by Jayewardena, and can be analyzed efficiently using Euclidean methods. We calculate fully non-perturbative, gauge-invariant correlation functions of the electric field as well as the fermion and analyze these correlators in the late-time limit. We compare these results with the perturbative picture, for example by verifying that the one-loop contribution to the fermion two-point function, as predicted from the exact solution, matches the direct computation of the one-loop Feynman diagram. We demonstrate many features endemic of quantum field theory in de Sitter space, including the appearance of late-time logarithms, their resummation to de Sitter invariant expressions, and Boltzmann suppressed non-perturbative phenomena, with surprising late-time features.

Constraining modified gravity with weak lensing peaks

Abstract It is well established that maximizing the information extracted from upcoming and ongoing stage-IV weak-lensing surveys requires higher-order summary statistics that complement the standard two-point statistics. In this work, we focus on weak-lensing peak statistics to test two popular modified gravity models, f(R) and nDGP, using the FORGE and BRIDGE weak-lensing simulations, respectively. From these simulations we measure the peak statistics as a function of both cosmological and modified gravity parameters simultaneously. Our findings indicate that the peak abundance is sensitive to the strength of modified gravity, while the peak two-point correlation function is sensitive to the nature of the screening mechanism in a modified gravity model. We combine these simulated statistics with a Gaussian Process Regression emulator and a Gaussian likelihood to generate stage-IV forecast posterior distributions for the modified gravity models. We demonstrate that, assuming small scales can be correctly modelled, peak statistics can be used to distinguish GR from f(R) and nDGP models at the two-sigma level with a stage-IV survey area of $300 \, \rm {deg}^2$ and $1000 \, \rm {deg}^2$, respectively. Finally, we show that peak statistics can constrain log10(|fR0|) = −6 to 2% precision, and log10(H0rc) = 0.5 to 25% precision.

Lattice QCD determination of the normalization of the leading-twist photon distribution amplitude and susceptibility of the quark condensate

The normalization of the leading-twist photon distribution amplitude (DA), fγ⊥, is an important ingredient in the study of exclusive processes involving the photon emission by means of QCD sum-rules. In this paper we determine the up-, down- and strange-quark contribution to fγ⊥ by exploiting its relation to the zero-momentum two-point correlation function of the electromagnetic current Jemμ and the electric component of the tensor current Tμν. To that end we employ the gauge ensembles obtained by using Nf=2+1+1 Wilson-Clover twisted-mass quark flavors, generated by the Extended Twisted Mass (ETM) Collaboration, and after adding all sources of systematic uncertainties, we obtain a total error of 1.5% and 3.5%, respectively, for the light- (u and d) and strange-quark contribution to fγ⊥(2 GeV) in the MS¯ scheme, thus improving their accuracy by a factor of 2.3 and 2.8, respectively. For the strange-quark contribution fγ,s⊥(2 GeV), we observe a discrepancy with respect to previous lattice calculations. By combining our result with the world average lattice value of the chiral condensate, we obtain for the susceptibility of the quark condensate χdMS¯(2 GeV)≃χuMS¯(2 GeV)=2.17(12) GeV−2. Published by the American Physical Society 2024

Correlation functions of boundary and defect conformal field theories

Applying the holographic method, we investigate correlation functions of boundary and defect conformal field theories. To describe boundary conformal field theory, we consider an end of the world brane in an asymptotic AdS space, which behaves as a boundary in the dual conformal field theory. In this holographic setup, we calculate correlation functions involving the reflection effect at the boundary. We show that, when the end of the world brane has no degrees of freedom, the holographic calculation reproduces the correlation functions known in the boundary conformal field theory. When the boundary has nontrivial boundary entropy, we calculate one- and two-point functions nontrivially relying on the boundary entropy. We further study correlation functions of defect conformal field theory after introducing a p brane. We directly derive a bulk-to-defect two-point function without introducing an image operator and determine the coefficient of the two-point function exactly in the holographic setup. Published by the American Physical Society 2024

Universal vortex statistics and stochastic geometry of Bose-Einstein condensation

