Minshan Zheng
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Research Interests
Minshan Zheng has a total of 6 co-authors. Here are the top co-authors by number of shared publications:
- Jaroslav Trnka
University of California
3 shared publications - Cameron Langer
Institute for Gravitation and the Cosmos, Department of Physics, Pennsylvania State University, University Park, USA
2 shared publications - Enrico Herrmann
University of California at Los Angeles
2 shared publications - Jacob L. Bourjaily
Pennsylvania State University
1 shared publication - Kokkimidis Patatoukos
Institute for Gravitation and the Cosmos, Department of Physics, Pennsylvania State University, University Park, USA
1 shared publication - Shruti Paranjape
Brown University
1 shared publication
Latest Publications
- Open Access
- 15 December 2022
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2022 (12) , 1-70
Non-planar BCFW Grassmannian geometries
In this paper, we study non-adjacent BCFW recursion relations and their connection to positive geometry. For an adjacent BCFW shift, the n-point NkMHV tree-level amplitude in $$ \mathcal{N} $$ = 4 SYM theory is expressed as a sum over planar on-shell diagrams, corresponding to canonical “dlog” forms on the cells in the positive Grassmannian G+(k, n). Non-adjacent BCFW shifts naturally lead to an expansion of the amplitude in terms of a different set of objects, which do not manifest the cyclic ordering and the hidden Yangian symmetry of the amplitude. We show that these terms can be interpreted as dlog forms on the non-planar Grassmannian geometries, generalizing the cells of the positive Grassmannian G+(k, n) to a larger class of objects which live in G(k, n). We focus mainly on the case of NMHV amplitudes and discuss in detail the Grassmannian geometries. We also propose an alternative way to calculate the associated on-shell functions and dlog forms using an intriguing connection between Grassmannian configurations and the geometry in the kinematical space.- 15 December 2022
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2022 (12) , 1-70
Open AccessNon-planar BCFW Grassmannian geometries
In this paper, we study non-adjacent BCFW recursion relations and their connection to positive geometry. For an adjacent BCFW shift, the n-point NkMHV tree-level amplitude in $$ \mathcal{N} $$ = 4 SYM theory is expressed as a sum over planar on-shell diagrams, corresponding to canonical “dlog” forms on the cells in the positive Grassmannian G+(k, n). Non-adjacent BCFW shifts naturally lead to an expansion of the amplitude in terms of a different set of objects, which do not manifest the cyclic ordering and the hidden Yangian symmetry of the amplitude. We show that these terms can be interpreted as dlog forms on the non-planar Grassmannian geometries, generalizing the cells of the positive Grassmannian G+(k, n) to a larger class of objects which live in G(k, n). We focus mainly on the case of NMHV amplitudes and discuss in detail the Grassmannian geometries. We also propose an alternative way to calculate the associated on-shell functions and dlog forms using an intriguing connection between Grassmannian configurations and the geometry in the kinematical space. - Open Access
- 21 March 2022
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2022 (3) , 1-41
Integrands of less-supersymmetric Yang-Mills at one loop
We construct a prescriptive, bubble power-counting basis of one-loop integrands suitable for representing amplitude integrands in less-supersymmetric (1 ≤ $$ \mathcal{N} $$ ≤ 4) Yang-Mills theory. With the exception of massless bubbles, all integrands have unambiguous, leading singularities as coefficients defined in field theory; for the massless bubbles on external legs, we find two natural choices which lead to different integrands that highlight distinct aspects of field theory. For concreteness, we give the all-multiplicity integrands for MHV amplitudes, and the split-helicity amplitude integrand for six-particle NMHV. The basis we construct is mostly pure and is divided into to separately UV- and IR-finite sectors of fixed transcendental weight, resulting in UV- and IR-finite ratio functions of n-particle helicity amplitudes.- 21 March 2022
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2022 (3) , 1-41
Open AccessIntegrands of less-supersymmetric Yang-Mills at one loop
We construct a prescriptive, bubble power-counting basis of one-loop integrands suitable for representing amplitude integrands in less-supersymmetric (1 ≤ $$ \mathcal{N} $$ ≤ 4) Yang-Mills theory. With the exception of massless bubbles, all integrands have unambiguous, leading singularities as coefficients defined in field theory; for the massless bubbles on external legs, we find two natural choices which lead to different integrands that highlight distinct aspects of field theory. For concreteness, we give the all-multiplicity integrands for MHV amplitudes, and the split-helicity amplitude integrand for six-particle NMHV. The basis we construct is mostly pure and is divided into to separately UV- and IR-finite sectors of fixed transcendental weight, resulting in UV- and IR-finite ratio functions of n-particle helicity amplitudes. - Open Access
- 8 January 2021
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2021 (1) , 1-101
Positive geometry, local triangulations, and the dual of the Amplituhedron
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. We show that all local positive spaces relevant for one-loop MHV amplitudes are characterized by certain sign-flip conditions and are associated with surprisingly simple logarithmic forms. In the maximal sign-flip case they are finite one-loop octagons. Particular combinations of sign-flip spaces can be glued into new local positive geometries. These correspond to local pentagon integrands that appear in the local expansion of the MHV one-loop amplitude. We show that, geometrically, these pentagons do not triangulate the original Amplituhedron space but rather its twin “Amplituhedron-Prime”. This new geometry has the same boundary structure as the Amplituhedron (and therefore the same logarithmic form) but differs in the bulk as a geometric space. On certain two-dimensional boundaries, where the Amplituhedron geometry reduces to a polygon, we check that both spaces map to the same dual polygon. Interestingly, we find that the pentagons internally triangulate that dual space. This gives a direct evidence that the chiral pentagons are natural building blocks for a yet-to-be discovered dual Amplituhedron.
- 8 January 2021
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2021 (1) , 1-101
Open AccessPositive geometry, local triangulations, and the dual of the Amplituhedron
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. We show that all local positive spaces relevant for one-loop MHV amplitudes are characterized by certain sign-flip conditions and are associated with surprisingly simple logarithmic forms. In the maximal sign-flip case they are finite one-loop octagons. Particular combinations of sign-flip spaces can be glued into new local positive geometries. These correspond to local pentagon integrands that appear in the local expansion of the MHV one-loop amplitude. We show that, geometrically, these pentagons do not triangulate the original Amplituhedron space but rather its twin “Amplituhedron-Prime”. This new geometry has the same boundary structure as the Amplituhedron (and therefore the same logarithmic form) but differs in the bulk as a geometric space. On certain two-dimensional boundaries, where the Amplituhedron geometry reduces to a polygon, we check that both spaces map to the same dual polygon. Interestingly, we find that the pentagons internally triangulate that dual space. This gives a direct evidence that the chiral pentagons are natural building blocks for a yet-to-be discovered dual Amplituhedron.