Higher Derivative Terms Research Articles

Higher-order-operator corrections to phase-transition parameters in dimensional reduction

The dynamics of phase transitions (PT) in quantum field theories at finite temperature is most accurately described within the framework of dimensional reduction. In this framework, thermodynamic quantities are computed within the 3-dimensional effective field theory (EFT) that results from integrating out the high-temperature Matsubara modes. However, strong-enough PTs, observable in gravitational wave (GW) detectors, occur often nearby the limit of validity of the EFT, where effective operators can no longer be neglected. Here, we perform a quantitative analysis of the impact of these interactions on the determination of PT parameters. We find that they allow for strong PTs in a wider region of parameter space, and that both the peak frequency and the amplitude of the resulting GW power spectrum can change by more than one order of magnitude when they are included. As a byproduct of this work, we derive equations for computing the bounce solution in the presence of higher-derivative terms, consistently with the EFT power counting.

Rethinking the effective field theory formulation of gravity

General relativity is highly successful in explaining a wide range of gravitational phenomena including the gravitational waves emitted by binary systems and the shadows cast by supermassive black holes. From a modern perspective the theory is not fundamental though, but constitutes the lowest order term in an effective field theory description of the gravitational force. As a consequence, the gravitational dynamics should receive corrections by higher-derivative terms. This essay discusses structural aspects associated with these corrections and summarizes their imprint on static, spherically symmetric geometries. Along these lines, we critically reassess the common practice of using local field redefinitions in order to simplify the dynamics at the danger of shifting physics effects into sectors which are beyond the approximation under consideration.

Gravitational index of the heterotic string

The fundamental heterotic string has a tower of BPS states whose supersymmetric index has an exponential growth in the charges. We construct the saddle-point of the gravitational path integral corresponding to this index. The saddle-point configuration is a supersymmetric rotating non-extremal Euclidean black hole. This configuration is singular in the two-derivative theory. We show that the addition of higher-derivative terms in four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 supergravity resolves the singularity. In doing so, we extend the recently-developed “new attractor mechanism” to include the effect of higher-derivative terms. Remarkably, the one-loop, four-derivative F-term contribution to the prepotential leads to a precise match of the gravitational and microscopic index. We also comment, using the effective theory near the horizon, on the possibility of a string-size near-extremal black hole. Our results clarify the meaning of different descriptions of this system in the literature. The thermal state transitions to a winding condensate and a gas of strings without ever reaching a small black hole, while the index is captured by the rotating Euclidean black hole solution and is constant and thus smoothly connected to the microscopic ensemble.

Black holes and wormholes beyond classical general relativity

In the paper only Static Spherically Symmetric space–times in four dimension are considered within modified gravity models. The non-singular static metrics, including black holes not admitting a de Sitter core in the center and traversable wormholes, are reconsidered within a class of higher-order F(R), satisfying the constraints F(0)=dFdR(0)=0. Furthermore, making use of the so called effective field theory formulation of gravity, the quantum corrections to Einstein–Hilbert action due to higher-derivative terms related to curvature invariants are investigated. In particular, in the case of Einstein–Hilbert action plus cubic curvature Goroff–Sagnotti contribution, the second order correction in the Goroff–Sagnotti coupling constant is computed. In general, it is shown that the effective metrics, namely Schwarzschild expression plus small quantum corrections are related to black holes, and not to traversable wormholes. In this framework, within the approximation considered, the resolution of singularity for r=0 is not accomplished. The related properties of these solutions are investigated.

L2$L^{2}$‐growth property for the wave equation with a higher derivative term

AbstractWe consider the Cauchy problem in for the wave equation with a higher derivative term. We derive sharp growth estimates of the ‐norm of the solution itself for the case of and . By imposing the weighted ‐initial velocity, we can get the lower and upper bound estimates of the solution itself. For the case of , we observe that the ‐growth behavior of the solution never occurs in the ‐framework of the initial data.

