Derivative Expansion Research Articles

The derivative expansion in asymptotically safe quantum gravity: general setup and quartic order

We present a general framework to systematically study the derivative expansion of asymptotically safe quantum gravity. It is based on an exact decoupling and cancellation of different modes in the Landau limit, and implements a correct mode count as well as a regularisation based on geometrical considerations. It is applicable independent of the truncation order. To illustrate the power of the framework, we discuss the quartic order of the derivative expansion and its fixed point structure as well as physical implications.

One-loop effective action of the [formula omitted] model at large μβ

In this note we consider a non-linear, large-NCPN−1 sigma model on a finite size interval with periodic boundary conditions, at finite temperature and chemical potential in the regime of βμ large. Our goal is to extend previous calculations and obtain the coefficients of the derivative expansion of the one-loop effective action in the region of βμ large by carrying out the appropriate analytical continuation. This calculation complements previous results and allows us to conclude that the ground state remains homogeneous in this regime as long as it is assumed to be a slowly varying function of the spatial coordinates. While this is reasonable at the two extremes of small or large chemical potential, for intermediate values of the chemical potential and small enough temperature, one might expect (by analogy with other models) that lower energy crystalline solutions may exist. In this case a simple derivative expansion, like the one discussed here, would need to be modified in order to capture these features.

Energy of a pointlike neutron in an external electromagnetic field

A point-like neutron in an external electromagnetic field experiences a shift in energy that mimicks the effect of an actual structural deformation of an extended neutron, i.e., a proper polarizability. In order to be able to differentiate between the former and the latter, a Foldy-Wouthuysen transformation is constructed which yields the energy shift of a point-like neutron quadratic in the external field in a derivative expansion, generalizing a long-known result for the dipole electric polarizability due to Foldy. The ten leading Foldy contributions to the energy are determined for a zero-momentum neutron. In addition, eliminating the momentum operator in favor of the velocity operator, analogous results are derived for a zero-velocity neutron. In this case, operator ordering ambiguities are encountered that permit only a determination of eight of the ten Foldy terms.

A different perspective on the vev insertion approximation for electroweak baryogenesis

In the vev insertion approximation (VIA) the spacetime dependent part of the mass matrix is treated as a perturbation. We calculate the source terms for baryogenesis expanding both the self-energy and propagator to first order in mass insertions, which gives the same results as the usual approach of calculating the self-energy at second order and using zeroth order propagators. This procedure shows explicitly the equivalence between including the mass in the free or in the interaction Lagrangian. The VIA source then originates from the same term in the kinetic equation as the semi-classical source, but at leading order in the derivative expansion (the expansion in diamond operators). On top, another type of derivative expansion is done, which we estimate to be valid for a bubble width larger than the inverse thermal width. This cuts off the divergence in the VIA source in the limit that the thermal width vanishes.

Renormalization-group study of Bose polarons

We study the properties of a single impurity in a dilute Bose gas, a Bose polaron, using the functional renormalization group. We use an ansatz for the effective action motivated by a derivative expansion, and we compute the energies of the attractive and repulsive branches of excitations in both two and three spatial dimensions. Three-body correlations play an important role in the attractive branch, and we account for those by including three-body couplings between two bath bosons and the impurity. Our calculations compare very favorably with state-of-the-art experimental measurements and numerical simulations.

Systematizing and addressing theory uncertainties of unitarization with the Inverse Amplitude Method

Effective Field Theories (EFTs) constructed as derivative expansions in powers of momentum, in the spirit of Chiral Perturbation Theory (ChPT), are a controllable approximation to strong dynamics as long as the energy of the interacting particles remains small, as they do not respect exact elastic unitarity. This limits their predictive power towards new physics at a higher scale if small separations from the Standard Model are found at the LHC or elsewhere. Unitarized chiral perturbation theory techniques have been devised to extend the reach of the EFT to regimes where partial waves are saturating unitarity, but their uncertainties have hitherto not been addressed thoroughly. Here we take one of the best known of them, the Inverse Amplitude Method (IAM), and carefully following its derivation, we quantify the uncertainty introduced at each step. We compare its hadron ChPT and its electroweak sector Higgs EFT applications. We find that the relative theoretical uncertainty of the IAM at the mass of the first resonance encountered in a partial-wave is of the same order in the counting as the starting uncertainty of the EFT at near-threshold energies, so that its unitarized extension should a priori be expected to be reasonably successful. This is so provided a check for zeroes of the partial wave amplitude is carried out and, if they appear near the resonance region, we show how to modify adequately the IAM to take them into account.

