This workshop is an opportunity for all SAGEX ESRs to present their recent research to the collaboration, as well as for the network to meet despite the restrictions imposed by the Covid-19 pandemic.
The meeting will take place in the mornings only (9.00 - 12.00 UK time) via Zoom, with joining information to be circulated by email. For further information please contact jenna.lane@qmul.ac.uk
Anomalous dimensions of local operators provide an important ingredient to fixing correlation functions in conformal field theories. The discovery of integrability in planar N=4 SYM let to big advances in their computation in that limit. Less is known about anomalous dimensions at the non-planar level. I will start by showing numerical results for the spectrum of anomalous dimensions for short operators in N=4 SYM and its beta-deformed version, and then how integrability can be used to obtain analytic results for the leading non-planar corrections to one-loop anomalous dimensions via non-degenerate perturbation theory. In doing so, I will present compact expressions for matrix elements of the dilatation operator in terms of off-shell scalar products and hexagon-like functions, and will give explicit examples of leading non-planar corrections to operator dimensions.
Recently, there are much progress in the study of the binary gravitational system, but very few are known for the system with one more body. We study the three-body no-spinning interaction from the perspective of effective field theory. We start with three worldlines coupled to Einstein gravity, which is perturbed around Minkowski space and then integrated out the gravitation field. We result in the three-body potential up to the second-order in Post-Minkowskian expansion. We check that it’s consistent with the binary system if two of the worldlines are taken to be identical.
Deep-inelastic structure functions are important observables for the measurement of physical constants and for the extraction of parton densities. I will report on the calculation of evolution operators for the structure functions in N-space in the asymptotic regime Q^2 >> m^2 and discuss their invariance on the factorization scheme.
It is a well-known result that scattering amplitudes in N=4 super Yang-Mills are related to correlation functions in the special limit where consecutive points become null separated. Furthermore, scattering amplitudes in N=4 enjoy dual conformal symmetry, so it is natural to expect the existence of a (light-cone) conformal block decomposition for these amplitudes. Making this assumption, the duality mentioned above then suggests that conformal blocks for amplitudes could be obtained from null limits of multi-point conformal blocks for correlators. Pointing in this direction, we therefore started to explore the mostly uncharted territory of five-points conformal blocks, gathering evidence that multi-point blocks can be obtained from differential equations associated to specific sets of commuting operators used in Gaudin models.
In the past the S-matrix of simply-laced Toda theories has been bootstrapped showing perfectly agreement with perturbative results. Higher order poles appearing in the conjectured S-matrix have been explained in terms of threshold singularities, corresponding to particular choices of the external kinematic at which more propagators inside Feynman diagrams go simultaneously on-shell along the loop integration. The number of Feynman diagrams contributing to such singular values grow incredibly fast with the order of pole considered, which is proportional to the number of loops. I will discuss a way to find the networks of such divergent diagrams and I will show that not all the Feynman diagrams entering in the network contribute to the result, many of them cancel each other in a way that can be traced back to the root system associated to the model. The only relevant terms come from some particular cuts of the diagrams sit on the boundary of the network. I will check this for second and third-order poles (which is 1 and 2 loops) in 4-point diagonal scattering processes.
I report on the computation of planar two-loop all-plus amplitudes. For the cut-constructible terms, the two loops factorize on fourdimensional cuts, which has allowed for the derivation of all-n results. I will present results based on a conjecture in the literature which suggests that such a factorization may also apply for the rational parts constructed from D-dimensional cuts. This has been observed for amplitudes with up to six gluons. I will also discuss possible applications to all-plus amplitudes in gravity.
