We apply positivity bounds directly to a $U(1)$ gauge theory with charged scalars and charged fermions, i.e. QED, minimally coupled to gravity. Assuming that the massless $t$-channel pole may be discarded, we show that the improved positivity bounds are violated unless new physics is introduced at the parametrically low scale $Λ_{\rm new} \sim (e m M_{\rm pl})^{1/2}$, consistent with similar results for scalar field theories, far lower than the scale implied by the weak gravity conjecture. This is sharply contrasted with previous treatments which focus on the application of positivity bounds to the low energy gravitational Euler-Heisenberg effective theory only. We emphasise that the low-cutoff is a consequence of applying the positivity bounds under the assumption that the pole may be discarded. We conjecture an alternative resolution that a small amount of negativity, consistent with decoupling limits, is allowed and not in conflict with standard UV completions, including weakly coupled ones.
The lattice regularized pure gauge compact U(1) theory is an ideal laboratory to explore how confinement is realized as its phase diagram has a confined and a deconfined phase that depends on the value of the coupling constant, i.e. on $β$. Herein, the connection between confinement and positivity violation through the Schwinger function associated with the Landau gauge photon propagator is investigated. The simulations reported show a very clear link between the realization of confinement and positivity violation of the photon Schwinger function and, therefore, of the photon Källén-Lehmann sp…
Scattering amplitudes mediated by graviton exchange display IR singularities in the forward limit. This obstructs standard application of positivity bounds based on twice subtracted dispersion relations. Such divergences can be cancelled only if the UV limit of the scattering amplitude behaves in a specific way, which implies a very non-trivial connection between the UV and IR behaviors of the amplitude. We show that this relation can be expressed in terms of an integral transform, obtaining analytic results when $t \log{s}\rightarrow 0$. Carefully applying this limit to dispersion relations, …
The presence of a massless spin-2 field in an effective field theory results in a $t$-channel pole in the scattering amplitudes that precludes the application of standard positivity bounds. Despite this, recent arguments based on compactification to three dimensions have suggested that positivity bounds may be applied to the $t$-channel pole subtracted amplitude. If correct this would have deep implications for UV physics and the Weak Gravity Conjecture. Within the context of a simple renormalizable field theory coupled to gravity we find that applying these arguments would constrain the low-e…
We show how calculable IR loop effects impact positivity bounds in Effective Field Theories with causal and unitary UV completions. We identify infrared singularities which appear in dispersion relations at $|t|\lesssim m^2$. In the massless limit, they weaken two-sided bounds based on crossing symmetry, such as the lower bound on the amplitude for Galileon scattering. For amplitudes that are analytic in $s$ even for large negative $t$, i.e. $|t|\gg m^2$, we propose a new simple analytic approach to dispersive bounds, which are instead insensitive to the singularities, and explicitly compute t…
The manifestly Lorentz covariant formulation of quantum electrodynamics disregards Coulomb instantaneous interaction and its consequence - instantaneous bound states (IBS's). In this article we consider the way of construction the IBS generating functional using the operator generalization of the initial data in the Dirac Hamiltonian approach to QED.
The low-energy electron-electron scattering potential is derived and discussed for the Maxwell-Chern-Simons model coupled to QED_3 with spontaneous symmetry breaking. One shows that the Higgs mechanism might favour electron-electron bound states.
