Embedding Feynman integral (Calabi-Yau) geometries in weighted projective space

Bourjaily, Jacob L.; McLeod, Andrew J.; Vergu, Cristian; Volk, Matthias; Hippel, Matt von; Wilhelm, Matthias

doi:10.1007/jhep01(2020)078

Cited by 71 publications

(65 citation statements)

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“…This seems to resonate with the considerable work in the last decade on the relation between non-commutativity and T-folds, S-folds, and "non-geometry" in general; see [105][106][107][108] and references therein. Separately, Calabi-Yau manifolds have been shown to independently appear in the momentum space of physical processes; see [109,110] and references therein. Clearly, the R 3,1 -factor and its dual in X X are diffeomorphic, but may well have different -and presumably complementary -metric properties, the study of which we defer for now.…”

Section: Jhep12(2019)166mentioning

confidence: 99%

On stringy de Sitter spacetimes

Berglund

Hübsch

Minić

2019

J. High Energ. Phys.

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We reexamine a family of models with a 3+1-dimensional de Sitter spacetime obtained in the standard tree-level low-energy limit of string theory with a non-trivial anisotropic axion-dilaton background. While such limiting approximations are encouraging but incomplete, our analysis reveals a host of novel features, and shows these models to relate standard and well understood supersymmetric string theory solutions. Finally, we conjecture that this de Sitter spacetime naturally arises by including more of the stringy degrees of freedom, such as a recently advanced variant of the non-commutative phasespace formalism, as well as the analytic continuation of a complex two-dimensional Fano variety arising as a small resolution in a Calabi-Yau 5-fold.

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Section: Jhep12(2019)166mentioning

confidence: 99%

On stringy de Sitter spacetimes

Berglund

Hübsch

Minić

2019

J. High Energ. Phys.

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“…Finally, the theory of primitive forms, which gave rise to higher residue pairings, has been developed in order to generalize the classic theory of elliptic integrals to more general spaces [6,8]. We expect it to play a crucial role in recent developments connecting Feynman integrals to Calabi-Yau geometries [108][109][110][111][112][113][114][115]. but distinct phases.…”

Section: Discussionmentioning

confidence: 99%

From infinity to four dimensions: higher residue pairings and Feynman integrals

Mizera

Pokraka

2020

J. High Energ. Phys.

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We study a surprising phenomenon in which Feynman integrals in D = 4 − 2ε space-time dimensions as ε → 0 can be fully characterized by their behavior in the opposite limit, ε → ∞. More concretely, we consider vector bundles of Feynman integrals over kinematic spaces, whose connections have a polynomial dependence on ε and are known to be governed by intersection numbers of twisted forms. They give rise to differential equations that can be obtained exactly as a truncating expansion in either ε or 1/ε. We use the latter for explicit computations, which are performed by expanding intersection numbers in terms of Saito's higher residue pairings (previously used in the context of topological Landau-Ginzburg models and mirror symmetry). These pairings localize on critical points of a certain Morse function, which correspond to regions in the loop-momentum space that were previously thought to govern only the large-D physics. The results of this work leverage recent understanding of an analogous situation for moduli spaces of curves, where the α → 0 and α → ∞ limits of intersection numbers coincide for scattering amplitudes of massless quantum field theories.

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“…4 As explained in [7,8] the PFDI can be obtained from the modified GKZ system by factoring it from the latter. 5 Also for other Feynman graphs the appearing integrals can be related to Calabi Yau integrals as pointed out in [12][13][14]. 6 See also [15] for a connection between maximal cut Feynman integrals and solutions to corresponding…”

Section: Introductionmentioning

confidence: 98%