The cooling of a Bose gas in finite time results in the formation of a Bose-Einstein condensate that is spontaneously proliferated with vortices. We propose that the vortex spatial statistics is described by a homogeneous Poisson point process (PPP) with a density dictated by the Kibble-Zurek mechanism (KZM). We validate this model using numerical simulations of the two-dimensional stochastic Gross-Pitaevskii equation (SGPE) for both a homogeneous and a hard-wall trapped condensate. The KZM scaling of the average vortex number with the cooling rate is established along with the universal character of the vortex number distribution. The spatial statistics between vortices is characterized by analyzing the two-point defect-defect correlation function, the corresponding spacing distributions, and the random tessellation of the vortex pattern using the Voronoi cell area statistics. Combining the PPP description with the KZM, we derive universal theoretical predictions for each of these quantities and find them in agreement with the SGPE simulations. Our results establish the universal character of the spatial statistics of point-like topological defects generated during a continuous phase transition and the associated stochastic geometry. Published by the American Physical Society 2024

Permutation invariant tensor models and partition algebras

Matrix models with continuous symmetry are powerful tools for studying quantum gravity and holography. Tensor models have also found applications in holographic quantum gravity. Matrix models with discrete permutation symmetry have been shown to satisfy large N factorisation properties relevant to holography, while also having applications to the statistical analysis of ensembles of real-world matrices. Here, we develop 3-index tensor models in dimension D with a discrete symmetry of permutations in the symmetric group S_{D} . We construct the most general permutation invariant Gaussian tensor model using the representation theory of symmetric groups and associated partition algebras. We define a representation basis for the 3-index tensors, where the two-point function is diagonalised. Inverting the change of basis gives an explicit formula for the two-point function in the tensor basis for general D .

Analytic and Numerical Approaches for Depictive 3-loop Integrals using Sector Decomposition

Abstract Four 3-loop two-point functions are studied analytically and numerically using a simplified sector decomposition method. The coefficients of the ultraviolet divergent part are determined analytically, and those of the finite part are computed numerically. The energy dependence of the integrals is shown explicitly, and a discussion of its behavior is presented.

Random telegraph processes with nonlocal memory.

We study two-state (dichotomous, telegraph) random ergodic continuous-time processes with dynamics depending on their past. We take into account the history of the process in an explicit form by introducing integral nonlocal memory term into conditional probability function. We start from an expression for the conditional transition probability function describing additive multistep binary random chain and show that the telegraph processes can be considered as continuous-time interpolations of discrete-time dichotomous random sequences. An equationinvolving the memory function and the two-point correlation function of the telegraph process is analytically obtained. This integral equationdefines the correlation properties of the processes with given memory functions. It also serves as a tool for solving the inverse problem, namely for generation of a telegraph process with a prescribed pair correlation function. We obtain analytically the correlation functions of the telegraph processes with two exactly solvable examples of memory functions and support these results by numerical simulations of the corresponding telegraph processes.

Celestial holography revisited. Part II. Correlators and Källén-Lehmann

In this work we continue the investigation of the extrapolate dictionary for celestial holography recently proposed in [1], at both the perturbative and non-perturbative level. Focusing on scalar field theories, we give a complete set of Feynman rules for extrapolate celestial correlation functions and their radial reduction in the hyperbolic slicing of Minkowski space. We prove to all orders in perturbation theory that celestial correlators can be rewritten in terms of corresponding Witten diagrams in EAdS which, in the hyperbolic slicing of Minkowski space, follows from the fact that the same is true in dS space. We then initiate the study of non-perturbative properties of celestial correlators, deriving the radial reduction of the Källén-Lehmann spectral representation of the exact Minkowski two-point function. We discuss the analytic properties of the radially reduced spectral function, which is a meromorphic function of the spectral parameter, and highlight a connection with the Watson-Sommerfeld transform.