Gravity with spacetime torsion

The duality between a higher-curvature f(R) gravity model and a scalar-tensor theory helps to bring out the role of the additional degree of freedom originating from the higher-derivative terms in the gravity action. Such a degree of freedom which appears as a scalar field has been shown to have multiple implications in the cosmological/astrophysical scenario. The present work proposes a novel generalization to this correspondence between f(R) gravity and a dual scalar-tensor theory when the affine connection is considered to have an antisymmetric part. It turns out that the f(R) action in the presence of spacetime torsion can be recast to a coupled scalar-tensor theory with a 2-rank massless antisymmetric tensor field in the Einstein frame, where the scalar field gets coupled with the antisymmetric field through derivative coupling(s).

Supersymmetry and trace formulas. Part I. Compact Lie groups

In the context of supersymmetric quantum mechanics we formulate new supersymmetric localization principle, with application to trace formulas for a full thermal partition function. Unlike the standard localization principle, this new principle allows to compute the supertrace of non-supersymmetric observables, and is based on the existence of fermionic zero modes. We describe corresponding new invariant supersymmetric deformations of the path integral; they differ from the standard deformations arising from the circle action and require higher derivatives terms. Consequently, we prove that the path integral localizes to periodic orbits and not only on constant ones. We illustrate the principle by deriving bosonic trace formulas on compact Lie groups, including classical Jacobi inversion formula.

Bulk-boundary and RPS thermodynamics from topology perspective

In this study, we investigate the bulk-boundary and restricted phase space (RPS) thermodynamics of Rissner-Nordström (R-N) AdS and 6-dimensional charged Gauss-Bonnet AdS black holes. Additionally, we examine the topological characteristics of the considered black holes and compare them with the results of extended thermodynamics. We determine that the topological behavior of the bulk-boundary thermodynamics is the same as that of the extended thermodynamics, whereas the RPS thermodynamics exhibits a distinct behavior. Furthermore, we demonstrate that within the RPS formalism, there is only one critical point with a topological charge of +1 . Moreover, in the RPS formalism, the inclusion of higher-derivative curvature terms in the form of Gauss-Bonnet gravity does not alter the topological classification of critical points in charged AdS black holes.

One-loop divergences of effective action in 6D, [formula omitted] supersymmetric four-derivative gauge theory

We consider six-dimensional higher-derivative N=(1,0) supersymmetric gauge theory coupled with the hypermultiplet. We use the background superfield method in six-dimensional N=(1,0) harmonic superspace to study the effective action in the theory. Using the dimensional regularization scheme we analyze the one-loop divergent contributions to the effective action. We demonstrate that UV behavior is determined by the higher-derivative term for gauge multiplet sector.

Sudden breakdown of effective field theory near cool Kerr-Newman black holes

It was recently shown that (near-)extremal Kerr black holes are sensitive probes of small higher-derivative corrections to general relativity. In particular, these corrections produce diverging tidal forces on the horizon in the extremal limit. We show that adding a black hole charge makes this effect qualitatively stronger. Higher-derivative corrections to the Kerr-Newman solution produce tidal forces that scale inversely in the black hole temperature. We find that, unlike the Kerr case, for realistic values of the black hole charge large tidal forces can arise before quantum corrections due to the Schwarzian mode become important, so that the near-horizon behavior of the black hole is dictated by higher-derivative terms in the effective theory.

Bulk-boundary thermodynamics of charged black holes in higher-derivative theory

The connection between bulk and boundary thermodynamics in Einstein–Maxwell theory is well established using AdS/CFT correspondence. In the context of general higher-derivative gravity coupled to a U(1) gauge field, we examine the resemblance of the first law of thermodynamics between bulk and boundary, followed by an extended phase space description on both sides. Higher-derivative terms related to different powers of the string theory parameter α′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha '$$\\end{document} emerged from a consistent truncation in the bulk supergravity action. We demonstrate that one must include the fluctuation of α′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha '$$\\end{document} in the bulk thermodynamics as a bookkeeping tool to match the bulk first law and Smarr relation with the boundary side. Consequently, the Euler relation and the boundary first law are altered by adding two central charges (a,c).\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\ exttt{a}}, {\ exttt{c}}).$$\\end{document} To support our general conclusion, we consider the black hole in Gauss–Bonnet gravity and the general four-derivative theory. Finally, we examine the bulk and boundary aspects of the extended phase space description for higher-derivative-corrected black holes.

