Florian Loebbert
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View article: Nonlocal Symmetries of Planar Feynman Integrals
Nonlocal Symmetries of Planar Feynman Integrals Open
We prove the invariance of scalar Feynman graphs of any planar topology under the Yangian level-one momentum symmetry given certain constraints on the propagator powers. The proof relies on relating this symmetry to a planarized version of…
View article: Hypergeometry from $\mathrm{\widehat P}$-Symmetry: Feynman Integrals in One and Two Dimensions
Hypergeometry from $\mathrm{\widehat P}$-Symmetry: Feynman Integrals in One and Two Dimensions Open
Feynman integrals with generic propagator powers in one and two spacetime dimensions are investigated from various perspectives. In particular, we argue that the class of track integrals at any loop order is fixed by the recently found $\m…
View article: The Feyn-structure of Yangian symmetry
The Feyn-structure of Yangian symmetry Open
A bstract Yangian-type differential operators are shown to constrain Feynman integrals beyond the restriction to integrable graphs. In particular, we prove that all position-space Feynman diagrams at tree level feature a Yangian level-one …
View article: Conformal four-point integrals: recursive structure, Toda equations and double copy
Conformal four-point integrals: recursive structure, Toda equations and double copy Open
A bstract We consider conformal four-point Feynman integrals to investigate how much of their mathematical structure in two spacetime dimensions carries over to higher dimensions. In particular, we discuss recursions in the loop order and …
View article: Conformal Four-Point Integrals: Recursive Structure, Toda Equations and Double Copy
Conformal Four-Point Integrals: Recursive Structure, Toda Equations and Double Copy Open
We consider conformal four-point Feynman integrals to investigate how much of their mathematical structure in two spacetime dimensions carries over to higher dimensions. In particular, we discuss recursions in the loop order and spacetime …
View article: Geometry from integrability: multi-leg fishnet integrals in two dimensions
Geometry from integrability: multi-leg fishnet integrals in two dimensions Open
A bstract We generalise the geometric analysis of square fishnet integrals in two dimensions to the case of hexagonal fishnets with three-point vertices. Our results support the conjecture that fishnet Feynman integrals in two dimensions, …
View article: The Basso-Dixon formula and Calabi-Yau geometry
The Basso-Dixon formula and Calabi-Yau geometry Open
A bstract We analyse the family of Calabi-Yau varieties attached to four-point fishnet integrals in two dimensions. We find that the Picard-Fuchs operators for fishnet integrals are exterior powers of the Picard-Fuchs operators for ladder …
View article: Geometry from Integrability: Multi-Leg Fishnet Integrals in Two Dimensions
Geometry from Integrability: Multi-Leg Fishnet Integrals in Two Dimensions Open
We generalise the geometric analysis of square fishnet integrals in two dimensions to the case of hexagonal fishnets with three-point vertices. Our results support the conjecture that fishnet Feynman integrals in two dimensions, together w…
View article: Integrability for Feynman integrals
Integrability for Feynman integrals Open
We give a brief overview of the Yangian symmetry of Feynman integrals. After a short introduction to the Yangian and integrability, we motivate the emergence of integrable structures for Feynman integrals via the fishnet limit of AdS/CFT. …
View article: The Basso-Dixon Formula and Calabi-Yau Geometry
The Basso-Dixon Formula and Calabi-Yau Geometry Open
We analyse the family of Calabi-Yau varieties attached to four-point fishnet integrals in two dimensions. We find that the Picard-Fuchs operators for fishnet integrals are exterior powers of the Picard-Fuchs operators for ladder integrals.…
View article: Report on scipost_202212_00046v1
Report on scipost_202212_00046v1 Open
We give a brief overview of the Yangian symmetry of Feynman integrals.After a short introduction to the Yangian and integrability, we motivate the emergence of integrable structures for Feynman integrals via the fishnet limit of AdS/CFT.We…
View article: Yangian-Invariant Fishnet Integrals in Two Dimensions as Volumes of Calabi-Yau Varieties
Yangian-Invariant Fishnet Integrals in Two Dimensions as Volumes of Calabi-Yau Varieties Open
We argue that ℓ-loop Yangian-invariant fishnet integrals in two dimensions are connected to a family of Calabi-Yau ℓ folds. The value of the integral can be computed from the periods of the Calabi-Yau, while the Yangian generators provide …
View article: Integrability for Feynman Integrals
Integrability for Feynman Integrals Open
We give a brief overview of the Yangian symmetry of Feynman integrals. After a short introduction to the Yangian and integrability, we motivate the emergence of integrable structures for Feynman integrals via the fishnet limit of AdS/CFT. …
View article: Yangian-invariant fishnet integrals in 2 dimensions as volumes of Calabi-Yau varieties
Yangian-invariant fishnet integrals in 2 dimensions as volumes of Calabi-Yau varieties Open
We argue that $\ell$-loop Yangian-invariant fishnet integrals in 2 dimensions are connected to a family of Calabi-Yau $\ell$-folds. The value of the integral can be computed from the periods of the Calabi-Yau, while the Yangian generators …
View article: Irrelevant deformations with boundaries and defects
Irrelevant deformations with boundaries and defects Open
We initiate the study of -like irrelevant solvable deformations in quantum field theory with boundaries and defects. For this purpose, we employ a general formalism developed in the context of spin chains, which allows us to derive …
View article: Massive Integrability: From Fishnet Theories to Feynman Graphs and Back
Massive Integrability: From Fishnet Theories to Feynman Graphs and Back Open
An overview of the massive generalization of Yangian symmetry for Feynman integrals is given. We illustrate the relation to a massive fishnet theory defined as a double-scaling limit of Coulomb-branch N=4 SYM theory.
