arXiv subjects

Andrew J. Tolley

Publications and source records attributed to Andrew J. Tolley.

At least 19 recordsLinked to original sources

arXiv2026

Six Particles, Infinite Optimism: Towards Positivity Bounds for Six-Point Amplitudes

The systematic generalisation of the well-established $S$-matrix positivity and bootstrap bounds from $2 \to 2$ scattering processes to higher-point amplitudes has, to date, remained elusive. To address this, we consider a large class of tree-level UV-completions of a single-scalar EFT. Specifically, we consider the most general renormalisable $N$-scalar theory in $D=4$. By explicitly computing tree-level amplitudes for four-, five- and six-point scattering and expanding at low energies, we can search for positivity relations among the expansion coefficients. We find that quite generally positivity bounds are unavailable due to contamination from a specific class of Feynman diagrams that are linear in sign-indefinite cubic couplings. However, by isolating a sector of the full crossing-symmetric low-energy amplitude that is unaffected by these sign-indefinite cubic couplings, we find that selected six-, five- and four-point Wilson coefficients organise into positive semi-definite matrices. While a violation of these positivity statements only implies that a given EFT is inconsistent with our class of UV completions, the result helps to guide towards what more general positivity bounds for higher-point interactions could, and could not, look like.

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arXiv2026

Unitary Dual-Resonance S-matrices

Dual-resonance models realize crossing symmetry, Regge behavior and infinitely many resonances in a compact analytic form but their canonical tree-level realizations fall short of genuine S-matrix unitarity. Here we explicitly construct fully unitary dual-resonance amplitudes distinct from the conventional worldsheet construction. The zero-width resonance towers are promoted into a physical absorptive spectrum that retains their characteristic crossing and Regge organization, while unitarizing the amplitude through a mechanism distinct from standard eikonalization. The resulting S-matrices are also local and analytic, and can contain controllable second-sheet Regge trajectories as well as substantial inelasticity. More broadly, our construction opens up a new route to charting the space of consistent strongly coupled S-matrices.

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arXiv2026

Diffeomorphic Scalar Duality

We show that every local scalar effective field theory admits a new kind of duality to an infinite class of local scalar field theories with distinct Lagrangians. The duality map takes the form of a field-dependent diffeomorphism, and cannot be obtained via purely local field redefinitions, nevertheless the dual theory has an identical $S$-matrix. The subset of interactions that maintain second-order equations of motion is non-trivially mapped into themselves under this transformation. We show how to couple generic scalar field theories to gravity in a way that preserves the duality. Crucially, this requires working in the Einstein-Cartan formalism, with the vielbein and spin connection treated as independent variables. When coupling to massless gravity, the duality is interpreted as a local field redefinition in which the vielbein transforms while the spin connection is held fixed; consequently, a torsion-free configuration is generically mapped to a dual configuration with non-zero torsion. We specify the general family of first-order gravitational theories that map into themselves under the duality. In the weak gravitational field limit, these reduce to scalar theories kinetically mixed with the graviton, which themselves form a family closed under the duality.

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arXiv2026

Gauging Open EFTs from the top down

We present explicit top-down calculations of Open EFTs for gauged degrees of freedom with a focus on the effects of gauge fixing. Starting from the in-in contour with two copies of the action, we integrate out the charged matter in various $U(1)$ gauge theories to obtain the Feynman-Vernon influence functional for the photon, or, in the case of symmetry breaking, for the photon and Stückelberg fields. The influence functional is defined through a quantum path integral, which -- as is always the case when quantizing gauge degrees of freedom -- contains redundancies that must be eliminated via a gauge-fixing procedure. We implement the BRST formalism in this setting. The in-in boundary conditions break the two copies of BRST symmetry down to a single diagonal copy. Nevertheless the single diagonal BRST is sufficient to ensure that the influence functional is itself gauge invariant under two copies of gauge symmetries, retarded and advanced, regardless of the choice of state or symmetry-breaking phase. We clarify how this is consistent with the decoupling limit where the global advanced symmetry is generically broken by the state. We illustrate our results with several examples: a gauge field theory analogue of the Caldeira-Leggett model, spinor QED with fermions integrated out, scalar QED in a thermal state, the Abelian Higgs-Kibble model in the spontaneously broken state with the Higgs integrated out, and Abelian Higgs-Kibble model coupled to a charged bath in a symmetry-broken phase. The latter serves as an example of an open system for Stückelberg/Goldstone fields.

