Vacuum Correlation Functions Research Articles

Chiral phase structure and critical end point in QCD

We map out the QCD phase structure at finite temperature and chemical potential for 2-flavour and 2+1-flavour QCD. This is done within a generalised functional approach to QCD put forward in [1]. Specifically we compute the quark propagator and the finite-temperature and density fluctuations of the gluon propagator and the quark-gluon vertex on the basis of precision data for vacuum correlation functions. The novel ingredient is the direct self-consistent computation of the DSEs for the three dominant dressings of the quark-gluon vertex, in contrast to the common use of STI-inspired vertices.For small densities the results for the chiral order parameter agree with the respective lattice and functional renormalisation group results, for large densities the present results are in a quantitative agreement with the latter, including the location of the critical end point.

Background-independent composite gravity

We explore a background-independent model of composite gravity. In a mean-field approximation, the vacuum expectation value of the composite metric satisfies Einstein’s equations (with corrections) as a consistency condition. A gravitational interaction then emerges in vacuum correlation functions. The action remains diffeomorphism invariant even as perturbation theory is organized about the dynamically selected vacuum spacetime. We discuss the role of nonphysical clock and rod fields in the analysis, the identification of physical observables, and the generalization to other theories including the standard model.

Equivalence between the in-in perturbation theories for quantum fields in Minkowski spacetime and in the Rindler wedge

We investigate the relation between the time-ordered vacuum correlation functions for interacting real scalar fields in Minkowski spacetime and in the Rindler wedge. The correlation functions are constructed perturbatively within the in-in formalism, often employed in calculations in more general spacetimes. We prove to all orders in perturbation theory that the time-ordered vacuum correlation functions can be calculated in the in-in formalism with internal vertices restricted to any Rindler wedge containing the external points. This implies that the Minkowski in-in (or in-out) perturbative expansion of the vacuum correlation functions is reproduced by the Rindler in-in perturbative expansion of these correlators in a thermal state at the Unruh temperature.

The L\u221e-algebra of the S-matrix

We point out that the one-particle-irreducible vacuum correlation functions of a QFT are the structure constants of an L∞-algebra, whose Jacobi identities hold whenever there are no local gauge anomalies. The LSZ prescription for S-matrix elements is identified as an instance of the “minimal model theorem” of L∞-algebras. This generalises the algebraic structure of closed string field theory to arbitrary QFTs with a mass gap and leads to recursion relations for amplitudes (albeit ones only immediately useful at tree-level, where they reduce to Berends-Giele-style relations as shown in [1]).

The conformal bootstrap at finite temperature

We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum correlation functions. We focus on thermal one- and two-point functions of local operators on the plane. The KMS condition for thermal two-point functions is cast as a crossing equation. By studying the analyticity properties of thermal two-point functions, we derive a “thermal inversion formula” whose output is the set of thermal one-point functions for all operators appearing in a given OPE. This involves identifying a kinematic regime which is the analog of the Regge regime for four-point functions. We demonstrate the effectiveness of the inversion formula by recovering the spectrum and thermal one-point functions in mean field theory, and computing thermal one-point functions for all higher-spin currents in the critical O(N) model at leading order in 1/N. Furthermore, we develop a systematic perturbation theory for thermal data in the large spin, low-twist spectrum of any CFT. We explain how the inversion formula and KMS condition may be combined to algorithmically constrain CFTs at finite temperature. Throughout, we draw analogies to the bootstrap for vacuum four-point functions. Finally, we discuss future directions for the thermal conformal bootstrap program, emphasizing applications to various types of CFTs, including those with holographic duals.

