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Browsing by Author "Lukowski, Tomasz"
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Amplituhedra, and Beyond
Ferro, Livia; Lukowski, Tomasz (2020-12-29)This review is a primer on recently established geometric methods for observables in quantum field theories. The main emphasis is on amplituhedra, i.e. geometries encoding scattering amplitudes for a variety of theories. ... -
Amplituhedron meets Jeffrey-Kirwan Residue
Ferro, Livia; Lukowski, Tomasz; Parisi, Matteo (2018-12-28)The tree amplituhedra A^(m)_n,k are mathematical objects generalising the notion of polytopes into the Grassmannian. Proposed for m=4 as a geometric construction encoding tree-level scattering amplitudes in planar N=4 super ... -
Boundaries of the Amplituhedron with amplituhedronBoundaries
Lukowski, Tomasz; Moerman, Robert (2021-02-01)Positive geometries provide a modern approach for computing scattering amplitudes in a variety of physical models. In order to facilitate the exploration of these new geometric methods, we introduce a MATHEMATICA package ... -
Cluster Adjacency for m=2 Yangian Invariants
Lukowski, Tomasz; Parisi, Matteo; Spradlin, Marcus; Volovich, Anastasia (2019-10-14)We 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 ... -
Expanding the Bethe/Gauge Dictionary
Bullimore, Mathew; Kim, Hee-Cheol; Lukowski, Tomasz (2017-11-09)We expand the Bethe/Gauge dictionary between the XXX Heisenberg spin chain and 2d N = (2,2) supersymmetric gauge theories to include aspects of the algebraic Bethe ansatz. We construct the wave functions of off-shell Bethe ... -
From Momentum Amplituhedron Boundaries to Amplitude Singularities and Back
Ferro, Livia; Lukowski, Tomasz; Moerman, Robert (2020-07-28)The momentum amplituhedron is a positive geometry encoding tree-level scattering amplitudes in $\mathcal{N}=4$ super Yang-Mills directly in spinor-helicity space. In this paper we classify all boundaries of the momentum ... -
The hypersimplex canonical forms and the momentum amplituhedron-like logarithmic forms
Lukowski, Tomasz; Stalknecht, Jonah (2022-04-20)In this paper we provide a formula for the canonical differential form of the hypersimplex Δ k,n for all n and k. We also study the generalization of the momentum amplituhedron Mn,k to m = 2, which has been conjectured to ... -
Kleiss-Kuijf relations from momentum amplituhedron geometry
Damgaard, David; Ferro, Livia; Lukowski, Tomasz; Moerman, Robert (2021-07-16)Abstract: In recent years, it has been understood that color-ordered scattering amplitudes can be encoded as logarithmic differential forms on positive geometries. In particular, amplitudes in maximally supersymmetric ... -
Large spin systematics in CFT
Alday, Luis F.; Bissi, Agnese; Lukowski, Tomasz (2015-11-16)Using conformal field theory (CFT) arguments we derive an infinite number of constraints on the large spin expansion of the anomalous dimensions and structure constants of higher spin operators. These arguments rely only ... -
Lessons from crossing symmetry at large N
Alday, Luis F.; Bissi, Agnese; Lukowski, Tomasz (2015-06-12)We consider the four-point correlator of the stress tensor multiplet in N=4 SYM. We construct all solutions consistent with crossing symmetry in the limit of large central charge c ~ N^2 and large g^2 N. While we find an ... -
The Momentum Amplituhedron
Damgaard, David; Ferro, Livia; Lukowski, Tomasz; Parisi, Matteo (2019-08-08)In this paper we define a new object, the momentum amplituhedron, which is the long sought-after positive geometry for tree-level scattering amplitudes in N = 4 super Yang-Mills theory in spinor helicity space. Inspired ... -
Momentum amplituhedron for N=6 Chern-Simons-matter Theory: Scattering amplitudes from configurations of points in Minkowski space
Lukowski, Tomasz; Stalknecht, Jonah (2023-10-17)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 ... -
Momentum Amplituhedron meets Kinematic Associahedron
Damgaard, David; Ferro, Livia; Lukowski, Tomasz; Moerman, Robert (2021-02-03)In this paper we study a relation between two positive geometries: the momen- tum amplituhedron, relevant for tree-level scattering amplitudes in N = 4 super Yang-Mills theory, and the kinematic associahedron, encoding ... -
N=4 Scattering Amplitudes and the Deformed Grassmannian
Ferro, Livia; Lukowski, Tomasz; Staudacher, Matthias (2014-12-01)Some time ago the general tree-level scattering amplitudes of N=4 Super Yang-Mills theory were expressed as certain Grassmannian contour integrals. These remarkable formulas allow to clearly expose the super-conformal, ... -
A new derivation of Luscher F-term and fluctuations around the giant magnon
Heller, Michal P.; Janik, Romuald A.; Lukowski, Tomasz (2008-01-29)In this paper we give a new derivation of the generalized Luscher F-term formula from a summation over quadratic fluctuations around a given soliton. The result is very general providing that S-matrix is diagonal and is ... -
On the Boundaries of the m=2 Amplituhedron
Lukowski, Tomasz (2022-12-23)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 ... -
Perturbative Four-Point Functions from the Analytic Conformal Bootstrap
Henriksson, Johan; Lukowski, Tomasz (2018-02-20)We apply the analytic conformal bootstrap method to study weakly coupled conformal gauge theories in four dimensions. We employ twist conformal blocks to find the most general form of the one-loop four-point correlation ... -
The positive tropical Grassmannian, the hypersimplex, and the m=2 amplituhedron
Lukowski, Tomasz; Parisi, Matteo; Williams, Lauren K. (2023-10-01)The positive Grassmannian [FIGURE] is a cell complex consisting of all points in the real Grassmannian whose Plücker coordinates are non-negative. In this paper we consider the image of the positive Grassmannian and its ... -
Prescriptive Unitarity from Positive Geometries
Ferro, Livia; Glew, Ross; Lukowski, Tomasz; Stalknecht, Jonah (2024-03-01)In this paper, we define the momentum amplituhedron in the four-dimensional split-signature space of dual momenta. It encodes scattering amplitudes at tree level and loop integrands for N=4 super Yang-Mills in the planar ... -
Revisiting N=4 superconformal blocks
Bissi, Agnese; Lukowski, Tomasz (2016-02-17)We 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 ...