Revisiting the spatially inhomogeneous condensates in the (1+1) -dimensional chiral Gross–Neveu model via the bosonic two-point function in the infinite-N limit

This work shows that the known phase boundary between the phase with chiral symmetry and the phase of spatially inhomogeneous chiral symmetry breaking in the phase diagram of the (1+1) -dimensional chiral Gross–Neveu (GN) model can be detected from the bosonic two-point function alone and thereby confirms and extends previous results (Schön and Thies 2000 At The Frontier of Particle Physics: Handbook of QCD, Boris Ioffe Festschrift vol 3 (World Scentific) ch 33, pp 1945–2032; Boehmer et al 2008 Phys. Rev. D 78 065043; Boehmer and Thies 2009 Phys. Rev. D 80 125038; Thies 2018 Phys. Rev. D 98 096019; Thies 2022 Phys. Rev. D 105 116003). The analysis is referred to as the stability analysis of the symmetric phase and does not require knowledge about spatial modulations of condensates. We perform this analysis in the infinite-N limit at nonzero temperature and nonzero quark and chiral chemical potentials also inside the inhomogeneous phase. Thereby we observe an interesting relation between the bosonic 1-particle irreducible two-point vertex function of the chiral GN model and the spinodal line of the GN model.

The beyond-halo mass effects of the cosmic web environment on galaxies

ABSTRACT Galaxy properties primarily depend on their host halo mass. Halo mass, in turn, depends on the cosmic web environment. We explore if the effect of the cosmic web on galaxy properties is entirely transitive via host halo mass, or if the cosmic web has an effect independent of mass. The secondary galaxy bias, sometimes referred to as ‘galaxy assembly bias’, is the beyond-mass component of the galaxy–halo connection. We investigate the link between the cosmic web environment and the secondary galaxy bias in simulations. We measure the secondary galaxy bias through the following summary statistics: projected two-point correlation function, $w_{\mathrm{p}}(r_{\mathrm{p}})$, and counts-in-cylinders statistics, $P(N_{\mathrm{CIC}})$. First, we examine the extent to which the secondary galaxy bias can be accounted for with a measure of the environment as a secondary halo property. We find that the total secondary galaxy bias preferentially places galaxies in more strongly clustered haloes. In particular, haloes at fixed mass tend to host more galaxies when they are more strongly associated with nodes or filaments. This tendency accounts for a significant portion, but not the entirety, of the total secondary galaxy bias effect. Secondly, we quantify how the secondary galaxy bias behaves differently depending on the host halo proximity to nodes and filaments. We find that the total secondary galaxy bias is relatively stronger in haloes more associated with nodes or filaments. We emphasize the importance of removing halo mass effects when considering the cosmic web environment as a factor in the galaxy–halo connection.

CFT reconstruction of local bulk operators in half-Minkowski space

We construct a holographic map that reconstructs massless fields (scalars, Maxwell field, and Fierz-Pauli field) in half-Minkowski spacetime in d+1 dimensions terms of smeared primary operators in a large-N factorizable CFT in Rd−1,1. This map is based on a Weyl (rescaling) transformation from the Poincaré wedge of AdS to the Minkowski half-space and on the Hamilton-Kabat-Lifschytz-Lowe smearing function, which reconstructs local bulk operators in the Poincaré AdS in terms of smeared operators on the conformal boundary of the Poincaré wedge. The massless scalar field is reconstructed up to the level of two-point functions, while the Maxwell field and massless spin-2 fields are reconstructed at the level of the one-point function. We also discuss potential ways the map can be generalized to higher dimensions, and to the full Minkowski space. Published by the American Physical Society 2024

Missing local operators, zeros, and twist-4 trajectories

The number of local operators in a CFT below a given twist grows with spin. Consistency with analyticity in spin then requires that at low spin, infinitely many Regge trajectories must decouple from local correlation functions, implying infinitely many vanishing conditions for OPE coefficients. In this paper we explain the mechanism behind this infinity of zeros. Specifically, the mechanism is related to the two-point function rather than the three-point function, explaining the vanishing of OPE coefficients in every correlator from a single condition. We illustrate our result by studying twist-4 Regge trajectories in the Wilson-Fisher CFT at one loop.