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arXiv2026

Schwinger-Keldysh Path Integral for Gauge theories

We develop the Schwinger-Keldysh path-integral formalism for open non-Abelian gauge theories that are gauge-fixed via the BRST method in covariant gauges. We focus on generic initial states, pure and mixed, specified at finite times suitable for non-equilibrium processes. We pay particular attention to the handling of the indefinite Hilbert space, the construction of BRST-invariant Schrodinger picture wavefunctionals, density matrices and inner product, the implementation of the Hata-Kugo prescription, and the role of boundary terms at both the initial and final times. We highlight the advantages of the Nakanishi-Lautrup field representation in dealing with initial/final conditions. The resulting Schwinger-Keldysh path integral is manifestly invariant under a diagonal (retarded) BRST symmetry for arbitrary physical initial states, whether pure or mixed. From this, we obtain the corresponding Ward-Takahashi-Slavnov-Taylor identities, valid perturbatively. Non-perturbatively the Gribov ambiguity is expected to break or modify the BRST symmetry. The naive advanced BRST symmetry is shown to be explicitly violated by the in-in boundary conditions. We show that the Feynman-Vernon influence functional derived by integrating out charged matter and/or hard gluon modes remains (perturbatively) BRST invariant. When the Open EFT action is expanded to second order in advanced fields it exhibits an exact symmetry under a contraction of the original BRST symmetry. This Keldysh BRST symmetry is equivalent to the BRST associated with the retarded gauge transformations together with a linearly realized BRST transformation of the advanced fields. These govern the structure of the leading terms in an Open EFT. We illustrate this with the explicit example of Hard Thermal Loop Effective Theory, and construct the general form of the Open EFT in a Higgs phase when all gauge symmetries are spontaneously broken.

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arXiv2026

Primal S-matrix bootstrap with dispersion relations

We propose a new method for constructing the consistent space of scattering amplitudes by parameterizing the imaginary parts of partial waves and utilizing dispersion relations, crossing symmetry, and full unitarity. Using this framework, we explicitly compute bounds on the leading couplings and examine the Regge behaviors of the constructed amplitudes. The method also readily accommodates spinning bound states, which we use to constrain glueball couplings. By incorporating dispersion relations, our approach inherently satisfies the Froissart-Martin/Jin-Martin bounds or softer high-energy behaviors by construction. This, in turn, allows us to formulate a new class of fractionally subtracted dispersion relations, through which we investigate the sensitivity of coupling bounds to the asymptotic growth rate.

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arXiv2026

Graviton propagation in ghost-free massive gravity

We consider the ghost-free dRGT massive gravity with two of its three possible mass terms. This theory has five gravitational degrees of freedom. On Minkowski spacetime these modes have helicity-2, -1 and -0 and propagate on the Minkowski lightcone in the high-frequency limit. However for a general background the degrees of freedom corresponding to the helicity-1 and -0 modes have characteristics different to that of the metric lightcone. Here we prove in all generality, that the two degrees of freedom corresponding to the helicity-2 mode always propagate on the metric lightcone for any background in the high-frequency limit, which has significant relevance for current and future observational tests of the theory.

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arXiv2025

Bispectrum Islands

Inspired by the amplitude bootstrap program, the spirit of this work is to constrain the space of consistent inflationary correlation functions - specifically, the bispectrum of curvature perturbations - using fundamental principles such as unitarity, locality, analyticity, and symmetries. To this end, we assume a setup for inflation in which de Sitter isometries are only mildly broken by the slow roll of the inflaton field, and study the bispectrum imprinted by a generic hidden sector during inflation. Assuming that the hidden sector's contributions to primordial non-Gaussianity are dominated by the exchange of a scalar operator (which does not preclude high-spin UV completions), we derive nontrivial positivity constraints on the resulting bispectrum $B(k_1,k_2,k_3)$. In particular, we show that $B$ must be negative in a certain region around the equilateral configuration. For instance, for isosceles triangles (with $k_2=k_3$) this region is given by $0.027\lesssim k_3/k_1\leq 2$. Furthermore, we demonstrate that unitarity imposes upper and lower bounds on the bispectrum shape, thereby carving out a Bispectrum Island where consistent shapes in our setup can reside. We complement our analysis by contemplating alternative setups where the coupling to the hidden sector is allowed to strongly break de Sitter boosts. We also identify situations that would push the bispectrum off the island and the profound physical features they would reveal.

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arXiv2025

Prospects for detecting new dark physics with the next generation of atomic clocks

Wide classes of new fundamental physics theories cause apparent variations in particle mass ratios in space and time. In theories that violate the weak equivalence principle (EP), those variations are not uniform across all particles and may be detected with atomic and molecular clock frequency comparisons. In this work we explore the potential to detect those variations with near-future clock comparisons. We begin by searching published clock data for variations in the electron-proton mass ratio. We then undertake a statistical analysis to model the noise in a variety of clock pairs that can be built in the near future according to the current state of the art, determining their sensitivity to various fundamental physics signals. Those signals are then connected to constraints on fundamental physics theories that lead directly or indirectly to an effective EP-violating, including those motivated by dark matter, dark energy, the vacuum energy problem, unification or other open questions of fundamental physics. This work results in projections for tight new bounds on fundamental physics that could be achieved with atomic and molecular clocks within the next few years. Our code for this work is packaged into a forecast tool that translates clock characteristics into bounds on fundamental physics.

