On unitarity of tree-level string amplitudes Arkani-Hamed, Nima; Eberhardt, Lorenz; Huang, Yu-tin ...
The journal of high energy physics,
02/2022, Letnik:
2022, Številka:
2
Journal Article
Recenzirano
Odprti dostop
A
bstract
Four-particle tree-level scattering amplitudes in string theory are magically consistent with unitarity, reflected in the non-trivial fact that beneath the critical dimension, the residues ...of the amplitudes on massive poles can be expanded in partial waves with all positive coefficients. While this follows (rather indirectly) from the no-ghost theorem, the simplicity of the statement and its fundamental importance for the physical consistency of string theory begs for a more direct and elementary understanding. In this note we take a step in this direction by presenting a new expression for the partial wave coefficients of string amplitudes, given by surprisingly simple double/triple contour integrals for open/closed strings. This representation allows us to directly prove unitarity of all superstring theories in
D
≤ 6 spacetime dimensions, and can also be used to determine various asymptotics of the partial waves at large mass levels.
Crossing symmetry asserts that particles are indistinguishable from antiparticles traveling back in time. In quantum field theory, this statement translates to the long-standing conjecture that ...probabilities for observing the two scenarios in a scattering experiment are described by one and the same function. Why could we expect it to be true? In this work we examine this question in a simplified setup and take steps towards illuminating a possible physical interpretation of crossing symmetry. To be more concrete, we consider planar scattering amplitudes involving any number of particles with arbitrary spins and masses to all loop orders in perturbation theory. We show that by deformations of the external momenta one can smoothly interpolate between pairs of crossing channels without encountering singularities or violating mass-shell conditions and momentum conservation. The analytic continuation can be realized using two types of moves. The first one makes use of an i ϵ prescription for avoiding singularities near the physical kinematics and allows us to adjust the momenta of the external particles relative to one another within their light cones. The second, more violent, step involves a rotation of subsets of particle momenta via their complexified light cones from the future to the past and vice versa. We show that any singularity along such a deformation would have to correspond to two beams of particles scattering off each other. For planar Feynman diagrams, these kinds of singularities are absent because of the particular flow of energies through their propagators. We prescribe a five-step sequence of such moves that combined together proves crossing symmetry for planar scattering amplitudes in perturbation theory, paving a way towards settling this question for more general scattering processes in quantum field theories.
We introduce an efficient algorithm for reducing bond dimensions in an arbitrary tensor network without changing its geometry. The method is based on a quantitative understanding of local ...correlations in a network. Together with a tensor network coarse-graining algorithm, it yields a proper renormalization group (RG) flow. Compared to existing methods, the advantages of our algorithm are its low computational cost, simplicity of implementation, and applicability to any network. We benchmark it by evaluating physical observables for the two-dimensional classical Ising model and find accuracy comparable with the best existing tensor network methods. Because of its graph independence, our algorithm is an excellent candidate for implementation of real-space RG in higher dimensions. We discuss some of the details and the remaining challenges in three dimensions. Source code for our algorithm is freely available.
A
bstract
We investigate configuration-space integrals over punctured Riemann spheres from the viewpoint of the motivic Galois coaction and double-copy structures generalizing the Kawai-Lewellen-Tye ...(KLT) relations in string theory. For this purpose, explicit bases of twisted cycles and cocycles are worked out whose orthonormality simplifies the coaction. We present methods to efficiently perform and organize the expansions of configuration-space integrals in the inverse string tension
α
′ or the dimensional-regularization parameter
ϵ
of Feynman integrals. Generating-function techniques open up a new perspective on the coaction of multiple polylogarithms in any number of variables and analytic continuations in the unintegrated punctures. We present a compact recursion for a generalized KLT kernel and discuss its origin from intersection numbers of Stasheff polytopes and its implications for correlation functions of two-dimensional conformal field theories. We find a non-trivial example of correlation functions in (
p
,
2) minimal models, which can be normalized to become uniformly transcendental in the
p
→ ∞ limit.
A
bstract
We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation of the ...differential equations satisfied by the master integrals, employing multivariate intersection numbers. We discuss a recursive algorithm for the computation of multivariate intersection numbers, and provide three different approaches for a direct decomposition of Feynman integrals, which we dub the
straight decomposition
, the
bottom-up decomposition
, and the
top-down decomposition
. These algorithms exploit the unitarity structure of Feynman integrals by computing intersection numbers supported on cuts, in various orders, thus showing the synthesis of the intersection-theory concepts with unitarity-based methods and integrand decomposition. We perform explicit computations to exemplify all of these approaches applied to Feynman integrals, paving a way towards potential applications to generic multi-loop integrals.