Solar system, astrophysics, and cosmology from the derivative expansion

In this paper we show how the solar system, the galactic, and the cosmological scales, are accommodated in a single framework, namely, in the derivative expansion framework. We construct a locally inertial static metric, based on the Einstein equations and on the derivative expansion method, which describes a Schwarzschild black hole immersed in dark matter and dark energy. The leading order metric in the expansion corresponds to the solar system, the first order metric to the galaxy, and the second order metric to cosmology. It is shown how this metric captures the main observations at each scale: in the solar system it trivially gives the Keplerian physics, in the galaxy it gives the flat part of the rotation curve and the Baryonic Tully-Fisher relation, and in the cosmological scale it gives the cosmological redshift, the accelerating expansion, and it coincides with the Robertson–Walker spacetime in the appropriate limit and approximation.

Systematics of the \u03b1\u2032 expansion in F-theory

Extracting reliable low-energy information from string compactifications notoriously requires a detailed understanding of the UV sensitivity of the corresponding effective field theories. Despite past efforts in computing perturbative string corrections to the tree-level action, neither a systematic approach nor a unified framework has emerged yet. We make progress in this direction, focusing on the moduli dependence of perturbative corrections to the 4D scalar potential of type IIB Calabi-Yau orientifold compactifications. We proceed by employing two strategies. First, we use two rescaling symmetries of type IIB string theory to infer the dependence of any perturbative correction on both the dilaton and the Calabi-Yau volume. Second, we use F/M-theory duality to conclude that KK reductions on elliptically-fibred Calabi-Yau fourfolds of the M-theory action at any order in the derivative expansion can only generate (α′)even corrections to the 4D scalar potential, which, moreover, all vanish for trivial fibrations. We finally give evidence that (α′)odd effects arise from integrating out KK and winding modes on the elliptic fibration and argue that the leading no-scale breaking effects at string tree-level arise from (α′)3 effects, modulo potential logarithmic corrections.

Exploring the landscape for soft theorems of nonlinear sigma models

We generalize soft theorems of the nonlinear sigma model beyond the mathcal{O} (p2) amplitudes and the coset of SU(N) × SU(N)/SU(N). We first discuss the universal flavor ordering of the amplitudes for the Nambu-Goldstone bosons, so that we can reinterpret the known mathcal{O} (p2) single soft theorem for SU(N) × SU(N)/SU(N) in the context of a general symmetry group representation. We then investigate the special case of the fundamental representation of SO(N), where a special flavor ordering of the “pair basis” is available. We provide novel amplitude relations and a Cachazo-He-Yuan formula for such a basis, and derive the corresponding single soft theorem. Next, we extend the single soft theorem for a general group representation to mathcal{O} (p4), where for at least two specific choices of the mathcal{O} (p4) operators, the leading non-vanishing pieces can be interpreted as new extended theory amplitudes involving bi-adjoint scalars, and the corresponding soft factors are the same as at mathcal{O} (p2). Finally, we compute the general formula for the double soft theorem, valid to all derivative orders, where the leading part in the soft momenta is fixed by the mathcal{O} (p2) Lagrangian, while any possible corrections to the subleading part are determined by the mathcal{O} (p4) Lagrangian alone. Higher order terms in the derivative expansion do not contribute any new corrections to the double soft theorem.