Scale-dependent cosmology from effective quantum gravity in the invariant framework

We explore the possibility of a consistent cosmology based on the gauge-fixing independent running of the gravitational and cosmological constants (G and Λ) in the framework of effective quantum gravity. In particular, their running in this framework was found to satisfy G∝Λ4. In the cosmological setting, the covariance of the theory provides energy conservation relations, which are impossible to satisfy with the unique scale parameter. However, by introducing the second sub-dominant scale corresponding to the higher-loop corrections and higher-derivative terms, one can close the system of equations for the running of parameters and arrive at the consistent cosmological solutions. This approach yields a change in the cosmological expansion history that affects the ratio of the Hubble parameter today to the Hubble parameter at high redshift.

Small kinetic mixing in string theory

Kinetic mixing between gauge fields of different U(1) factors is a well-studied phenomenon in 4d EFT. In string compactifications with U(1)s from sequestered D-brane sectors, kinetic mixing becomes a key target for the UV prediction of a phenomenologically important EFT operator. Surprisingly, in many cases kinetic mixing is absent due to a non-trivial cancellation. In particular, D3-D3 kinetic mixing in type-IIB vanishes while D3-anti-D3 mixing does not. This follows both from exact CFT calculations on tori as well as from a leading-order 10d supergravity analysis, where the key cancellation is between the C2 and B2 contribution. We take the latter approach, which is the only one available in realistic Calabi-Yau settings, to a higher level of precision by including sub-leading terms of the brane action and allowing for non-vanishing C0. The exact cancellation persists, which we argue to be the result of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext{SL}}\\left(2,{\\mathbb{R}}\\right)$$\\end{document} self-duality. We note that a B2C2 term on the D3-brane, which is often missing in the recent literature, is essential to obtain the correct zero result. Finally, allowing for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext{SL}}\\left(2,{\\mathbb{R}}\\right)$$\\end{document}-breaking fluxes, kinetic mixing between D3-branes arises at a volume-suppressed level. We provide basic explicit formulae, both for kinetic as well as magnetic mixing, leaving the study of phenomenologically relevant, more complex situations for the future. We also note that describing our result in 4d supergravity appears to require higher-derivative terms — an issue which deserves further study.

Effective field theory of black hole perturbations in vector-tensor gravity

We formulate the effective field theory (EFT) of vector-tensor gravity for perturbations around an arbitrary background with a timelike vector profile, which can be applied to study black hole perturbations. The vector profile spontaneously breaks both the time diffeomorphism and the U(1) symmetry, leaving their combination and the spatial diffeomorphism as the residual symmetries in the unitary gauge. We derive two sets of consistency relations which guarantee the residual symmetries of the EFT. Also, we provide the dictionary between our EFT coefficients and those of generalized Proca (GP) theories, which enables us to identify a simple subclass of the EFT that includes the GP theories as a special case. For this subclass, we consider the stealth Schwarzschild(-de Sitter) background solution with a constant temporal component of the vector field and study the decoupling limit of the longitudinal mode of the vector field, explicitly showing that the strong coupling problem arises due to vanishing sound speeds. This is in sharp contrast to the case of gauged ghost condensate, in which perturbations are weakly coupled thanks to certain higher-derivative terms, i.e., the scordatura terms. This implies that, in order to consistently describe this type of stealth solutions within the EFT, the scordatura terms must necessarily be taken into account in addition to those already included in the simple subclass.

Testing Higher Derivative Gravity through Tunnelling

Higher derivative terms in the gravitational action are natural from the perspective of quantum gravity, but are perceived as leading to a lack of well-posedness. The Gauss–Bonnet term has second-order equations of motion, but does not impact gravitational dynamics in 4D, so one might expect that it is not physically relevant. We discuss how signatures can show up in tunnelling processes and whether these will likely be physically accessible in Higgs vacuum decay.