What can be measured asymptotically? Caron-Huot, Simon; Giroux, Mathieu; Hannesdottir, Holmfridur S. ...
The journal of high energy physics,
01/2024, Letnik:
2024, Številka:
1
Journal Article
Recenzirano
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A
bstract
We consider asymptotic observables in quantum field theories in which the S-matrix makes sense. We argue that in addition to scattering amplitudes, a whole compendium of inclusive ...observables exists where the time-ordering is relaxed. These include expectation values of electromagnetic or gravitational radiation fields as well as out-of-time-order amplitudes. We explain how to calculate them in two ways: by relating them to amplitudes and products of amplitudes, and by using a generalization of the LSZ reduction formula. As an application, we discuss one-loop master integrals contributing to gravitational radiation in the post-Minkowski expansion, emphasizing the role of classical cut contributions and highlighting the different infrared physics of in-in observables.
Δ-algebra and scattering amplitudes Cachazo, Freddy; Early, Nick; Guevara, Alfredo ...
The journal of high energy physics,
1/2, Letnik:
2019, Številka:
2
Journal Article
Recenzirano
Odprti dostop
A
bstract
In this paper we study an algebra that naturally combines two familiar operations in scattering amplitudes: computations of volumes of polytopes using triangulations and constructions of ...canonical forms from products of smaller ones. We mainly concentrate on the case of
G
(2
, n
) as it controls both general MHV leading singularities and CHY integrands for a variety of theories. This commutative algebra has also appeared in the study of configuration spaces and we called it the Δ-algebra. As a natural application, we generalize the well-known square move. This allows us to generate infinite families of new moves between non-planar on-shell diagrams. We call them
sphere moves
. Using the Δ-algebra we derive familiar results, such as the KK and BCJ relations, and prove novel formulas for higher-order relations. Finally, we comment on generalizations to
G
(
k, n
).
A
bstract
We present new formulas for
n
-particle tree-level scattering amplitudes of six-dimensional
N
=
1
1
super Yang-Mills (SYM) and
N
=
2
2
supergravity (SUGRA). They are written as integrals ...over the moduli space of certain rational maps localized on the (
n
− 3)! solutions of the scattering equations. Due to the properties of spinor-helicity variables in six dimensions, the even-
n
and odd-
n
formulas are quite different and have to be treated separately. We first propose a manifestly supersymmetric expression for the even-
n
amplitudes of
N
=
1
1
SYM theory and perform various consistency checks. By considering soft-gluon limits of the even-
n
amplitudes, we deduce the form of the rational maps and the integrand for
n
odd. The odd-
n
formulas obtained in this way have a new redundancy that is intertwined with the usual SL(2
,
ℂ) invariance on the Riemann sphere. We also propose an alternative form of the formulas, analogous to the Witten-RSV formulation, and explore its relationship with the symplectic (or Lagrangian) Grassmannian. Since the amplitudes are formulated in a way that manifests double-copy properties, formulas for the six-dimensional
N
=
2
2
SUGRA amplitudes follow. These six-dimensional results allow us to deduce new formulas for five-dimensional SYM and SUGRA amplitudes, as well as massive amplitudes of four-dimensional
N
=
4
SYM on the Coulomb branch.
Crossing beyond scattering amplitudes Caron-Huot, Simon; Giroux, Mathieu; Hannesdottir, Holmfridur S. ...
The journal of high energy physics,
04/2024, Letnik:
2024, Številka:
4
Journal Article
Recenzirano
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A
bstract
We find that different asymptotic measurements in quantum field theory can be related to one another through new versions of
crossing symmetry
. Assuming analyticity, we conjecture ...generalized crossing relations for multi-particle processes and the corresponding paths of analytic continuation. We prove them to all multiplicity at tree-level in quantum field theory and string theory. We illustrate how to practically perform analytic continuations on loop-level examples using different methods, including unitarity cuts and differential equations. We study the extent to which anomalous thresholds away from the usual physical region can cause an analytic obstruction to crossing when massless particles are involved. In an appendix, we review and streamline historical proofs of four-particle crossing symmetry in gapped theories.
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