Duality-invariant extensions of Einstein-Maxwell theory

We investigate higher-derivative extensions of Einstein-Maxwell theory that are invariant under electromagnetic duality rotations, allowing for non-minimal couplings between gravity and the gauge field. Working in a derivative expansion of the action, we characterize the Lagrangians giving rise to duality-invariant theories up to the eight-derivative level, providing the complete list of operators that one needs to include in the action. We also characterize the set of duality-invariant theories whose action is quadratic in the Maxwell field strength but which are non-minimally coupled to the curvature. Then we explore the effect of field redefinitions and we show that, to six derivatives, the most general duality-preserving theory can be mapped to Maxwell theory minimally coupled to a higher-derivative gravity containing only four non-topological higher-order operators. We conjecture that this is a general phenomenon at all orders, i.e., that any duality-invariant extension of Einstein-Maxwell theory is perturbatively equivalent to a higher-derivative gravity minimally coupled to Maxwell theory. Finally, we study charged black hole solutions in the six-derivative theory and we investigate additional constraints on the couplings motivated by the weak gravity conjecture.

Second order equilibrium transport in strongly coupled mathcal{N} = 4 supersymmetric SU(Nc) Yang-Mills plasma via holography

A relativistic fluid in 3+1 dimensions with a global U(1) symmetry admits nine independent static susceptibilities at the second order in the hydrodynamic derivative expansion, which capture the response of the fluid in thermal equilibrium to the presence of external time-independent sources. Of these, seven are time-reversal mathbbm{T} invariant and can be obtained from Kubo formulas involving equilibrium two-point functions of the energy-momentum tensor and the U(1) current. Making use of the gauge/gravity duality along with the aforementioned Kubo formulas, we compute all seven mathbbm{T} invariant second order susceptibilities for the mathcal{N} = 4 supersymmetric SU(Nc) Yang-Mills plasma in the limit of large Nc and at strong ’t-Hooft coupling λ. In particular, we consider the plasma to be charged under a U(1) subgroup of the global SU(4) R-symmetry of the theory. We present analytic expressions for three of the seven mathbbm{T} invariant susceptibilities, while the remaining four are computed numerically. The dual gravitational description for the charged plasma in thermal equilibrium in the absence of background electric and magnetic fields is provided by the asymptotically AdS5 Reissner-Nordström black brane geometry. The susceptibilities are extracted by studying perturbations to the bulk geometry as well as to the bulk gauge field. We also present an estimate of the second order transport coefficient κ, which determines the response of the fluid to the presence of background curvature, for QCD, and compare it with previous determinations made using different techniques.

Nonplanar dust acoustic waves in a four-component dusty plasma with double spectral distributed electrons: modulational instability and rogue waves

A theoretical investigation of nonplanar (cylindrical and spherical) amplitude modulation of dust acoustic waves (DAWs) in a four component dusty plasma including positive and negative dusts, Maxwellian ions and double spectral electron distribution (DSED) is carried out. The focusing modified nonlinear Schrödinger equation (MNLSE) is derived using the derivative expansion perturbation technique (DEPT). The limit of DSED to Maxwell distribution is discussed. The effects of the two spectral indices, r and q , on the modulational instability (MI) growth rate are examined and it is deduced that increasing the value of r and q raises the MI growth rate. Additionally, the structure of the first and second-order dust acoustic (DA) rogue waves in the modulational unstable region is analyzed. The influences of both of r and q on the rogue wave amplitude (energy) are investigated. We found that increasing the value of r enhances the rogue wave amplitude while the opposite behavior is found by increasing q values. The findings of the present study are useful to interpret some physical phenomena in various plasma situations that found in space regions, such as Titan (the largest moon) of Saturn, auroral region and asteroid zones, where the effectiveness of non-Maxwellian particles such as DSED is existed.

Abstract 1109: A novel strategy to cope with osimertinib resistance in non-small cell lung cancer by treatment with a PIM kinase inhibitor in combination with a MERTK-selective kinase inhibitor

