29 research outputs found
Revisiting N=4 superconformal blocks
21 pages; v2: version published in JHEPWe study four-point correlation functions of four generic half-BPS supermultiplets of N=4 SCFT in four dimensions. We use the two-particle Casimir of four-dimensional superconformal algebra to derive superconformal blocks which contribute to the partial wave expansion of such correlators. The derived blocks are defined on analytic superspace and allow us in principle to find any component of the four-point correlator. The lowest component of the result agrees with the superconformal blocks found by Dolan and Osborn.Peer reviewe
From nesting to dressing
In integrable field theories the S-matrix is usually a product of a
relatively simple matrix and a complicated scalar factor. We make an
observation that in many relativistic integrable field theories the scalar
factor can be expressed as a convolution of simple kernels appearing in the
nested levels of the nested Bethe ansatz. We formulate a proposal, up to some
discrete ambiguities, how to reconstruct the scalar factor from the nested
Bethe equations and check it for several relativistic integrable field
theories. We then apply this proposal to the AdS asymptotic Bethe ansatz and
recover the dressing factor in the integral representation of Dorey, Hofman and
Maldacena.Comment: 23 pages, no figures; v2: small improvements, references adde
On the Boundaries of the m=2 Amplituhedron
© 2022 Association Publications de l’Institut Henri Poincaré. Published by EMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY), https://creativecommons.org/licenses/by/4.0/Amplituhedra A_{n,k}^{(m)} are geometric objects of great interest in modern mathematics and physics: for mathematicians they are combinatorially rich generalizations of polygons and polytopes, based on the notion of positivity; for physicists, the amplituhedron A^{(4)}_{n,k} encodes the scattering amplitudes of the planar N=4 super Yang-Mills theory. In this paper we study the structure of boundaries for the amplituhedron A_{n,k}^{(2)}. We classify all boundaries of all dimensions and provide their graphical enumeration. We find that the boundary poset for the amplituhedron is Eulerian and show that the Euler characteristic of the amplituhedron equals one. This provides an initial step towards proving that the amplituhedron for m=2 is homeomorphic to a closed ball.Peer reviewe
Cluster Adjacency for m=2 Yangian Invariants
11 pages, 3 figuresWe classify the rational Yangian invariants of the toy model of Yang-Mills theory in terms of generalised triangles inside the amplituhedron . We enumerate and provide an explicit formula for all invariants for any number of particles and any helicity degree . Each invariant manifestly satisfies cluster adjacency with respect to the cluster algebra.Peer reviewe
Baxter Operators and Hamiltonians for "nearly all" Integrable Closed gl(n) Spin Chains
We continue our systematic construction of Baxter Q-operators for spin
chains, which is based on certain degenerate solutions of the Yang-Baxter
equation. Here we generalize our approach from the fundamental representation
of gl(n) to generic finite-dimensional representations in quantum space. The
results equally apply to non-compact representations of highest or lowest
weight type. We furthermore fill an apparent gap in the literature, and provide
the nearest-neighbor Hamiltonians of the spin chains in question for all cases
where the gl(n) representations are described by rectangular Young diagrams, as
well as for their infinite-dimensional generalizations. They take the form of
digamma functions depending on operator-valued shifted weights.Comment: 26 pages, 1 figur
Momentum amplituhedron for N=6 Chern-Simons-matter Theory: Scattering amplitudes from configurations of points in Minkowski space
© 2023 The Author(s). Published by the American Physical Society. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY), https://creativecommons.org/licenses/by/4.0/In this Letter, we define the Aharony-Bergman-Jafferis-Maldacena loop momentum amplituhedron, which is a geometry encoding Aharony-Bergman-Jafferis-Maldacena planar tree-level amplitudes and loop integrands in the three-dimensional spinor helicity space. Translating it to the space of dual momenta produces a remarkably simple geometry given by configurations of spacelike separated off-shell momenta living inside a curvy polytope defined by momenta of scattered particles. We conjecture that the canonical differential form on this space gives amplitude integrands, and we provide a new formula for all one-loop n-particle integrands in the positive branch. For higher loop orders, we utilize the causal structure of configurations of points in Minkowski space to explain the singularity structure for known results at two loops.Peer reviewe
The Loop Momentum Amplituhedron
In this paper we focus on scattering amplitudes in maximally supersymmetric
Yang-Mills theory and define a long sought-after geometry, the loop momentum
amplituhedron, which we conjecture to encode tree and (the integrands of) loop
amplitudes in spinor helicity variables. Motivated by the structure of
amplitude singularities, we define an extended positive space, which enhances
the Grassmannian space featuring at tree level, and a map which associates to
each of its points tree-level kinematic variables and loop momenta. The image
of this map is the loop momentum amplituhedron. Importantly, our formulation
provides a global definition of the loop momenta. We conjecture that for all
multiplicities and helicity sectors, there exists a canonical logarithmic
differential form defined on this space, and provide its explicit form in a few
examples.Comment: 17 pages, 1 figur
The ABJM Momentum Amplituhedron -- ABJM Scattering Amplitudes From Configurations of Points in Minkowski Space
In this paper, we define the ABJM loop momentum amplituhedron, which is a
geometry encoding ABJM planar tree-level amplitudes and loop integrands in the
three-dimensional spinor helicity space. Translating it to the space of dual
momenta produces a remarkably simple geometry given by configurations of
space-like separated off-shell momenta living inside a curvy polytope defined
by momenta of scattered particles. We conjecture that the canonical
differential form on this space gives amplitude integrands, and we provide a
new formula for all one-loop -particle integrands in the positive branch.
For higher loop orders, we utilize the causal structure of configurations of
points in Minkowski space to explain the singularity structure for known
results at two loops.Comment: 6 pages, 3 figure
The hypersimplex canonical forms and the momentum amplituhedron-like logarithmic forms
In this paper we provide a formula for the canonical differential form of the
hypersimplex for all and . We also study the
generalization of the momentum amplituhedron to , and
we conclude that the existing definition does not possess the desired
properties. Nevertheless, we find interesting momentum amplituhedron-like
logarithmic differential forms in the version of the spinor helicity
space, that have the same singularity structure as the hypersimplex canonical
forms.Comment: 18 pages, 2 figure