Einstein–Cartan pseudoscalaron inflation

We study a class of early universe cosmological models based on Einstein–Cartan gravity and including a higher derivative term corresponding to a power of the Holst scalar curvature. The resulting effective action is basically given by General Relativity and an additional neutral pseudoscalar field (the pseudoscalaron), unequivocally related to the corresponding components of the torsion, that necessarily acquire a dynamics. The induced pseudoscalaron potential provides a realistic inflationary phase together with a very rich postinflationary epoch, resulting from the coupling of the pseudoscalaron to ordinary matter.

Emergence of species scale black hole horizons

The scale at which quantum gravity becomes manifest, the species scale Λs, has recently been argued to take values parametrically lower than the Planck scale. We use black holes of vanishing horizon area (small black holes) in effective field theories coupled to quantum gravity to shed light on how the three different physical manifestations of the species scale Λs relate to each other. (i) Near the small black hole core, a scalar field runs to infinite distance in moduli space, a regime in which the Swampland Distance Conjecture predicts a tower of exponentially light states, which lower Λs. (ii) We integrate out modes in the tower and generate via Emergence a set of higher derivative corrections, showing that Λs is the scale at which such terms become relevant. (iii) Finally, higher derivative terms modify the black hole solution and grant it a non-zero, species scale sized stretched horizon of radius Λs−1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\Lambda}_s^{-1} $$\\end{document}, showcasing the species scale as the size of the smallest possible black hole describable in the effective theory.We present explicit 4d examples of small black holes in 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 supergravity, and the 10d example of type IIA D0-branes. The emergence of the species scale horizon for D0-branes requires a non-trivial interplay of different 8-derivative terms in type IIA and M-theory, providing a highly non-trivial check of our unified description of the different phenomena associated to the species scale.

De Sitter-eating O-planes in supercritical string theory

It has been proposed that flux compactifications of supercritical string theories (i.e., with spacetime dimension D > 10) have dS vacua, with large D acting as a control parameter for corrections to the classical spacetime effective action. In this paper, we provide a detailed analysis of the self-consistency of such models, focussing on α′ and backreaction corrections. We first show that all supercritical AdS, Minkowski and dS vacua in this setting have gtrsim mathcal{O}(1) curvature and/or field strengths in the string frame. This may be in tension with suppressing α′ corrections unless the coefficients of the higher-derivative terms have a sufficiently strong large-D suppression. We then argue that an additional and more severe problem arises in the dS case due to the backreaction of O-planes. In particular, we argue using a combination of geometric bounds and string-theory constraints that the O-plane backreaction is large in supercritical dS models. This implies that a large part of the naive classical geometry is eaten up by singular holes and thus indicates a breakdown of the classical description. Our finding resonates with several other recent results suggesting that string theory does not admit dS vacua in regimes where string and backreaction corrections are under control. As byproducts of our analysis, we derive a number of technical results that are useful beyond the specific applications in this paper. In particular, we compute the leading backreaction corrections to the smeared solution in a general flux compactification from D to d dimensions for an arbitrary distribution of O-planes and D-branes. We further argue for a general estimate for Green’s functions on compact manifolds (and therefore for the backreaction corrections) in terms of their diameter, volume and dimension.

Planar electrodynamics modified by higher-derivative terms

Planar electrodynamics modified by higher-derivative terms

Lorentz-breaking Rarita-Schwinger model

In this paper, we formulate the simplest Lorentz-breaking extension for the spin-3/2 field theory and couple it to the Abelian gauge field in a Lorentz violating (LV) manner. Next, we calculate the lower LV quantum corrections, that is, the Carroll-Field-Jackiw (CFJ) term, which, being superficially divergent, turns out to be finite but ambiguous, and also the higher-derivative CFJ term. Besides, we compute the aether term, being the lowest CPT-even LV term, involving the second order in the LV vector.