The consistency of the EFT of two interacting spin-2 fields is checked by applying forward limit positivity bounds on the scattering amplitudes to exclude the region of parameter space devoid of a standard UV completion. We focus on two classes of theories that have the highest possible EFT cutoff, namely those theories modelled on ghost-free interacting theories of a single massive spin-2 field. We find that the very existence of interactions between the spin-2 fields implies more stringent bounds on all the parameters of the EFT, even on the spin-2 self-interactions. This arises for two reas…
In this note, we study the connections between infrared (IR) and ultraviolet (UV) behaviors of scattering amplitudes of massless channels by exploiting dispersion relations and positivity bounds. Given forward scattering amplitudes, which scale as $\mathcal{A}(s)\sim s^M$ in the IR ($s\to0$) and could be embedded into UV completions satisfying unitarity, analyticity, crossing symmetry and polynomial boundedness $|\mathcal{A}(s)|< c\, |s|^N$ ($|s|\to\infty$), with $M$ and $N$ integers, we show that the inequality $2\ceil*{\frac{N}{2}}\ge M \ge \ceil*{\frac{N}{2}}$ must hold, where $\ceil*{x}$ i…
The self-field approach to quantum electrodynamics (QED) is used to study the bound state problem in light-front two-dimensional QED with massive matter fields. A composite matter field describing bound states is introduced and the relativistic bound state equation for the composite field including a self-potential is obtained. The Hamiltonian form of the bound state equation in terms of the invariant mass squared operator is given. The eigenvalue problem of this operator is solved for a fixed value of the self-potential, the corresponding eigenfunctions and the mass spectrum are found. In the…
Killing-Yano tensors are natural generalizations of Killing vectors to arbitrary rank anti-symmetric tensor fields. It was recently shown that Killing-Yano tensors lead to conserved gravitational charges, called Y-ADM charges. These new charges are interesting because they measure, for example, the mass density of a p-brane, rather than the total ADM mass which may be infinite. In this paper, we show that the spinorial techniques used by Witten, in his proof of the positive energy theorem, may be straightforwardly extended to study the positivity properties of the Y-ADM mass density for p-bran…
Using mass perturbation theory, we infer the bound-state spectrum of massive QED$_2$ and compute some decay widths of unstable bound states. Further, we discuss scattering processes, where all the resonances and particle production thresholds are properly taken into account by our methods.
A lower bound is placed on the fermionic determinant of Euclidean quantum electrodynamics in three dimensions in the presence of a smooth, finite--flux, static, unidirectional magnetic field $\mathbf{B}(\mathbf{r})=(0,0,B(\mathbf{r}))$, where $B(\mathbf{r})\geq 0$ or $B(\mathbf{r})\leq 0$ and $\mathbf r$ is a point in the $xy\mbox{-plane}$. Bounds are also obtained for the induced spin for $2+1$ dimensional QED in the presence of $\mathbf{B}(\mathbf{r})$. An upper bound is placed on the fermionic determinant of Euclidean QED in four dimensions in the presence of a strong, static, directionally…
We study the validity of positivity bounds in the presence of a massless graviton, assuming the Regge behavior of the amplitude. Under this assumption, the problematic $t$-channel pole is canceled with the UV integral of the imaginary part of the amplitude in the dispersion relation, which gives rise to finite corrections to the positivity bounds. We find that low-energy effective field theories (EFT) with "wrong" sign are generically allowed. The allowed amount of the positivity violation is determined by the Regge behavior. This violation is suppressed by $M_{\rm pl}^{-2}α'$ where $α'$ is th…
Focusing on four-Higgs interactions, we analyse the robustness of tree-level-derived positivity bounds on Standard Model effective field theory (SMEFT) operators under quantum corrections. Among other results, we demonstrate that: (i) Even in the simplest extensions of the Standard Model, e.g. with one new scalar singlet or with a neutral triplet, some positivity bounds are strictly violated; (ii) the mixing of the dimension-eight operators under renormalisation, which we compute here for the first time, can drive them out of their positivity region; (iii) the running of the dimension-eight in…
Recently, a new set of positivity bounds with $t$ derivatives have been discovered. We explore the generic features of these generalized positivity bounds with loop amplitudes and apply these bounds to constrain the parameters in chiral perturbation theory up to the next-to-next-to-leading order. We show that the generalized positivity bounds give rise to stronger constraints on the $\bar l_i$ constants, compared to the existing axiomatic bounds. The parameter space of the $b_i$ constants is constrained by the generalized positivity bounds to be a convex region that is enclosed for many sectio…
The Bound State in QED is described in systematic way by means of nonlocal irreducible representations of the nonhomogeneous Poincare group and Dirac's method of quantization. As an example of application of this method we calculate triangle diagram $Para-Positronium \to γγ$. We show that the Hamiltonian approach to Bound State in QED leads to anomaly-type contribution to creation of pair of parapositronium by two photon.
