arXiv subjects

Clifford Cheung

Publications and source records attributed to Clifford Cheung.

At least 37 records · Page 2Linked to original sources

arXiv2023

Bespoke Dual Resonance

Dual resonance is one of the great miracles of string theory. At a fundamental level, it implies that the particles exchanged in different channels are subtly equivalent. Furthermore, it is inextricably linked to the property of exceptionally tame high-energy behavior. In this paper, we present explicit, closed-form expressions for a new class of dual resonant amplitudes describing an infinite tower of spins for an arbitrary mass spectrum. In particular, the input of our construction is a user-defined, fully customizable choice of masses. The resulting "bespoke" amplitudes are well behaved in the ultraviolet and analytic except at simple poles whose residues are polynomial in the momentum transfer, in accordance with locality. The absence of branch cuts can be seen using Newton's identities, but can also be made manifest by expressing the amplitudes as a simple dlog integral of the Veneziano amplitude that remaps the linear Regge trajectories of the string to a tunable spectrum. We identify open regions of parameter space that firmly deviate from string theory but nevertheless comport with partial wave unitarity. Last but not least, we generalize our construction to the scattering of any number of particles in terms of a dlog transform of the Koba-Nielsen worldsheet integral formula.

hep-th↗

arXiv2023

On Entropy Growth in Perturbative Scattering

Inspired by the second law of thermodynamics, we study the change in subsystem entropy generated by dynamical unitary evolution of a product state in a bipartite system. Working at leading order in perturbative interactions, we prove that the quantum $n$-Tsallis entropy of a subsystem never decreases, $ΔS_n \geq 0$, provided that subsystem is initialized as a statistical mixture of states of equal probability. This is true for any choice of interactions and any initialization of the complementary subsystem. When this condition on the initial state is violated, it is always possible to explicitly construct a "Maxwell's demon" process that decreases the subsystem entropy, $ΔS_n < 0$. Remarkably, for the case of particle scattering, the circuit diagrams corresponding to $n$-Tsallis entropy are the same as the on-shell diagrams that have appeared in the modern scattering amplitudes program, and $ΔS_n \geq 0$ is intimately related to the nonnegativity of cross-sections.

hep-th↗

arXiv2023

Stringy Dynamics from an Amplitudes Bootstrap

We describe an analytic procedure whereby scattering amplitudes are bootstrapped directly from an input mass spectrum and a handful of physical constraints: crossing symmetry, boundedness at high energies, and finiteness of exchanged spins. For an integer spectrum, this procedure gives a first principles derivation of a new infinite parameter generalization of the Veneziano amplitude that is unitary while exhibiting dual resonance and consistent high-energy behavior. Lifting to a $q$-deformed integer spectrum, we derive the Coon amplitude and its analogous generalizations. Finally, we apply this logic to derive an infinite class of deformed Virasoro-Shapiro amplitudes.

hep-th↗

arXiv2023

Veneziano Variations: How Unique are String Amplitudes?

String theory offers an elegant and concrete realization of how to consistently couple states of arbitrarily high spin. But how unique is this construction? In this paper we derive a novel, multi-parameter family of four-point scattering amplitudes exhibiting i) polynomially bounded high-energy behavior and ii) exchange of an infinite tower of high-spin modes, albeit with a finite number of states at each resonance. These amplitudes take an infinite-product form and, depending on parameters, exhibit mass spectra that are either unbounded or bounded, thus corresponding to generalizations of the Veneziano and Coon amplitudes, respectively. For the bounded case, masses converge to an accumulation point, a peculiar feature seen in the Coon amplitude but more recently understood to arise naturally in string theory. Importantly, our amplitudes contain free parameters allowing for the customization of the slope and offset of the spin-dependence in the Regge trajectory. We compute all partial waves for this multi-parameter class of amplitudes and identify unitary regions of parameter space. For the unbounded case, we apply similar methods to derive new deformations of the Veneziano and Virasoro-Shapiro amplitudes.

