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

Cluster Adjacency for m=2 Yangian Invariants

11 pages, 3 figuresWe classify the rational Yangian invariants of the $m=2$ toy model of $\mathcal{N}=4$ Yang-Mills theory in terms of generalised triangles inside the amplituhedron $\mathcal{A}_{n,k}^{(2)}$. We enumerate and provide an explicit formula for all invariants for any number of particles $n$ and any helicity degree $k$. Each invariant manifestly satisfies cluster adjacency with respect to the $Gr(2,n)$ 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

A Shortcut to the Q-Operator

Baxter's Q-operator is generally believed to be the most powerful tool for the exact diagonalization of integrable models. Curiously, it has hitherto not yet been properly constructed in the simplest such system, the compact spin-1/2 Heisenberg-Bethe XXX spin chain. Here we attempt to fill this gap and show how two linearly independent operatorial solutions to Baxter's TQ equation may be constructed as commuting transfer matrices if a twist field is present. The latter are obtained by tracing over infinitely many oscillator states living in the auxiliary channel of an associated monodromy matrix. We furthermore compare and differentiate our approach to earlier articles addressing the problem of the construction of the Q-operator for the XXX chain. Finally we speculate on the importance of Q-operators for the physical interpretation of recent proposals for the Y-system of AdS/CFT.Comment: 41 pages, 2 figures; v2: references added; v3: version published in J. Stat. Mec

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

Profit planning

"10/77/1.5M""This manual discusses some practical uses of break-even analysis in foodservice operations. It does not present the complete application of the use of the break-even system. This manual is designed primarily to make foodservice operators aware of the break-even concept as an effective managerial tool for profit planning."--First paragraph.Robert F. Lukowski (State Extension Specialist, Food Service/Lodging Management, University of Missouri--Columbia

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