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arXiv2024

Deformations of Extremal Black Holes and the UV

It has recently been noted that deformations of extremal AdS black holes in four and higher dimensions are generically non-smooth or singular on the horizon. Further, it was found that certain deformations of asymptotically flat extremal black holes are marginal, causing the nature of the horizon to be strongly sensitive to UV corrections -- in particular, Wilson coefficients associated with consistent UV completions generically lead to worse behaviour on the horizon. In this work, we extend the discussion of deformed horizons in the presence of UV corrections to extremal charged black holes in AdS, where we find a tower of marginal perturbations for different black hole masses. We argue that the apparent UV sensitivity of marginal modes is, in fact, a feature of the UV theory which is correctly reproduced by the EFT, and illustrate this with explicit UV completions confirming the validity of the EFT. We demonstrate that the same holds for a scalar-Maxwell EFT with known UV completion. In the gravitational case, the sign of EFT corrections to marginal perturbations is generally connected with the signs implied by positivity bounds, with UV completions generically leading to worse behaviour on the horizon. We conjecture that this result is more generic, and use this to derive more general positivity bounds motivated by the weak gravity conjecture, which we illustrate with further evidence.

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arXiv2024

Simulating a numerical UV Completion of Quartic Galileons

The Galileon theory is a prototypical effective field theory that incorporates the Vainshtein screening mechanism--a feature that arises in some extensions of General Relativity, such as massive gravity. The Vainshtein effect requires that the theory contain higher order derivative interactions, which results in Galileons, and theories like them, failing to be technically well-posed. While this is not a fundamental issue when the theory is correctly treated as an effective field theory, it nevertheless poses significant practical problems when numerically simulating this model. These problems can be tamed using a number of different approaches: introducing an active low-pass filter and/or constructing a UV completion at the level of the equations of motion, which controls the high momentum modes. These methods have been tested on cubic Galileon interactions, and have been shown to reproduce the correct low-energy behavior. Here we show how the numerical UV-completion method can be applied to quartic Galileon interactions, and present the first simulations of the quartic Galileon model using this technique. We demonstrate that our approach can probe physics in the regime of the effective field theory in which the quartic term dominates, while successfully reproducing the known results for cubic interactions.

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arXiv2024

Scalar Radiation with a Quartic Galileon

The class of Galileon scalar fields theories encapsulate the Vainshtein screening mechanism which is characteristic of a large range of infrared modified theories of gravity. Such theories can lead to testable departures from General Relativity through fifth forces and new scalar modes of gravitational radiation. However, the inherent non-linearity of the Vainshtein mechanism has limited analytic attempts to describe Galileon theories with both cubic and quartic interactions. To improve on this, we perform direct numerical simulations of the quartic Galileon model for a rotating binary source and infer the power spectrum of given multipoles. To tame numerical instabilities we utilize a low-pass filter, extending previous work on the cubic Galileon. Our findings show that the multipole expansion is well-defined and under control. Moreover, our results confirm that despite being a non-linear scalar, the dominant Galileon radiation is quadrupole, and we find a new scaling behaviour deep inside the Vainshtein region.

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arXiv2024

Surfin' pp-waves with Good Vibrations: Causality in the presence of stacked shockwaves

Relativistic causality constrains the $S$-matrix both through its analyticity, and by imposing lower bounds on the scattering time delay. These bounds are easiest to determine for spacetimes which admit either a timelike or null Killing vector. We revisit a class of pp-wave spacetimes and carefully determine the scattering time delay for arbitrary incoming states in the eikonal, semi-classical, and Born approximations. We apply this to the EFT of gravity in arbitrary dimensions. It is well-known that higher-dimension operators such as the Gauss-Bonnet term, when treated perturbatively at low energies, can appear to make both positive and negative contributions to the time delays of the background geometry. We show that even when multiple shockwaves are stacked, the corrections to the scattering time delay relative to the background are generically unresolvable within the regime of validity of the effective field theory so long as the Wilson coefficients are of order unity. This is in agreement with previously derived positivity/bootstrap bounds and the requirement that infrared causality be maintained in consistent low-energy effective theories, irrespective of the UV completion.