Environmental effects on low surface brightness galaxies in the IllustrisTNG simulation

ABSTRACT Employing the TNG100 run of the IllustrisTNG project, we characterize the environment of low surface brightness galaxies (LSBGs) across varying scales, from their associated dark matter haloes to their distribution within the broader cosmic structure. We find no significant differences in the halo concentration index $c_{200}$ between LSBGs and their high surface brightness galaxy (HSBG) counterparts, with LSBGs residing in haloes with higher spin parameter $\lambda$ and slightly more spherical shapes than HSBGs. LSBGs show a stronger alignment between the dark and stellar angular momentum vectors than their high surface brightness counterparts. The relative abundance of LSBGs within groups and clusters displays a central deficit, hinting at potential destruction upon reaching these core regions. Studying the density field, we find a preference for rotation-dominated LSBGs to reside in low-density environments, while dispersion-dominated LSBGs thrive in high-density regions where galaxy interactions govern their evolution, an observation corroborated by our analysis of the two-point correlation function $\xi (r)$. Our examination of the cosmic web reveals no significant differences in the distance to the closest large-scale structure, barring a few exceptions. This suggests a limited impact of large-scale spatial distribution on mechanisms driving LSBG evolution. All together, we conclude that the halo vicinity and local environment at the scale of galaxy clusters, where mechanisms such as galaxy mergers and tidal stripping, as well as stellar and gas accretion take place, is the most likely environment that favour the emergence of LSBGs with different morphologies, mostly driven by the presence or absence of important local interaction phenomena.

Renormalization group flows in AdS and the bootstrap program

We study correlation functions of the bulk stress tensor and boundary operators in Quantum Field Theories (QFT) in Anti-de Sitter (AdS) space. In particular, we derive new sum rules from the two-point function of the stress tensor and its three-point function with two boundary operators. In AdS2, this leads to a bootstrap setup that involves the central charge of the UV limit of the bulk QFT and may allow to follow a Renormalization Group (RG) flow non-perturbatively by continuously varying the AdS radius. Along the way, we establish the convergence properties of the newly discovered local block decomposition of the three-point function.

Derivation of the nonequilibrium generalized Langevin equation from a time-dependent many-body Hamiltonian.

It has become standard practice to describe systems that remain far from equilibrium even in their steady state by Langevin equationswith colored noise which is chosen independently from the friction contribution. Since these Langevin equationsare typically not derived from first-principle Hamiltonian dynamics, it is not clear whether they correspond to physically realizable scenarios. By exact Mori projection in phase space we derive the nonequilibrium generalized Langevin equation(GLE) for an arbitrary phase-space dependent observable A from a generic many-body Hamiltonian with a time-dependent external force h(t) acting on the same observable A. This is the same Hamiltonian from which the standard fluctuation-dissipation theorem is derived, which reflects the generality of our approach. The observable A could, for example, be the position of an atom, of a molecule or of a macroscopic object, the distance between two such entities or a more complex phase-space function such as the reaction coordinate of a chemical reaction or of the folding of a protein. The Hamiltonian could, for example, describe a fluid, a solid, a viscoelastic medium, or even a turbulent inhomogeneous environment. The GLE, which is a closed-form equationof motion for the observable A, is obtained in explicit form to all orders in h(t) and without restrictions on the type of many-body Hamiltonian or the observable A. If the dynamics of the observable A corresponds to a Gaussian process, the resultant GLE has a similar form as the equilibrium Mori GLE, and in particular the friction memory kernel is given by the two-point autocorrelation function of the sum of the complementary and the external force h(t). This is a nontrivial and useful result, as many observables that characterize nonequilibrium systems display Gaussian statistics. For non-Gaussian nonequilibrium observables correction terms appear in the GLE and in the relation between the force autocorrelation and the friction memory kernel, which are explicitly given in terms of cubic correlation functions of A. Interpreting the external force h(t) as a stochastic process, we derive nonequilibrium corrections to the fluctuation-dissipation theorem and present methods to extract all GLE parameters from experimental or simulation time-series data, thus making our nonequilibrium GLE a practical tool to study and model general nonequilibrium systems.

