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-Matrix Bootstrap

Miró, Joan Elias; Guerrieri, Andrea L.; Hebbar, Aditya; Penedones, João; Vieira, Pedro

doi:10.1103/physrevlett.123.221602

Cited by 66 publications

(110 citation statements)

References 33 publications

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“…(70) The infinite set of parameters µ i can be consistently truncated and determined (along with the offset ζ) using the crossing equations as explained in [4] (see appendix A). The factors containing λ and µ i are part of the central structure C(θ), whereas the product of gamma functions has precisely the form G(θ + ζ)G(−θ + ζ) of (68) 12 . The analytic structure is depicted in figure 11 (a).…”

Section: C3 the σ 2 = 0 Linementioning

confidence: 99%

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The O(N) S-matrix monolith

Córdova

Kruczenski

et al. 2020

J. High Energ. Phys.

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We consider the scattering matrices of massive quantum field theories with no bound states and a global O(N ) symmetry in two spacetime dimensions. In particular we explore the space of two-to-two S-matrices of particles of mass m transforming in the vector representation as restricted by the general conditions of unitarity, crossing, analyticity and O(N ) symmetry. We found a rich structure in that space by using convex maximization and in particular its convex dual minimization problem. At the boundary of the allowed space special geometric points such as vertices were found to correspond to integrable models. The dual convex minimization problem provides a novel and useful approach to the problem allowing, for example, to prove that generically the S-matrices so obtained saturate unitarity and, in some cases, that they are at vertices of the allowed space. arXiv:1909.06495v2 [hep-th]

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Section: C3 the σ 2 = 0 Linementioning

confidence: 99%

“…In the primal problem we parametrize crossing symmetric S-matrices. We can use dispersion relations as in [3] and [4] or complex plane foliations as in [8] and [12]. Here we use a Fourier decomposition and focus on functions with a fixed period.…”

Section: D1 Primal Problem (Normals)mentioning

confidence: 99%

The O(N) S-matrix monolith

Córdova

Kruczenski

et al. 2020

J. High Energ. Phys.

Self Cite

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“…In fact, the conditions are obeyed for every function in the heptagon function space through weight 5, and at weight 6 for all but a unique parity-even function. 3 Thus, the first place they could be violated (working from the left to the right in the symbol entries) is beginning in the 5-6 pair of slots, for parity-even {6, 1, . .…”

Section: Tropical Fans At Function Levelmentioning

confidence: 99%

“…[1]). One recent incarnation of this program imposes fairly general constraints on scattering (typically 2 → 2 scattering), and leads, for example in two spacetime dimensions, to bounds on couplings and other parameters which are often satisfied by particular known theories [2][3][4][5]. In contrast, the planar N = 4 super-Yang-Mills (SYM) amplitude bootstrap program starts with a fixed theory, the simplest gauge theory in four dimensions, and aims to compute arbitrary scattering amplitudes, typically in perturbation theory but without ever directly inspecting the loop integrand.…”

Section: Jhep10(2020)031 Introductionmentioning

confidence: 99%

Lifting heptagon symbols to functions

Dixon

Liu

2020

J. High Energ. Phys.

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Seven-point amplitudes in planar $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory have previously been constructed through four loops using the Steinmann cluster bootstrap, but only at the level of the symbol. We promote these symbols to actual functions, by specifying their first derivatives and boundary conditions on a particular two-dimensional surface. To do this, we impose branch-cut conditions and construct the entire heptagon function space through weight six. We plot the amplitudes on a few lines in the bulk Euclidean region, and explore the properties of the heptagon function space under the coaction associated with multiple polylogarithms.

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“…Recent years have seen a lot of attention in the study of specific types of irrelevant deformations of classical and quantum field theories. Particularly, the class of deformations with Zamolodchikov's TT operator [1][2][3] are of interest in the context of AdS/CF T [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and effective String Theory [19][20][21][22][23]. A deformation by a given operator of a known field theory induces a flow which in the case of irrelevant deformations is driven by the deformation at high energies.…”

Section: Introductionmentioning

confidence: 99%