View article: Massive Integrability: From Fishnet Theories to Feynman Graphs and Back
Massive Integrability: From Fishnet Theories to Feynman Graphs and Back Open
An overview of the massive generalization of Yangian symmetry for Feynman integrals is given. We illustrate the relation to a massive fishnet theory defined as a double-scaling limit of Coulomb-branch N=4 SYM theory.
View article: Yangian bootstrap for massive Feynman integrals
Yangian bootstrap for massive Feynman integrals Open
We extend the study of the recently discovered Yangian symmetry of massive Feynman integrals and its relation to massive momentum space conformal symmetry. After proving the symmetry statements in detail at one and two loop orders, we empl…
View article: Report on scipost_202011_00017v1
Report on scipost_202011_00017v1 Open
We extend the study of the recently discovered Yangian symmetry of massive Feynman integrals and its relation to massive momentum space conformal symmetry.After proving the symmetry statements in detail at one and two loop orders, we emplo…
View article: Report on scipost_202011_00017v1
Report on scipost_202011_00017v1 Open
We extend the study of the recently discovered Yangian symmetry of massive Feynman integrals and its relation to massive momentum space conformal symmetry.After proving the symmetry statements in detail at one and two loop orders, we emplo…
View article: Three-body effective potential in general relativity at second post-Minkowskian order and resulting post-Newtonian contributions
Three-body effective potential in general relativity at second post-Minkowskian order and resulting post-Newtonian contributions Open
We study the Post-Minkowskian (PM) and Post-Newtonian (PN) expansions of the\ngravitational three-body effective potential. At order 2PM a formal result is\ngiven in terms of a differential operator acting on the maximal generalized cut\no…
View article: Three-Body Effective Potential in General Relativity at 2PM and Resulting PN Contributions
Three-Body Effective Potential in General Relativity at 2PM and Resulting PN Contributions Open
We study the Post-Minkowskian (PM) and Post-Newtonian (PN) expansions of the gravitational three-body effective potential. At order 2PM a formal result is given in terms of a differential operator acting on the maximal generalized cut of t…
View article: Massive fishnets
Massive fishnets Open
A bstract Recently, infinite families of massive Feynman integrals were found to feature an unexpected Yangian symmetry. In the massless case, similar integrability properties are understood via the interpretation of individual Feynman int…
View article: Massive Conformal Symmetry and Integrability for Feynman Integrals
Massive Conformal Symmetry and Integrability for Feynman Integrals Open
In the context of planar holography, integrability plays an important role for solving certain massless quantum field theories such as N=4 super Yang-Mills theory. In this Letter, we show that integrability also features in the building bl…
View article: Yangian Symmetry for the Masses
Yangian Symmetry for the Masses Open
In the context of planar holography, integrability plays an important role for solving certain massless quantum field theories such as N=4 SYM theory. In this letter we show that integrability also features in the building blocks of massiv…
View article: Yangian bootstrap for conformal Feynman integrals
Yangian bootstrap for conformal Feynman integrals Open
We explore the idea to bootstrap Feynman integrals using integrability. In\nparticular, we put the recently discovered Yangian symmetry of conformal\nFeynman integrals to work. As a prototypical example we demonstrate that the\nD-dimension…
View article: Consistent conformal extensions of the standard model
Consistent conformal extensions of the standard model Open
The question of whether classically conformal modifications of the standard model are consistent with experimental observations has recently been subject to renewed interest. The method of Gildener and Weinberg provides a natural framework…
View article: Nonlocal symmetries and factorized scattering
Nonlocal symmetries and factorized scattering Open
Conventionally, factorized scattering in two dimensions is argued to be a\nconsequence of the conservation of local higher charges. However, integrability\nmay well be realized via nonlocal charges, while higher local charges are not\nknow…
View article: Yangian symmetry for bi-scalar loop amplitudes
Yangian symmetry for bi-scalar loop amplitudes Open
A bstract We establish an all-loop conformal Yangian symmetry for the full set of planar amplitudes in the recently proposed integrable bi-scalar field theory in four dimensions. This chiral theory is a particular double scaling limit of γ…