Nucleon form factors in dispersively improved chiral effective field theory: Scalar form factor

We propose a method for calculating the nucleon form factors (FFs) of $G$-parity-even operators by combining Chiral Effective Field Theory ($\chi$EFT) and dispersion analysis. The FFs are expressed as dispersive integrals over the two-pion cut at $t > 4 M_\pi^2$. The spectral functions are obtained from the elastic unitarity condition and expressed as products of the complex $\pi\pi \rightarrow N\bar N$ partial-wave amplitudes and the timelike pion FF. $\chi$EFT is used to calculate the ratio of the partial-wave amplitudes and the pion FF, which is real and free of $\pi\pi$ rescattering in the $t$-channel ($N/D$ method). The rescattering effects are then incorporated by multiplying with the squared modulus of the empirical pion FF. The procedure results in a marked improvement compared to conventional $\chi$EFT calculations of the spectral functions. We apply the method to the nucleon scalar FF and compute the scalar spectral function, the scalar radius, the $t$-dependent FF, and the Cheng-Dashen discrepancy. Higher-order chiral corrections are estimated through the $\pi N$ low-energy constants. Results are in excellent agreement with dispersion-theoretical calculations. We elaborate several other interesting aspects of our method. The results show proper scaling behavior in the large-$N_c$ limit of QCD because the $\chi$EFT calculation includes $N$ and $\Delta$ intermediate states. The squared modulus of the timelike pion FF required by our method can be extracted from Lattice QCD calculations of vacuum correlation functions of the operator at large Euclidean distances. Our method can be applied to the nucleon FFs of other operators of interest, such as the isovector-vector current, the energy-momentum tensor, and twist-2 QCD operators (moments of generalized parton distributions).

On path-dependence of the QCD correlation functions

Gauge-invariant hadronic and vacuum correlation functions in QCD contain the systems of Wilson lines and loops having complicated geometrical structure. Path-dependence propagates, therefore, into such important properties of the quantum correlators as the renormalization-group behaviour, light-cone peculiarities, evolution, etc. In the present paper, I briefly overview several instructive examples of the manifestations of the structure of paths in the hadronic and vacuum correlation functions with explicit transverse momentum/distance dependence. In particular, the transverse-momentum dependent (TMD) parton densities and the skewed jet quenching parameter in Euclidean and Minkowski space-time are addressed.

Correlators, Feynman Diagrams, and Quantum No-hair in deSitter Spacetime

We provide a parametric representation for position-space Feynman integrals of a massive, self-interacting scalar field in deSitter spacetime, for an arbitrary graph. The expression is given as a multiple contour integral over a kernel whose structure is determined by the set of all trees (or forests) within the graph, and it belongs to a class of generalized hypergeometric functions. We argue from this representation that connected deSitter n-point vacuum correlation functions have exponential decay for large proper time-separation, and also decay for large spatial separation, to arbitrary orders in perturbation theory. Our results may be viewed as an analog of the so-called cosmic-no-hair theorem in the context of a quantized test scalar field. This work has significant overlap with a paper by Marolf and Morrison, which is being released simultaneously.

Thermal photons from heavy ion collisions: A spectral function approach

We analyze the photon rates from a hadronic gas in equilibrium using chiral reduction formulas and a density expansion. The chiral reduction is carried to second order in the pion density which in principal includes all kinetic processes of the type $X\to \pi\gamma$ and $X\to \pi\pi\gamma$. The resulting rates are encoded in the form of vacuum correlation functions which are amenable to experiment. The hadronic rates computed in this work along with the known perturbative QGP rates are integrated over the space-time evolution of a hydrodynamic model tuned to hadronic observables. The resulting yields are compared to the recent photon and low mass dilepton measurements at the SPS and RHIC. Predictions for the LHC are made.

Method of vacuum correlation functions: Results and prospects

Basic results obtained within the QCD method of vacuum correlation functions over the past 20 years in the context of investigations into strong-interaction physics at the Institute of Theoretical and Experimental Physics (ITEP, Moscow) are formulated Emphasis is placed primarily on the prospects of the general theory developed within QCD by employing both nonperturbative and perturbative methods. On the basis of ab initio arguments, it is shown that the lowest two field correlation functions play a dominant role in QCD dynamics. A quantitative theory of confinement and deconfinement, as well as of the spectra of light and heavy quarkonia, glueballs, and hybrids, is given in terms of these two correlation functions. Perturbation theory in a nonperturbative vacuum (background perturbation theory) plays a significant role, not possessing drawbacks of conventional perturbation theory and leading to the infrared freezing of the coupling constant α s.

