# The correlahedron

@article{Eden2017TheC, title={The correlahedron}, author={Burkhard Eden and Pauline Heslop and Lionel Mason}, journal={Journal of High Energy Physics}, year={2017}, volume={2017}, pages={1-42} }

A bstractWe introduce a new geometric object, the correlahedron, which we conjecture to be equivalent to stress-energy correlators in planar N=4$$ \mathcal{N}=4 $$ super Yang-Mills. Re-expressing the Grassmann dependence of correlation functions of n chiral stress-energy multiplets with Grassmann degree 4k in terms of 4(n + k)-linear bosonic variables, the resulting expressions have an interpretation as volume forms on a Gr(n+k, 4+n+k) Grassmannian, analogous to the expressions for planar…

## 28 Citations

### The twistor Wilson loop and the amplituhedron

- PhysicsJournal of High Energy Physics
- 2018

A bstractThe amplituhedron provides a beautiful description of perturbative superamplitude integrands in N=4$$ \mathcal{N}=4 $$ SYM in terms of purely geometric objects, generalisations of polytopes.…

### Unwinding the amplituhedron in binary

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A bstractWe present new, fundamentally combinatorial and topological characterizations of the amplituhedron. Upon projecting external data through the amplituhedron, the resulting configuration of…

### A note on NMHV form factors from the Graßmannian and the twistor string

- Mathematics
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A bstractIn this note we investigate Graßmannian formulas for form factors of the chiral part of the stress-tensor multiplet in N=4$$ \mathcal{N}=4 $$ superconformal Yang-Mills theory. We present an…

### Amplituhedron-like geometries

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We consider amplituhedron-like geometries which are defined in a similar way to the intrinsic definition of the amplituhedron but with non-maximal winding number. We propose that for the cases with…

### Determinants in self-dual N=4 SYM and twistor space

- Mathematics
- 2023

We consider correlation functions of supersymmetrized determinant operators in self-dual super Yang-Mills (SYM). These provide a generating function for correlators of arbitrary single-trace half-BPS…

### Positive geometry, local triangulations, and the dual of the Amplituhedron

- Mathematics
- 2020

We initiate the systematic study of local positive spaces which arise in the context of the Amplituhedron construction for scattering amplitudes in planar maximally supersymmetric Yang-Mills theory.…

### Multi-particle amplitudes from the four-point correlator in planar N$$ \mathcal{N} $$ = 4 SYM

- MathematicsJournal of High Energy Physics
- 2018

A bstractA non-trivial consequence of the super-correlator/super-amplitude duality is that the integrand of the four-point correlation function of stress-tensor multiplets in planar N$$ \mathcal{N}…

### Multi-particle amplitudes from the four-point correlator in planar N = 4 SYM

- Mathematics
- 2018

: A non-trivial consequence of the super-correlator/super-amplitude duality is that the integrand of the four-point correlation function of stress-tensor multiplets in planar N = 4 super Yang-Mills…

### Amplituhedron meets Jeffrey–Kirwan residue

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2018

The tree amplituhedra are mathematical objects generalising the notion of polytopes into the Grassmannian. Proposed for as a geometric construction encoding tree-level scattering amplitudes in planar…

### Internal boundaries of the loop amplituhedron

- Mathematics
- 2022

The strict definition of positive geometry implies that all maximal residues of its canonical form are ±1. We observe, however, that the loop integrand of the amplitude in planar N = 4 super…

## 46 References

### Positive amplitudes in the amplituhedron

- Geology
- 2014

A bstractThe all-loop integrand for scattering amplitudes in planar N=4$$ \mathcal{N}=4 $$ SYM is determined by an “amplitude form” with logarithmic singularities on the boundary of the…

### Evidence for a nonplanar amplituhedron

- Geology
- 2015

A bstractThe scattering amplitudes of planar N$$ \mathcal{N} $$ = 4 super-Yang-Mills exhibit a number of remarkable analytic structures, including dual conformal symmetry and logarithmic…

### Unwinding the amplituhedron in binary

- Physics
- 2017

A bstractWe present new, fundamentally combinatorial and topological characterizations of the amplituhedron. Upon projecting external data through the amplituhedron, the resulting configuration of…

### Bootstrapping correlation functions in N = 4 SYM

- Mathematics
- 2018

We describe a new approach to computing the chiral part of correlation functions of stresstensor supermultiplets in N = 4 SYM that relies on symmetries, analytic properties and the structure of the…

### Local integrals for planar scattering amplitudes

- Mathematics
- 2012

A bstractRecently, an explicit, recursive formula for the all-loop integrand of planar scattering amplitudes in $ \mathcal{N} = {4} $ SYM has been described, generalizing the BCFW formula for tree…

### The amplituhedron from momentum twistor diagrams

- Physics
- 2014

A bstractWe propose a new diagrammatic formulation of the all-loop scattering amplitudes/Wilson loops in planar N$$ \mathcal{N} $$ = 4 SYM, dubbed the “momentum-twistor diagrams”. These are…

### Anatomy of the amplituhedron

- Geology, Mathematics
- 2014

A bstractWe initiate a comprehensive investigation of the geometry of the amplituhedron, a recently found geometric object whose volume calculates the integrand of scattering amplitudes in planar…

### N$$ \mathcal{N} $$ = 4 super-Yang-Mills in LHC superspace part II: non-chiral correlation functions of the stress-tensor multiplet

- Physics
- 2016

A bstractWe study the multipoint super-correlation functions of the full non-chiral stress-tensor multiplet in N$$ \mathcal{N} $$ = 4 super-Yang-Mills theory in the Born approximation. We derive…

### Into the amplituhedron

- Geology
- 2013

A bstractWe initiate an exploration of the physics and geometry of the amplituhedron, starting with the simplest case of the integrand for four-particle scattering in planar N=4$$ \mathcal{N}=4 $$…