hep-th↗

arXiv2022

Non-perturbative Double Copy in Flatland

We derive a non-perturbative, Lagrangian-level formulation of the double copy in two spacetime dimensions. Our results elucidate the field theoretic underpinnings of the double copy in a broad class of scalar theories which can include masses and higher-dimension operators. An immediate corollary is the amplitudes-level double copy at all orders in perturbation theory. Applied to certain integrable models, the double copy defines an isomorphism between Lax connections, Wilson lines, and infinite towers of conserved currents. We also implement the double copy at the level of non-perturbative classical solutions, both analytically and numerically, and present a generalization of the double copy map that includes a fixed tower of higher-dimension corrections given by the Moyal algebra.

hep-th↗

arXiv2022

Geometry-Kinematics Duality

We propose a mapping between geometry and kinematics that implies the classical equivalence of any theory of massless bosons -- including spin and exhibiting arbitrary derivative or potential interactions -- to a nonlinear sigma model (NLSM) with a momentum-dependent metric in field space. From this kinematic metric we construct a corresponding kinematic connection, covariant derivative, and curvature, all of which transform appropriately under general field redefinitions, even including derivatives. We show explicitly how all tree-level on-shell scattering amplitudes of massless bosons are equal to those of the NLSM via the replacement of geometry with kinematics. Lastly, we describe how the recently introduced geometric soft theorem of the NLSM, which universally encodes all leading and subleading soft scalar theorems, also captures the soft photon theorems.

hep-th↗

arXiv2022

On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes

We define a perturbatively calculable quantity--the on-shell correlator--which furnishes a unified description of particle dynamics in curved spacetime. Specializing to the case of flat and anti-de Sitter space, on-shell correlators coincide precisely with on-shell scattering amplitudes and boundary correlators, respectively. Remarkably, we find that symmetric manifolds admit a generalization of on-shell kinematics in which the corresponding momenta are literally the isometry generators of the spacetime acting on the external kinematic data. These isometric momenta are intrinsically non-commutative but exhibit on-shell conditions that are identical to those of flat space, thus providing a common language for computing and representing on-shell correlators which is agnostic about the underlying geometry. Afterwards, we compute tree-level on-shell correlators for biadjoint scalar (BAS) theory and the nonlinear sigma model (NLSM) and learn that color-kinematics duality is manifested at the level of fields under a mapping of the color algebra to the algebra of gauged isometries on the spacetime manifold. Last but not least, we present a field theoretic derivation of the fundamental BCJ relations for on-shell correlators following from the existence of certain conserved currents in BAS theory and the NLSM.

hep-th↗

arXiv2021

Covariant Color-Kinematics Duality

We show that color-kinematics duality is a manifest property of the equations of motion governing currents and field strengths. For the nonlinear sigma model (NLSM), this insight enables an implementation of the double copy at the level of fields, as well as an explicit construction of the kinematic algebra and associated kinematic current. As a byproduct, we also derive new formulations of the special Galileon (SG) and Born-Infeld (BI) theory. For Yang-Mills (YM) theory, this same approach reveals a novel structure -- covariant color-kinematics duality -- whose only difference from the conventional duality is that $1/\Box$ is replaced with covariant $1/D^2$. Remarkably, this structure implies that YM theory is itself the covariant double copy of gauged biadjoint scalar (GBAS) theory and an $F^3$ theory of field strengths encoding a corresponding kinematic algebra and current. Directly applying the double copy to equations of motion, we derive general relativity (GR) from the product of Einstein-YM and $F^3$ theory. This exercise reveals a trivial variant of the classical double copy that recasts any solution of GR as a solution of YM theory in a curved background. Covariant color-kinematics duality also implies a new decomposition of tree-level amplitudes in YM theory into those of GBAS theory. Using this representation we derive a closed-form, analytic expression for all BCJ numerators in YM theory and the NLSM for any number of particles in any spacetime dimension. By virtue of the double copy, this constitutes an explicit formula for all tree-level scattering amplitudes in YM, GR, NLSM, SG, and BI.