Curvature vacuum correlations in quantum gravity

Under the flat Minkowski space-time background,in the harmonic and the arbitrary coordinate systems,we obtained the graviton free propagators in the n-dimensional general relativity (GR) and the high derivative gravity respectively,calculated the expressions of the leading terms of several two-point curvature vacuum correlation functions,and proved that they are zero in the GR,but in the high derivative gravity they are not zero.

Static potential in a baryon within the method of vacuum correlation functions

The static three-quark potential in arbitrary configuration of quarks is calculated analytically. It is shown to be in a full agreement with the precise numerical simulations in lattice QCD. The results of the work have important application in nuclear physics, as they allow to perform accurate analytic calculations of spectra of the baryons.

Vacuum Correlations in Quantized Gravity

The leading terms of some curvature vacuum correlation functions in n dimensional quantized higher-derivative gravity are calculated, resulting in that these correlation functions are not zero, and the relations on the graviton propagator and the vacuum correlations between the higher-derivative gravity and the R-gravity are discussed.

Towards Euclidean theory of infrared singular quantum fields

A new generalized formulation of the spectral condition is proposed for quantum fields with highly singular infrared behavior whose vacuum correlation functions are well defined only under smearing with analytic test functions in momentum space. The Euclidean formulation of QFT developed by Osterwalder and Schrader is extended to theories with infrared singular indefinite metric. The corresponding generalization of the reconstruction theorem is obtained. The fulfilment of the generalized spectral condition is verified for quantum fields representable by infinite series in the Wick powers of indefinite metric free fields.

Thermal QCD sum rules for mesons

A recently proposed scheme is used to saturate the spectral side of the QCD sum rules derived from the thermal, two-point correlation functions of the vector and the axial-vector currents. At low temperature, it constructs the spectral representation from all the one-loop Feynman diagrams for the two-point functions. The old saturation scheme treats incorrectly some of these contributions. We end up with the familiar QCD sum rules obtained from the difference of the two corresponding vacuum correlation functions. The possibility of obtaining new sum rules in other media is discussed.

Curvature Vacuum Correlations in N -Dimensional Einstein Gravity

Under the flat Euclidean space–time background, the expressions for the leading terms of several two-point curvature vacuum correlation functions in N-dimensional Einstein gravity are calculated by using the perturbative expansion of the metric. It is shown that the contributions of the leading terms of such two-point curvature vacuum correlation functions are all vanishing.

CURVATURE VACUUM CORRELATIONS IN FOUR-DERIVATIVE GRAVITY

Under the flat Minkowski space–time background, in the harmonic coordinate system, we calculate the expressions of the leading terms of several two-point curvature vacuum correlation functions in n dimensional four-derivative gravity, resulting in that the two-point curvature vacuum correlation functions are not zero, and discuss the relations between the four-derivative gravity and the R-gravity for the graviton propagator and the curvature correlation functions.

Calculation of Curvature Vacuum Correlations in R-Gravity

Under the flat Minkowski space-time background, using the perturbative expansion of the metric density, we calculate the expressions of the leading terms of several two-point curvature vacuum correlation functions in N-dimensional R-gravity, resulting in that the contributions of the leading terms of the curvature vacuum correlation functions are all vanishing.

Dilepton and photon emission rates from a hadronic gas. III

We extend our early analyses of the dilepton and photon emission rates from a hadronic gas to account for strange mesons using a density expansion. The emission rates are reduced to vacuum correlation functions using three-flavor chiral reduction formulas, and the latter are assessed in terms of empirical data. Using a fire- ball, we compare our results to the low and intermediate mass dilepton data available from CERN. Our results suggest that a baryon free hadronic gas does not account for the excess of low mass dielectrons observed at CERES but does well in accounting for the intermediate dimuons at HELIOS. The same observations apply to the recent low and high ${p}_{t}$ dielectron rates from CERES.

Operator product expansion and its thermal average

QCD sum rules at finite temperature, like the ones at zero temperature, require the coefficients of local operators, which arise in the short distance expansion of the thermal average of two-point functions of currents. We extend the configuration space method, applied earlier at zero temperature, to the case at finite temperature. We find that, upto dimension four, two new operators arise, in addition to the two appearing already in the vacuum correlation functions. It is argued that the new operators would contribute substantially to the sum rules, when the temperature is not too low.