Full positivity bounds for anomalous quartic gauge couplings in SMEFT
University of Science and Technology of China（中国科学技术大学）；Interdisciplinary Center for Theoretical Study, University of Science and Technology of China（中国科学技术大学交叉理论研究中心）；Peng Huanwu Center for Fundamental Theory（彭桓武基础研究中心）
We derive new effective field theory (EFT) positivity bounds on the elastic $2\to2$ scattering amplitudes of massive spinning particles from the standard UV properties of unitarity, causality, locality and Lorentz invariance. By bounding the $t$ derivatives of the amplitude (which can be represented as angular momentum matrix elements) in terms of the total ingoing helicity, we derive stronger unitarity bounds on the $s$- and $u$-channel branch cuts which determine the dispersion relation. In contrast to previous positivity bounds, which relate the $t$-derivative to the forward-limit EFT ampli…
Triple crossing positivity bounds for multi-field theories
University of Science and Technology of China（中国科学技术大学）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Center for High Energy Physics, Peking University（北京大学高能物理中心）；Peng Huanwu Center for Fundamental Theory（彭桓武理论物理中心）
Positivity bounds are powerful tools to constrain effective field theories. Utilizing the partial wave expansion in the dispersion relation and the full crossing symmetry of the scattering amplitude, we derive several sets of generically nonlinear positivity bounds for a generic scalar effective field theory: We refer to these as the $PQ$, $D^{\rm su}$, $D^{\rm stu}$ and $\bar{D}^{\rm stu}$ bounds. While the $PQ$ bounds and $D^{\rm su}$ bounds only make use of the $s\leftrightarrow u$ dispersion relation, the $D^{\rm stu}$ and $\bar{D}^{\rm stu}$ bounds are obtained by further imposing the $s\…
Positivity bounds from thermal field theory entropy
Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院，中国科学院大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；University of Chinese Academy of Sciences (UCAS)（中国科学院大学）
Propagator positivity bounds for cosmological correlators
Leung Center for Cosmology and Particle Astrophysics, National Taiwan University（国立台湾大学梁中心宇宙学与粒子天体物理学）；Department of Physics and Astronomy, Queen Mary University of London（伦敦玛丽女王大学物理与天文系）
The EEC-Hedron: Positivity Bounds on Energy Correlators
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Yale University（耶鲁大学）；Heriot-Watt University（赫瑞-瓦特大学）；Fudan University（复旦大学）；Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS)（上海数学与交叉学科研究院）；Carnegie Mellon University（卡内基梅隆大学）
The positivity bounds, derived from the axiomatic principles of quantum field theory (QFT), constrain the signs of Wilson coefficients and their linear combinations in the Standard Model Effective Field Theory (SMEFT). The precise determination of these bounds, however, can become increasingly difficult as more and more SM modes and operators are taken into account. We study two approaches that aim at obtaining the full set of bounds for a given set of SM fields: 1) the traditional elastic positivity approach, which exploits the elastic scattering amplitudes of states with arbitrarily superpos…
The main objective of this work is to isolate Effective Field Theory scattering amplitudes in the space of non-perturbative two-to-two amplitudes, using the S-matrix Bootstrap. We do so by introducing the notion of Effective Field Theory cutoff in the S-matrix Bootstrap approach. We introduce a number of novel numerical techniques and improvements both for the primal and the linearized dual approach. We perform a detailed comparison of the full unitarity bounds with those obtained using positivity and linearized unitarity. Moreover, we discuss the notion of Spin-Zero and UV dominance along the…
Theories such as massive Galileons and massive gravity can satisfy the presently known improved positivity bounds provided they are weakly coupled. We discuss the form of the EFT Lagrangian for a weakly coupled UV completion of massive gravity which closely parallels the massive Galileon, and perform the power counting of corrections to the scattering amplitude and the positivity bounds. The Vainshtein mechanism which is central to the phenomenological viability of massive gravity is entirely consistent with weak coupling since it is classical in nature. We highlight that the only implication …