hep-th↗

arXiv2021

Geometric Soft Theorems

We derive a universal soft theorem for every scattering amplitude with at least one massless particle in an arbitrary theory of scalars. Our results follow from the geometry of field space and are valid for any choice of mass spectrum, potential terms, and higher-derivative interactions. For a vanishing potential, the soft limit of every amplitude is equal to the field-space covariant derivative of an amplitude with one fewer particle. Furthermore, the Adler zero and the dilaton soft theorem are special cases of our results. We also discuss more exotic scenarios in which the soft limit is non-trivial but still universal. Last but not least, we derive new theorems for multiple-soft limits which directly probe the field-space curvature, as well as on-shell recursion relations applicable to two-derivative scalar field theories exhibiting no symmetries whatsoever.

hep-th↗

arXiv2020

Hidden Conformal Invariance of Scalar Effective Field Theories

We argue that conformal invariance is a common thread linking several scalar effective field theories that appear in the double copy and scattering equations. For a derivatively coupled scalar with a quartic ${\cal O}(p^4)$ vertex, classical conformal invariance dictates an infinite tower of additional interactions that coincide exactly with Dirac-Born-Infeld theory analytically continued to spacetime dimension $D=0$. For the case of a quartic ${\cal O}(p^6)$ vertex, classical conformal invariance constrains the theory to be the special Galileon in $D=-2$ dimensions. We also verify the conformal invariance of these theories by showing that their amplitudes are uniquely fixed by the conformal Ward identities. In these theories, conformal invariance is a much more stringent constraint than scale invariance.

hep-th↗

arXiv2020

Symmetry and Unification from Soft Theorems and Unitarity

We argue that symmetry and unification can emerge as byproducts of certain physical constraints on dynamical scattering. To accomplish this we parameterize a general Lorentz invariant, four-dimensional theory of massless and massive scalar fields coupled via arbitrary local interactions. Assuming perturbative unitarity and an Adler zero condition, we prove that any finite spectrum of massless and massive modes will necessarily unify at high energies into multiplets of a linearized symmetry. Certain generators of the symmetry algebra can be derived explicitly in terms of the spectrum and three-particle interactions. Furthermore, our assumptions imply that the coset space is symmetric.

hep-th↗

arXiv2020

Scattering Amplitudes and the Navier-Stokes Equation

We explore the scattering amplitudes of fluid quanta described by the Navier-Stokes equation and its non-Abelian generalization. These amplitudes exhibit universal infrared structures analogous to the Weinberg soft theorem and the Adler zero. Furthermore, they satisfy on-shell recursion relations which together with the three-point scattering amplitude furnish a pure S-matrix formulation of incompressible fluid mechanics. Remarkably, the amplitudes of the non-Abelian Navier-Stokes equation also exhibit color-kinematics duality as an off-shell symmetry, for which the associated kinematic algebra is literally the algebra of spatial diffeomorphisms. Applying the double copy prescription, we then arrive at a new theory of a tensor bi-fluid. Finally, we present monopole solutions of the non-Abelian and tensor Navier-Stokes equations and observe a classical double copy structure.

hep-th↗

arXiv2020

Mining the Geodesic Equation for Scattering Data

The geodesic equation encodes test-particle dynamics at arbitrary gravitational coupling, hence retaining all orders in the post-Minkowskian (PM) expansion. Here we explore what geodesic motion can tell us about dynamical scattering in the presence of perturbatively small effects such as tidal distortion and higher derivative corrections to general relativity. We derive an algebraic map between the perturbed geodesic equation and the leading PM scattering amplitude at arbitrary mass ratio. As examples, we compute formulas for amplitudes and isotropic gauge Hamiltonians for certain infinite classes of tidal operators such as electric or magnetic Weyl to any power, and for higher derivative corrections to gravitationally interacting bodies with or without electric charge. Finally, we present a general method for calculating closed-form expressions for amplitudes and isotropic gauge Hamiltonians in the test-particle limit at all orders in the PM expansion.

