Two-loop Order In Perturbation Theory Research Articles

Baryonic effects in the Effective Field Theory of Large-Scale Structure and an analytic recipe for lensing in CMB-S4

Upcoming Large-Scale Structure surveys will likely become the next leading sources of cosmological information, making it crucial to have a precise understanding of the influence of baryons on cosmological observables. The Effective Field Theory of Large-Scale Structure (EFTofLSS) provides a consistent way to predict the clustering of dark matter and baryons on large scales, where their leading corrections in perturbation theory are given by a simple and calculable functional form even after the onset of baryonic processes. In this paper, we extend the two-fluid-like system up to two-loop order in perturbation theory. Along the way, we show that a new linear counterterm proportional to the relative velocity of the fluids could generically be present, but we show that its effects are expected to be small in our universe. Regardless, we show how to consistently perform perturbation theory in the presence of this new term. We find that the EFTofLSS at two-loop order can accurately account for the details of baryonic processes on large scales. We compare our results to a hydrodynamical N-body simulation at many redshifts and find that the counterterms associated with the leading corrections to dark matter and baryons start to differ between redshifts z ≈ 3 and z ≈ 2, signaling the onset of star-formation physics. We then use these fits to compute the lensing power spectrum, show that the understanding of baryonic processes will be important for analyzing CMB-S4 data, and show that the two-loop EFTofLSS accurately captures these effects for ℓ ≲ 2000. Our results are also potentially of interest for current and future weak lensing surveys.

Renormalization Approach to the Gribov Process: Numerical Evaluation of Critical Exponents in Two Subtraction Schemes

We study universal quantities characterizing the second order phase transition in the Gribov process. To this end, we use numerical methods for the calculation of the renormalization group functions up to two-loop order in perturbation theory in the famousε-expansion. Within this procedure the anomalous dimensions are evaluated using two different subtraction schemes: the minimal subtraction scheme and the null-momentum scheme. Numerical calculation of integrals was done on the HybriLIT cluster using the Vegas algorithm from the CUBA library. The comparison with existing analytic calculations shows that the minimal subtraction scheme yields more precise results.

The Minkowski quantum vacuum does not gravitate

We show that a non-zero renormalised value of the zero-point energy in λϕ4-theory over Minkowski spacetime is in tension with the scalar-field equation at two-loop order in perturbation theory.

A note on multiply wound BPS Wilson loops in ABJM

We consider BPS Wilson loops in planar ABJM theory, wound multiple times around the great circle. We compute the expectation value of the 1/6-BPS and 1/2-BPS Wilson loops to three- and two-loop order in perturbation theory, respectively, dealing with the combinatorics of multiple winding via recursive relations. For the 1/6-BPS Wilson loop we perform the computation at generic framing and at framing 1 we find agreement with the localization result. For the 1/2-BPS Wilson loop we compute the expectation value at trivial framing and by comparison with the matrix model expression we extract the framing dependence of the fermion diagrams.

Direct and fast calculation of regularized cosmological power spectrum at two-loop order

We present a specific prescription for the calculation of cosmological power spectra, exploited here at two-loop order in perturbation theory (PT), based on the multi-point propagator expansion. In this approach power spectra are constructed from the regularized expressions of the propagators that reproduce both the resummed behavior in the high-k limit and the standard PT results at low-k. With the help of N-body simulations, we show that such a construction gives robust and accurate predictions for both the density power spectrum and the correlation function at percent-level in the weakly non-linear regime. We then present an algorithm that allows accelerated evaluations of all the required diagrams by reducing the computational tasks to one-dimensional integrals. This is achieved by means of pre-computed kernel sets defined for appropriately chosen fiducial models. The computational time for two-loop results is then reduced from a few minutes, with the direct method, to a few seconds with the fast one. The robustness and applicability of this method are tested against the power spectrum cosmic emulator from which a wide variety of cosmological models can be explored. The fortran program with which direct and fast calculations of power spectra can be done, RegPT, is publicly released as part of this paper.

