76 research outputs found
Bootstrapping two-loop Feynman integrals for planar N=4 sYM
We derive analytic results for the symbol of certain two-loop Feynman
integrals relevant for seven- and eight-point two-loop scattering amplitudes in
planar super-Yang--Mills theory. We use a bootstrap inspired
strategy, combined with a set of second-order partial differential equations
that provide powerful constraints on the symbol ansatz. When the complete
symbol alphabet is not available, we adopt a hybrid approach. Instead of the
full function, we bootstrap a certain discontinuity for which the alphabet is
known. Then we write a one-fold dispersion integral to recover the complete
result. At six and seven points, we find that the individual Feynman integrals
live in the same space of functions as the amplitude, which is described by the
9- and 42-letter cluster alphabets respectively. Starting at eight points
however, the symbol alphabet of the MHV amplitude is insufficient for
individual integrals. In particular, some of the integrals require algebraic
letters involving four-mass box square-root singularities. We point out that
these algebraic letters are relevant at the amplitude level directly starting
with NMHV amplitudes even at one loop.Comment: 49 page
Manifesting enhanced cancellations in supergravity: integrands versus integrals
Examples of "enhanced ultraviolet cancellations" with no known
standard-symmetry explanation have been found in a variety of supergravity
theories. By examining one- and two-loop examples in four- and five-dimensional
half-maximal supergravity, we argue that enhanced cancellations in general
cannot be exhibited prior to integration. In light of this, we explore
reorganizations of integrands into parts that are manifestly finite and parts
that have poor power counting but integrate to zero due to integral identities.
At two loops we find that in the large loop-momentum limit the required
integral identities follow from Lorentz and SL(2) relabeling symmetry. We carry
out a nontrivial check at four loops showing that the identities generated in
this way are a complete set. We propose that at loops the combination of
Lorentz and SL() symmetry is sufficient for displaying enhanced
cancellations when they happen, whenever the theory is known to be ultraviolet
finite up to loops.Comment: 28 pages, 5 figure
Leading Nonlinear Tidal Effects and Scattering Amplitudes
We present the two-body Hamiltonian and associated eikonal phase, to leading post-Minkowskian order, for infinitely many tidal deformations described by operators with arbitrary powers of the curvature tensor. Scattering amplitudes in momentum and position space provide systematic complementary approaches. For the tidal operators quadratic in curvature, which describe the linear response to an external gravitational field, we work out the leading post-Minkowskian contributions using a basis of operators with arbitrary numbers of derivatives which are in one-to-one correspondence with the worldline multipole operators. Explicit examples are used to show that the same techniques apply to both bodies interacting tidally with a spinning particle, for which we find the leading contributions from quadratic in curvature tidal operators with an arbitrary number of derivatives, and to effective field theory extensions of general relativity. We also note that the leading post-Minkowskian order contributions from higher-dimension operators manifest double-copy relations. Finally, we comment on the structure of higher-order corrections
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