We derive positivity bounds for scattering amplitudes of particles with arbitrary spin using unitarity, analyticity and crossing symmetry. The bounds imply the positivity of certain low-energy coefficients of the effective action that controls the dynamics of the light degrees of freedom. We show that low-energy amplitudes strictly softer than $O(p^4)$ do not admit unitary ultraviolet completions unless the theory is free. This enforces a bound on the energy growth of scattering amplitudes in the region of validity of the effective theory. We discuss explicit examples including the Goldstino f…
Positivity bounds provide conditions that a consistent UV-completion exists for a quantum field theory. We examine their application to Horndeski gravity models reconstructed from the effective field theory (EFT) of dark energy. This enables us to assess whether particular phenomenological parameterizations of the EFT functions reconstruct theories that respect or violate the positivity bounds. We find that commonly adopted EFT parametrizations, cast in terms of the dark energy density or power laws of the scale factor, only satisfy the positivity bounds in non-trivial regions of the parameter…
Assuming unitarity, locality, causality, and Lorentz invariance of the, otherwise unknown, UV completion, we derive a new set of constraints on the effective field theory coefficients for the most general, ghost-free Generalized Proca and Proca Nuevo massive vector models. For the Generalized Proca model, we include new interactions that had not been previously considered in the context of positivity bounds and find these additional terms lead to a widened parameter space for the previously considered interactions. Although, the Generalized Proca and Proca Nuevo models are inequivalent, we fin…
We derive positivity bounds on low energy effective field theories which admit gapped, analytic, unitary, Lorentz invariant, and possibly non-local UV completions, by considering 2 to 2 scatterings of Jaffe fields whose Lehmann-Källén spectral density can grow exponentially. Several properties of S-matrix, such as analyticity properties, are assumed in our derivation. Interestingly, we find that some of the positivity bounds obtained in the literature, such as sub-leading order forward-limit bounds, must be satisfied even when UV completions fall into non-localizable theories in Jaffe's langua…
The diphoton channel at lepton colliders, $e^+e^- (μ^+μ^-) \to γγ$, has a remarkable feature that the leading new physics contribution comes only from dimension-eight operators. This contribution is subject to a set of positivity bounds, derived from the fundamental principles of Quantum Field Theory, such as unitarity, locality, analyticity and Lorentz invariance. These positivity bounds are thus applicable to the most direct observable -- the diphoton cross section. This unique feature provides a clear, robust, and unambiguous test of these principles. We estimate the capability of various f…
The EFT coefficients in any gapped, scalar, Lorentz invariant field theory must satisfy positivity requirements if there is to exist a local, analytic Wilsonian UV completion. We apply these bounds to the tree level scattering amplitudes for a massive Galileon. The addition of a mass term, which does not spoil the non-renormalization theorem of the Galileon and preserves the Galileon symmetry at loop level, is necessary to satisfy the lowest order positivity bound. We further show that a careful choice of successively higher derivative corrections are necessary to satisfy the higher order posi…
In order to calculate QED corrections to hadronic physical quantities by means of lattice simulations, a coherent description of electrically-charged states in finite volume is needed. In the usual periodic setup, Gauss's law and large gauge transformations forbid the propagation of electrically-charged states. A possible solution to this problem, which does not violate the axioms of local quantum field theory, has been proposed by Wiese and Polley, and is based on the use of C* boundary conditions. We present a thorough analysis of the properties and symmetries of QED in isolation and QED cou…
Requiring the existence of a unitary, causal and local UV-completion places a set of positivity bounds on the corresponding effective field theories (EFTs). We discuss the obstructions and possibility in applying the positivity bound to cosmology, in particular the EFT of cosmological perturbations. Taking a $c_T=1$ beyond-Horndeski EFT as an illustrative example, we derive such bounds, which incorporate the cosmological correction of order $H^2/Λ^2$, $Λ$ being the cutoff scale. The derived bounds are applied to slow-roll inflation with beyond Horndeski operators. It is found that the cosmolog…