Universal critical behavior of noisy coupled oscillators: A renormalization group study

We show that the synchronization transition of a large number of noisy coupled oscillators is an example for a dynamic critical point far from thermodynamic equilibrium. The universal behaviors of such critical oscillators, arranged on a lattice in a d -dimensional space and coupled by nearest-neighbors interactions, can be studied using field-theoretical methods. The field theory associated with the critical point of a homogeneous oscillatory instability (or Hopf bifurcation of coupled oscillators) is the complex Ginzburg-Landau equation with additive noise. We perform a perturbative renormalization group (RG) study in a (4-epsilon)-dimensional space. We develop an RG scheme that eliminates the phase and frequency of the oscillations using a scale-dependent oscillating reference frame. Within Callan-Symanzik's RG scheme to two-loop order in perturbation theory, we find that the RG fixed point is formally related to the one of the model A dynamics of the real Ginzburg-Landau theory with an O2 symmetry of the order parameter. Therefore, the dominant critical exponents for coupled oscillators are the same as for this equilibrium field theory. This formal connection with an equilibrium critical point imposes a relation between the correlation and response functions of coupled oscillators in the critical regime. Since the system operates far from thermodynamic equilibrium, a strong violation of the fluctuation-dissipation relation occurs and is characterized by a universal divergence of an effective temperature. The formal relation between critical oscillators and equilibrium critical points suggests that long-range phase order exists in critical oscillators above two dimensions.

Feynman diagrams to three loops in three-dimensional field theory

The two-point integrals contributing to the self-energy of a particle in a three-dimensional quantum field theory are calculated to two-loop order in perturbation theory as well as the vacuum ones contributing to the effective potential to three-loop order. For almost every integral an expression in terms of elementary and dilogarithm functions is obtained. For two integrals, the master integral and the Mercedes integral, a one-dimensional integral representation is obtained with an integrand consisting only of elementary functions. The results are applied to a scalar λφ 4 theory.

Effective diffusivity in non-isotropic gradient flows

We study the effective diffusivity tensor for particles in a random gradient flow that, statistically, lacks rotational symmetry. The effective diffusivity tensor is computed up to two-loop order in perturbation theory and the 'Ward identity' that relates this tensor to the effective coupling is verified to the same order. We re-examine the renormalization group calculation that produced a very accurate numerical value for the effective diffusivity in the rotationally symmetric case and formulate two versions based on distinct divisions of the random potential field that gives rise to the flow. Both types of renormalization group calculation give good results when compared with numerical simulations. However, at two-loop order in perturbation theory the two methods differ in detail from each other and from the exact perturbation calculation. This is in contrast to the corresponding results in the isotropic case.

A two-loop calculation of the mass gap for the O( N) model in finite volume

The mass gap for the quantum O( N) non-linear sigma model in a finite volume in two dimensions is calculated to two-loop order in perturbation theory. This result is used to estimate the mass gap of the infinite-volume O(3) model to be about 2.1 Λ MS ± 10% . The calculation is carried out using dimensional regularization with both compact and non-compact extra dimensions, with the same result in both cases.

Determination of large QCD corrections near the boundary of phase space

Here we present a rule which determines the coefficients of the leading and next to leading logarithms which appear in the Wilson coefficient function near the boundary of phase space. The validity of this rule is checked up to two-loop order in perturbation theory for two model field theories. In order to include the next to leading logarithms we propose a new resummation technique of the large corrections.

Asymptotic chiral invariance

We discuss the conditions under which chiral symmetries become exact at asymptotic momenta, utilizing the homogeneous Callan-Symanzik equations so that momenta are not restricted to the deep Euclidean domain as others have done previously. In particular, we consider as our prototype the chiral SU(2) \ensuremath{\bigotimes} SU(2) $\ensuremath{\sigma}$ model of Gell-Mann and Levy without fermions, where we allow for both spontaneous symmetry breaking and explicit breaking of the symmetry via a term in the Lagrangian linear in the $\ensuremath{\sigma}$ field. To check our general results, we calculate to two-loop order in perturbation theory the coefficients of the homogeneous Callan-Symanzik equations along with the interesting amplitudes of the theory and finally show that under suitable conditions the symmetry-broken theory and the symmetry-conserved theory both approach the same massless, symmetric theory as the momenta become asymptotic.