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arXiv2024

Causality Constraints on Gravitational Effective Field Theories

We consider the effective field theory of gravity around black holes, and show that the coefficients of the dimension-8 operators are tightly constrained by causality considerations. Those constraints are consistent with -- but tighter than -- previously derived causality and positivity bounds and imply that the effects of one of the dimension-8 operators by itself cannot be observable while remaining consistent with causality. We then establish in which regime one can expect the generic dimension-8 and lower order operators to be potentially observable while preserving causality, providing a theoretical prior for future observations. We highlight the importance of "infrared causality" and show that the requirement of "asymptotic causality" or net (sub)luminality would fail to properly diagnose violations of causality.

gr-qc↗

arXiv2023

Subadditive Average Distances and Quantum Promptness

A central property of a classical geometry is that the geodesic distance between two events is \emph{additive}. When considering quantum fluctuations in the metric or a quantum or statistical superposition of different spacetimes, additivity is generically lost at the level of expectation values. In the presence of a superposition of metrics, distances can be made diffeomorphism invariant by considering the frame of a family of free-falling observers or a pressureless fluid, provided we work at sufficiently low energies. We propose to use the average squared distance between two events $\langle d^2(x,y)\rangle$ as a proxy for understanding the effective quantum (or statistical) geometry and the emergent causal relations among such observers. At each point, the average squared distance $\langle d^2(x,y)\rangle$ defines an average metric tensor. However, due to non-additivity, $\langle d^2(x,y)\rangle$ is not the (squared) geodesic distance associated with it. We show that departures from additivity can be conveniently captured by a bi-local quantity $C(x,y)$. Violations of additivity build up with the mutual separation between $x$ and $y$ and can correspond to $C<0$ (subadditive) or $C>0$ (superadditive). We show that average Euclidean distances are always subadditive: they satisfy the triangle inequality but generally fail to saturate it. In Lorentzian signature there is no definite result about the sign of $C$, most physical examples give $C<0$ but there exist counterexamples. The causality induced by subadditive Lorentzian distances is unorthodox but not pathological. Superadditivity violates the transitivity of causal relations. On these bases, we argue that subadditive distances are the expected outcome of dynamical evolution, if relatively generic physical initial conditions are considered.

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arXiv2023

Causal Effective Field Theories

Physical principles such as unitarity, causality, and locality can constrain the space of consistent effective field theories (EFTs) by imposing two-sided bounds on the allowed values of Wilson coefficients. In this paper, we consider the bounds that arise from the requirement of low-energy causality alone, without appealing to any assumptions about UV physics. We focus on shift-symmetric theories, and consider bounds that arise from the propagation around both a homogeneous and a spherically-symmetric background. We find that low-energy causality, namely the requirement that there are no resolvable time advances within the regime of validity of the EFT, produces two-sided bounds in agreement with compact positivity constraints previously obtained from $2 \rightarrow 2$ scattering amplitude dispersion relations using full crossing symmetry.

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arXiv2023

A dynamical formulation of ghost-free massive gravity

We present a formulation of ghost-free massive gravity with flat reference metric that exhibits the full non-linear constraint algebraically, in a way that can be directly implemented for numerical simulations. Motivated by the presence of higher order operators in the low-energy effective description of massive gravity, we show how the inclusion of higher-order gradient (dissipative) terms leads to a well-posed formulation of its dynamics. While the formulation is presented for a generic combination of the minimal and quadratic mass terms on any background, for concreteness, we then focus on the numerical evolution of the minimal model for spherically symmetric gravitational collapse of scalar field matter. This minimal model does not carry the relevant interactions to switch on an active Vainshtein mechanism, at least in spherical symmetry, thus we do not expect to recover usual GR behaviour even for small graviton mass. Nonetheless we may ask what the outcome of matter collapse is for this gravitational theory. Starting with small initial data far away from the centre, we follow the matter through a non-linear regime as it falls towards the origin. For sufficiently weak data the matter disperses. However for larger data we generally find that the classical evolution breaks down due to the theory becoming infinitely strongly coupled without the presence of an apparent horizon shielding this behaviour from an asymptotic observer.

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arXiv2022

Constraints on Regge behaviour from IR physics

We consider positivity constraints applicable to the Effective Field Theory (EFT) of gravity in arbitrary dimensions. By considering scattering of indefinite initial and final states, we highlight the existence of a gravitational scattering amplitude for which full crossing symmetry is manifest and utilize the recently developed crossing symmetric dispersion relations to derive compact non-linear bounds. We show that the null constraints built into these dispersion relations lead to a finite energy sum rule for gravity which may be extended to a one-parameter family of continuous moment sum rules. These sum rules enforce a UV-IR relation which imposes constraints on both the Regge trajectory and residue. We also highlight a situation where the Regge trajectory is uniquely determined in terms of the sub-Regge scale amplitude. Generically the Regge behaviour may be split into an IR sensitive part calculable within a given EFT which mainly depends on the lightest fields in Nature, and an IR independent part which are subject to universal positivity constraints following from unitarity and analyticity.

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