From general analyticity and unitarity requirements on the UV theory, positivity bounds on the Wilson coefficients of the dimension-8 operators composed of 4 fermions and two derivatives appearing in the Standard Model Effective Field Theory have been derived recently. We explore the fate of these bounds in the context of models endowed with a Minimal Flavor Violation (MFV) structure, models in which the flavor structure of higher dimensional operators is inherited from the one already contained in the Yukawa sector of the Standard Model Lagrangian. Our goal is to check whether the general pos…
We derive the first positivity bounds for low-energy Effective Field Theories (EFTs) that are not invariant under Lorentz boosts. "Positivity bounds" are the low-energy manifestation of certain fundamental properties in the UV -- to date they have been used to constrain a wide variety of EFTs, however since all of the existing bounds require Lorentz invariance they are not directly applicable when this symmetry is broken, such as for most cosmological and condensed matter systems. From the UV axioms of unitarity, causality and locality, we derive an infinite family of bounds which (derivatives…
We derive constraints on scalar field theories coupled to gravity by using recently developed positivity bounds in the presence of gravity. It is found that a canonically-normalized real scalar cannot have an arbitrarily flat potential unless some new physics enters well below the Planck scale. An upper bound on the scale of new physics is determined by loop corrections to the self-energy. Our result provides a swampland condition for scalar potentials.
We use generalized elastic positivity bounds to constrain the parameter space of multi-field spin-2 effective field theories. These generalized bounds involve inelastic scattering amplitudes between particles with different masses, which contain kinematic singularities even in the $t=0$ limit. We apply these bounds to the pseudo-linear spin-2 theory, the cycle spin-2 theory and the line spin-2 theory respectively. For the pseudo-linear theory, we exclude the remaining operators that are unconstrained by the usual elastic positivity bounds, thus excluding all the leading (or highest cutoff) int…
Positivity bounds - constraints on any low-energy effective field theory imposed by the fundamental axioms of unitarity, causality and locality in the UV - have recently been used to constrain scalar-tensor theories of dark energy. However, the coupling to matter fields has so far played a limited role. We show that demanding positivity when including interactions with standard matter fields leads to further constraints on the dark energy parameter space. We demonstrate how implementing these bounds as theoretical priors affects cosmological parameter constraints and explicitly illustrate the …
We derive positivity bounds on EFT coefficients in theories where boosts are spontaneously broken. We employ the analytic properties of the retarded Green's function of conserved currents (or of the stress-energy tensor) and assume the theory becomes conformal in the UV. The method is general and applicable to both cosmology and condensed matter systems. As a concrete example, we look at the EFT of conformal superfluids which describes the universal low-energy dynamics of CFT's at large chemical potential and we derive inequalities on the coefficients of the operators, in three dimensions, at …
Models that provide experimentally testable violations of ordinary Quantum Mechanics have been recently proposed. These models are based on non-unitary time evolutions of density matrices that are generated by linear positive maps. We discuss the consequences of imposing a stronger condition on those maps, known as complete positivity. It turns out that experimental data on the neutral kaon system giving upper bounds to the parameters characterizing positive maps, also give bounds to those determining completely positive ones.
We apply the recently developed positivity bounds for particles with spin, applied away from the forward limit, to the low energy effective theories of massive spin-1 and spin-2 theories. For spin-1 theories, we consider the generic Proca EFT which arises at low energies from a heavy Higgs mechanism, and the special case of a charged Galileon for which the EFT is reorganized by the Galileon symmetry. For spin-2, we consider generic $Λ_5$ massive gravity theories and the special `ghost-free' $Λ_3$ theories. Remarkably we find that at the level of 2-2 scattering, the positivity bounds applied to…
