748 research outputs found
All-loop cuts from the Amplituhedron
The definition of the amplituhedron in terms of sign flips involves both
one-loop constraints and the "mutual positivity" constraint. To gain an
understanding of the all-loop integrand of sYM requires
understanding the crucial role played by mutual positivity. This paper is an
attempt towards developing a procedure to introduce the complexities of mutual
positivity in a systematic and controlled manner. As the first step in this
procedure, we trivialize these constraints and understand the geometry
underlying the remaining constraints to all loops and multiplicities. We
present a host of configurations which correspond to various faces of the
amplituhedron. The results we derive are valid at all multiplicities and loop
orders for the maximally helicity violating (MHV) configurations. These include
detailed derivations for the results in arXiv:1810.08208 [hep-th]. We conclude
by indicating how one might move beyond trivial mutual positivity by presenting
a series of configuration which re-introduce it bit by bit.Comment: 40 pages, 15 figures, 1 tabl
Building Bases of Loop Integrands
We describe a systematic approach to the construction of loop-integrand bases
at arbitrary loop-order, sufficient for the representation of general quantum
field theories. We provide a graph-theoretic definition of `power-counting' for
multi-loop integrands beyond the planar limit, and show how this can be used to
organize bases according to ultraviolet behavior. This allows amplitude
integrands to be constructed iteratively. We illustrate these ideas with
concrete applications. In particular, we describe complete integrand bases at
two loops sufficient to represent arbitrary-multiplicity amplitudes in four (or
fewer) dimensions in any massless quantum field theory with the ultraviolet
behavior of the Standard Model or better. We also comment on possible
extensions of our framework to arbitrary (including regulated) numbers of
dimensions, and to theories with arbitrary mass spectra and charges. At three
loops, we describe a basis sufficient to capture all
`leading-(transcendental-)weight' contributions of any four-dimensional quantum
theory; for maximally supersymmetric Yang-Mills theory, this basis should be
sufficient to represent all scattering amplitude integrands in the theory---for
generic helicities and arbitrary multiplicity.Comment: 76 pages, 6 tables, hundreds of figures. Ancillary file includes our
results for three loop
An Elliptic Yangian-Invariant, `Leading Singularity'
We derive closed formulae for the first examples of non-algebraic, elliptic
`leading singularities' in planar, maximally supersymmetric Yang-Mills theory
and show that they are Yangian-invariant.Comment: 4+2 pages; 2 figures. Ancillary files include computer-usable
formula
All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
We give a closed-form, prescriptive representation of all-multiplicity
two-loop MHV amplitude integrands in fully-color-dressed (non-planar) maximally
supersymmetric Yang-Mills theory.Comment: Corrected a sign mistake for the pentabox numerators (table IV).
Minor improvements and references added in v2. 4+3 pages, 22 figures, 4
tables, infinity of new amplitudes. Ancillary files contain a Mathematica
implementation of our resul
One-Loop Corrections to Bubble Nucleation Rate at Finite Temperature
We present an evaluation of the 1-loop prefactor in the lifetime of a
metastable state which decays at finite temperature by bubble nucleation. Such
a state is considered in one-component phi^4 model in three space dimensions.
The calculation serves as a prototype application of a fast numerical method
for evaluating the functional determinants that appear in semiclassical
approximations.Comment: DO-TH-93/18, 15 pages, 11 Figures available on request, LaTeX, no
macros neede
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