Abstract Osimertinib is currently the preferred treatment for EGFR-mutated non-small cell lung cancer (NSCLC) patients due to its superior therapeutic efficacy and prolonged overall survival compared to earlier generation EGFR tyrosine kinase inhibitors, but durable responses to osimertinib treatment are rare due to acquired drug resistance. Thus, there is an urgent need for novel strategies to treat osimertinib-resistant NSCLC. Recently, we found that treatment with MRX-2843, a novel MERTK-selective kinase inhibitor currently in Phase I clinical trials, resulted in dose-dependent inhibition of cell expansion and colony formation in an osimertinib-resistant (osiR) H4006 derivative cell line. An unbiased screen of 378 kinase inhibitors was carried out to identify compounds that synergized with MRX-2843 to inhibit expansion of an osiR derivative of the EGFR-mutated H4011 cell line. Treatment with 1µM PIM kinase inhibitor SGI-1776 or 100nM MRX-2843 alone reduced cell density by 5±3% and 44±7%, respectively, while treatment with MRX-2843 and SGI-1776 combined mediated an 82±0.4% decrease. Synergy was also observed in H4006 osiR and H1650 osiR derivative cell lines. Furthermore, treatment with PIM447, a structurally distinct PIM kinase inhibitor, and MRX-2843 decreased cell expansion more effectively than either agent alone. Mechanistically, treatment with a PIM kinase inhibitor in combination with MRX-2843 decreased downstream PI3K-AKT and MAPK-ERK signaling more effectively than single agents. Additionally, combined treatment with MRX-2843 and SGI-1776 prevented colony formation, while single agents had limited effect. In all, these data indicate that combining MRX-2843 and a PIM TKI may control osimertinib resistant tumor growth, providing a potential treatment strategy for osimertinib resistant EGFR-mutated NSCLC patients for whom the choices are still limited. Citation Format: Dan Yan, Zikang Tan, Xiaodong Wang, Stephen V. Frye, H. Shelton Earp, III, Deborah DeRyckere, Douglas K. Graham. A novel strategy to cope with osimertinib resistance in non-small cell lung cancer by treatment with a PIM kinase inhibitor in combination with a MERTK-selective kinase inhibitor [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2021; 2021 Apr 10-15 and May 17-21. Philadelphia (PA): AACR; Cancer Res 2021;81(13_Suppl):Abstract nr 1109.

Assessment of systematic theory uncertainties in IAM unitarization

Effective Field Theories (EFTs) for Goldstone Boson scattering at a low order allow the computation of near–threshold observables in terms of a few coefficients arranged by a counting. As a matter of principle they should make sense up to an energy scale E ∼ 4πF but the expansion in powers of momentum violates exact elastic unitarity and renders the derivative expansion unreliable at much lower energies. If new–physics deviations from the Standard Model are found and encoded in low-energy coefficients, perhaps at the LHC, it will be profitable to extend the reach of the EFT to regimes where partial waves are saturating unitarity. The methods known in hadron physics as “Unitarized Chiral Perturbation Theory” extend the EFT up to its nominal reach or up to the first new physics resonance or structure (if found below that energy reach) in the partial wave amplitude, but they usually have unknown uncertainties. We recapitulate our analysis of the systematic theory uncertainties of the well known Inverse Amplitude Method (IAM).

Exact solutions and residual regulator dependence in functional renormalisation group flows

We construct exact solutions to the functional renormalisation group equation of the O(N) model and the Gross–Neveu model at large N for 2 < d < 4, without specifying the form of the regulator. This allows to investigate which quantities are independent of the choice of regulator without being plagued by truncation artefacts. We find that only universal quantities, like critical exponents, and qualitative features, like the existence of a finite vacuum expectation value, are regulator-independent, whereas values of coupling constants are generically arbitrary. We also provide a general algorithm to construct a concrete operator basis for truncations in the derivative expansion and the Blaizot–Méndez–Wschebor scheme.

Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization

We employ the functional renormalization group framework at the second order in the derivative expansion to study the O(N)O(N) models continuously varying the number of field components NN and the spatial dimensionality dd. We in particular address the Cardy-Hamber prediction concerning nonanalytical behavior of the critical exponents \nuν and \etaη across a line in the (d,N)(d,N) plane, which passes through the point (2,2)(2,2). By direct numerical evaluation of \eta(d,N)η(d,N) and \nu^{-1}(d,N)ν−1(d,N) as well as analysis of the functional fixed-point profiles, we find clear indications of this line in the form of a crossover between two regimes in the (d,N)(d,N) plane, however no evidence of discontinuous or singular first and second derivatives of these functions for d&gt;2d&gt;2. The computed derivatives of \eta(d,N)η(d,N) and \nu^{-1}(d,N)ν−1(d,N) become increasingly large for d\to 2d→2 and N\to 2N→2 and it is only in this limit that \eta(d,N)η(d,N) and \nu^{-1}(d,N)ν−1(d,N) as obtained by us are evidently nonanalytical. By scanning the dependence of the subleading eigenvalue of the RG transformation on NN for d&gt;2d&gt;2 we find no indication of its vanishing as anticipated by the Cardy-Hamber scenario. For dimensionality dd approaching 3 there are no signatures of the Cardy-Hamber line even as a crossover and its existence in the form of a nonanalyticity of the anticipated form is excluded.