We find, for the first time, that scattering amplitudes in massive scalar QCD can satisfy the color-kinematics duality off-shell at the loop level, explicitly building color-dual representations at one-loop. Specifically we construct the four-point scattering between two distinct massive scalars, and the one-loop five-point scattering amplitude encoding the first correction to radiation. Indeed no Feynman rules need be involved in the construction of these results; we demonstrate that factorization and color-kinematics are sufficient to entirely bootstrap these calculations, allowing us to recurse from three-point amplitudes entirely constrained by symmetry. Double-copy immediately provides the associated predictions for massive matter coupled by gravity. In this way we see that the inertial mass of fundamentally charged matter in the gauge theory becomes gravitational mass in the double-copy. A natural consequence of double-copy is the contribution of internal massless scalar states. Once the contribution of these massless scalar states have been removed, these calculations are especially of interest in the classical limit as they encode the classical gravitational interaction of non-rotating black holes.
We show how to double-copy Heavy Quark Effective Theory (HQET) to Heavy Black Hole Effective Theory (HBET) for spin s≤1. In particular, the double copy of spin-s HQET with scalar QCD produces spin-s HBET, while the double copy of spin-1/2 HQET with itself gives spin-1 HBET. Finally, we present novel all-order-in-mass Lagrangians for spin-1 heavy particles.
We will describe how to extract wave scattering theory from scattering amplitudes with external massless particles, both in the low energy and the high energy regime. Since massless particles do not have a rest frame, using a completely localized wavefunction as it was done in the massive case is not enough in general to perform the classical limit. Indeed, such limit can be generically achieved only with an infinite number of massless particles, i.e. with the so-called "coherent states". Explicit examples will be provided.
This talk will present two methods that allow to solve algorithmically order by order in the dimensional regularization parameter epsilon differential systems involving master integrals appearing in amplitude computations. If the system is first order factorizable, the solutions (more precisely the coefficients of their epsilon-expansions) will be given in terms of iterated integrals defined over hyperexponential functions. An implementation of the first method in Mathematica and concrete examples of computations will also be presented.
The on-shell superspace formulation of N=4 SYM allows the writing of all possible scattering processes in one compact object called the super-amplitude. Famously, the NMHV sectors of the super-amplitude integrand can be extracted from generalized polyhedra called the amplituhedron. In this talk I will present a natural generalization of the amplituhedron that we conjecture to correspond to the product of two parity conjugate superamplitudes. The product two superamplitudes is also a physically relevant object and corresponds to a particular limit of the supercorrelator. I will conclude by discussing how the conjecture could be extended to the product of arbitrary super amplitudes and some possible application of this new geometric formulation for amplitudes computations.
In this talk we present a formalism to compute classical solutions in General Relativity directly from scattering amplitudes. We will focus on gravitational shock waves solutions describing the gravitational field of an ultrarelativistic black hole. Using amplitude techniques, the distributional profile of these solutions will be recovered in a natural way bypassing the introduction of boosts and singular coordinate transformations as used in General Relativity. We will show how the exactness of the classical solution follows from unitarity and we will conclude the talk presenting a novel relation between gravitational shock waves and gyraton solutions with spin.
The dual conformal box integral in Minkowski space is not fully determined by the four-point conformal invariants. Depending on the kinematic region its value is on a 'branch' of the Bloch-Wigner function which occurs in the Euclidean case. Dual special conformal transformations in Minkowski space can change the kinematic region in such a way that the value of the integral jumps to another branch of this function, encoding a subtle breaking of dual conformal invariance for the integral. We describe the classification of conformally equivalent configurations of four points in Minkowski space. We show that starting with any configuration, one can reach up to four branches of the integral using dual special conformal transformations.
Very recently on-shell methods have been applied to the computation of certain classical observables in various field theories, including General Relativity. In this talk I will discuss how these techniques can be applied in the study of Effective Field Theories of gravity with higher dimensional operators, with a particular focus on how we can extract information about the violation of causality in this framework.
On-shell methods are by now a very well established and powerful alternative to Feynman-digrams and Lagrangian based calculations. In this talk I will discuss some aspects of their recent application to Standard Model EFTs, starting from the counting of independent operators of given mass-dimension up to the calculation of the anomalous dimension matrix.