Relaxation dynamics in the alternating XY chain following a quantum quench

We investigate the relaxation dynamics of the fermion two-point correlation function Cmn(t)=〈ψ(t)∣cm†cn∣ψ(t)〉 in the XY chain with alternating nearest-neighbor hopping interaction after a quench. We find that the deviation δ C mn (t) = C mn (t) − C mn (∞) decays with time following the power law behavior t −μ , where the exponent μ depends on whether the quench is to the commensurate phase (μ = 1) or incommensurate phase ( μ=12 ). This decay of δ C mn (t) arises from the transient behavior of the double-excited quasiparticle occupations and the transitions between different excitation spectra. Furthermore, we find that the steady value C mn (∞) only involves the average fermion occupation numbers (i.e. the average excited single particle) over the time-evolved state, which are different from the ground state expectation values. We also observe nonanalytic singularities in the steady value C mn (∞) for the quench to the critical points of the quantum phase transitions (QPTs), suggesting its potential use as a signature of QPTs.

Unleashing cosmic shear information with the tomographic weak lensing PDF

In this work, we demonstrate the constraining power of the tomographic weak lensing convergence PDF for StageIV-like source galaxy redshift bins and shape noise. We focus on scales of 10 to 20 arcmin in the mildly nonlinear regime, where the convergence PDF and its changes with cosmological parameters can be predicted theoretically. We model the impact of reconstructing the convergence from the shear field using the well-known Kaiser-Squires formalism. We cross-validate the predicted and the measured convergence PDF derived from convergence maps reconstructed using simulated shear catalogues. Employing a Fisher forecast, we determine the constraining power for (Ωm,S8,w0). We find that adding a 5-bin tomography improves the κ−PDF constraints by a factor of {3.8,1.3,1.6} for (Ωm,S8,w0) respectively. Additionally, we perform a joint analysis with the shear two-point correlation functions, finding an enhancement of around a factor of 1.5 on all parameters with respect to the two-point statistics alone. These improved constraints come from disentangling from w0 by extracting non-Gaussian information, in particular, including the PDF skewness at different redshift bins. We also study the effect of varying the number of parameters to forecast, in particular we add h, finding that the convergence PDF maintains its constraining power while the precision from two-point correlations degrades by a factor of {1.7,1.4,1.8} for , respectively.

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.

Estimation of line-of-sight velocities of individual galaxies using neural networks – I. Modelling redshift–space distortions at large scales

ABSTRACT We present a scheme based on artificial neural networks (ANNs) to estimate the line-of-sight velocities of individual galaxies from an observed redshift–space galaxy distribution. We find an estimate of the peculiar velocity at a galaxy based on galaxy counts and barycentres in shells around it. By training the network with environmental characteristics, such as the total mass and mass centre within each shell surrounding every galaxy in redshift space, our ANN model can accurately predict the line-of-sight velocity of each individual galaxy. When this velocity is used to eliminate the RSD effect, the two-point correlation function (TPCF) in real space can be recovered with an accuracy better than 1 per cent at s > 8 $\, h^{-1}\, \mathrm{Mpc}$, and 4 per cent on all scales compared to ground truth. The real-space power spectrum can be recovered within 3 per cent on k< 0.5 $\, \mathrm{Mpc}^{-1}\, h$, and less than 5 per cent for all k modes. The quadrupole moment of the TPCF or power spectrum is almost zero down to s = 10 $\, h^{-1}\, \mathrm{Mpc}$ or all k modes, indicating an effective correction of the spatial anisotropy caused by the RSD effect. We demonstrate that on large scales, without additional training with new data, our network is adaptable to different galaxy formation models, different cosmological models, and mock galaxy samples at high-redshifts and high biases, achieving less than 10 per cent error for scales greater than 15 $\, h^{-1}\, \mathrm{Mpc}$. As it is sensitive to large-scale densities, it does not manage to remove Fingers of God in large clusters, but works remarkably well at recovering real-space galaxy positions elsewhere. Our scheme provides a novel way to predict the peculiar velocity of individual galaxies, to eliminate the RSD effect directly in future large galaxy surveys, and to reconstruct the three-dimensional cosmic velocity field accurately.