Comparison between fluid-gravity and membrane-gravity dualities for Einstein–Maxwell system

Derivative expansion and large-D expansion are two perturbation techniques, which are used to generate dynamical black-brane solutions to Einstein’s equations in presence of negative cosmological constant. In this paper we have compared these two techniques and established the equivalence of the gravity solutions generated by these two different techniques in appropriate regime of parameter space up to first non-trivial order in both the perturbation parameters for Einstein–Maxwell systems, generalizing the earlier works of [, ] for non-charged systems. An one-to-one map between dynamical black-brane geometry and AdS space, which also exists at finite number of dimensions, has also been established.

Hydrodynamic fluctuations and long-time tails in a fluid on an anisotropic background

The effective low-energy late-time description of many body systems near thermal equilibrium provided by classical hydrodynamics in terms of dissipative transport phenomena receives important corrections once the effects of stochastic fluctuations are taken into account. One such physical effect is the occurrence of long-time power law tails in correlation functions of conserved currents. In the hydrodynamic regime k→0 this amounts to non-analytic dependence of the correlation functions on the frequency ω. In this article, we consider a relativistic fluid with a conserved global U(1) charge in the presence of a strong background magnetic field, and compute the long-time tails in correlation functions of the stress tensor. The presence of the magnetic field renders the system anisotropic. In the absence of the magnetic field, there are three out-of-equilibrium transport parameters that arise at the first order in the hydrodynamic derivative expansion, all of which are dissipative. In the presence of a background magnetic field, there are ten independent out-of-equilibrium transport parameters at the first order, three of which are non-dissipative and the rest are dissipative. We provide the most general linearized equations about a given state of thermal equilibrium involving the various transport parameters in the presence of a magnetic field, and use them to compute the long-time tails for the fluid.

Exploring new corners of asymptotically safe unimodular quantum gravity

The renormalization group flow of unimodular quantum gravity is investigated within two different classes of truncations of the flowing effective action. In particular, we search for nontrivial fixed-point solutions for polynomial expansions of the $f(R)$-type as well as of the $F({R}_{\ensuremath{\mu}\ensuremath{\nu}}{R}^{\ensuremath{\mu}\ensuremath{\nu}})+RZ({R}_{\ensuremath{\mu}\ensuremath{\nu}}{R}^{\ensuremath{\mu}\ensuremath{\nu}})$ family on a maximally symmetric background. We close the system of beta functions of the gravitational couplings with anomalous dimensions of the graviton and Faddeev-Popov ghosts treated according to two independent prescriptions: one based on the so-called background approximation and the other based on a hybrid approach which combines the background approximation with simultaneous vertex and derivative expansions. For consistency, in the background approximation, we employ a background-dependent correction to the flow equation which arises from the proper treatment of the functional measure of the unimodular path integral. We also investigate how different canonical choices of the endomorphism parameter in the regulator function affect the fixed-point structure. Although we find evidence for the existence of a nontrivial fixed point for the two classes of polynomial projections, the $f(R)$ truncation exhibits better (apparent) convergence properties. Furthermore, we consider the inclusion of matter fields without self-interactions minimally coupled to the unimodular gravitational action and we find evidence for compatibility of asymptotically safe unimodular quantum gravity with the field content of the Standard Model and some of its common extensions.

STrEAMlining EFT Matching

This paper presents STrEAM (SuperTrace Evaluation Automated for Matching), a Mathematica package that calculates all functional supertraces which arise when matching a generic UV model onto a relativistic Effective Field Theory (EFT) at one loop and to arbitrary order in the heavy mass expansion. STrEAM implements the covariant derivative expansion to automate the most tedious step of the streamlined functional matching prescription presented in Ref. [1]. The code and an example notebook are available at this link.