hep-th↗

arXiv2020

Tidal Effects in the Post-Minkowskian Expansion

Tools from scattering amplitudes and effective field theory have recently been repurposed to derive state-of-the-art results for the black hole binary inspiral in the post-Minkowskian expansion. In the present work we extend this approach to include the tidal effects of mass and current quadrupoles on the conservative dynamics of non-spinning neutron star mergers. We compute the leading and, for the first time, next-to-leading order post-Minkowskian finite size corrections to the conservative Hamiltonian, together with their associated scattering amplitudes and scattering angles. Our expressions are gauge invariant and, in the extreme mass ratio limit, consistent with the dynamics of a tidally deformed test body in a Schwarzschild background. Furthermore, they agree completely with existing results at leading post-Minkowskian and second post-Newtonian orders.

hep-th↗

arXiv2020

Entanglement and the Double Copy

We construct entangled states of gluons that scatter exactly as if they were gravitons. Operationally, these objects implement the double copy at the level of the wave function. Our analysis begins with a general ansatz for a wave function characterizing gluons in two copies of ${\rm SU}(N)$ gauge theory. Given relatively minimal assumptions following from permutation invariance and dimensional analysis, the three- and four-particle wave functions generate scattering amplitudes that automatically coincide exactly with gravity, modulo normalization. For five-particle scattering the match is not automatic but imposing certain known selection rules on the amplitude is sufficient to uniquely reproduce gravity. The resulting amplitudes exhibit a color-dressed and permutation-invariant form of the usual double copy relations. We compute the entanglement entropy between the two gauge theory copies and learn that these states are maximally-entangled at large $N$. Moreover, this approach extends immediately to effective field theories, where Born-Infeld photons and Galileons can be similarly recast as entangled gluons and pions.

hep-th↗

arXiv2020

Classical Gravitational Scattering at ${\cal O}(G^3)$ from Feynman Diagrams

We perform a Feynman diagram calculation of the two-loop scattering amplitude for gravitationally interacting massive particles in the classical limit. Conveniently, we are able to sidestep the most taxing diagrams by exploiting the test-particle limit in which the system is fully characterized by a particle propagating in a Schwarzschild spacetime. We assume a general choice of graviton field basis and gauge fixing that contains as a subset the well-known deDonder gauge and its various cousins. As a highly nontrivial consistency check, all gauge parameters evaporate from the final answer. Moreover, our result exactly matches that of Bern et al., here verified up to sixth post-Newtonian order while also reproducing the same unique velocity resummation at third post-Minkowksian order.

hep-th↗

arXiv2020

Black Hole Binary Dynamics from the Double Copy and Effective Theory

We describe a systematic framework for computing the conservative potential of a compact binary system using modern tools from scattering amplitudes and effective field theory. Our approach combines methods for integration and matching adapted from effective field theory, generalized unitarity, and the double-copy construction, which relates gravity integrands to simpler gauge-theory expressions. With these methods we derive the third post-Minkowskian correction to the conservative two-body Hamiltonian for spinless black holes. We describe in some detail various checks of our integration methods and the resulting Hamiltonian.

hep-th↗

arXiv2019

Entropy Bounds on Effective Field Theory from Rotating Dyonic Black Holes

We derive new bounds on higher-dimension operator coefficients in four-dimensional Einstein-Maxwell theory. Positivity of classically-generated corrections to the Wald entropy of thermodynamically stable, rotating dyonic black holes implies a multiparameter family of field basis invariant inequalities that exhibit electromagnetic duality and are satisfied by examples from field and string theory. These bounds imply that effective operators modify the extremality condition of large black holes so as to permit their decay to smaller ones, thus satisfying the weak gravity conjecture.

hep-th↗