Knowledge Management System of Institute of Theoretical Physics, CAS
Arkani-Hamed, Nima; He, Song2,3,4,5 ; Lam, Thomas6,7
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| Stringy canonical forms | |
| Source Publication | JOURNAL OF HIGH ENERGY PHYSICS
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| Language | 英语 |
| Abstract | Canonical forms of positive geometries play an important role in revealing hidden structures of scattering amplitudes, from amplituhedra to associahedra. In this paper, we introduce "stringy canonical forms", which provide a natural definition and extension of canonical forms for general polytopes, deformed by a parameter alpha '. They are defined by real or complex integrals regulated with polynomials with exponents, and are meromorphic functions of the exponents, sharing various properties of string amplitudes. As alpha ' -> 0, they reduce to the usual canonical form of a polytope given by the Minkowski sum of the Newton polytopes of the regulating polynomials, or equivalently the volume of the dual of this polytope, naturally determined by tropical functions. At finite alpha ', they have simple poles corresponding to the facets of the polytope, with the residue on the pole given by the stringy canonical form of the facet. There is the remarkable connection between the alpha ' -> 0 limit of tree-level string amplitudes, and scattering equations that appear when studying the alpha ' -> infinity limit. We show that there is a simple conceptual understanding of this phenomenon for any stringy canonical form: the saddle-point equations provide a diffeomorphism from the integration domain to the interior of the polytope, and thus the canonical form can be obtained as a pushforward via summing over saddle points. When the stringy canonical form is applied to the ABHY associahedron in kinematic space, it produces the usual Koba-Nielsen string integral, giving a direct path from particle to string amplitudes without an a priori reference to the string worldsheet. We also discuss a number of other examples, including stringy canonical forms for finite-type cluster algebras (with type A corresponding to usual string amplitudes), and other natural integrals over the positive Grassmannian. |
| 2021 | |
| ISSN | 1029-8479 |
| Issue | 2Pages:69 |
| Cooperation Status | 国际 |
| Subject Area | Physics |
| MOST Discipline Catalogue | Physics, Particles & Fields |
| DOI | 10.1007/JHEP02(2021)069 |
| Indexed By | SCIE |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.itp.ac.cn/handle/311006/27489 |
| Collection | SCI期刊论文 |
| Affiliation | 1.Inst Adv Studies, Sch Nat Sci, Princeton, NJ 08540 USA 2.Harvard Univ, Ctr Math Sci & Applicat, Cambridge, MA 02138 USA 3.Chinese Acad Sci, Inst Theoret Phys, CAS Key Lab Theoret Phys, Beijing 100190, Peoples R China 4.UCAS, Sch Fundamental Phys & Math Sci, Hangzhou Inst Adv Study, Hangzhou 310024, Peoples R China 5.ICTP AP Int Ctr Theoret Phys Asia Pacific, Beijing, Peoples R China 6.Univ Chinese Acad Sci, Sch Phys Sci, 19A Yuquan Rd, Beijing 100049, Peoples R China 7.Univ Michigan, Dept Math, 530 Church St, Ann Arbor, MI 48109 USA 8.MIT, Dept Math, 77 Massachusetts Ave, Cambridge, MA 02139 USA |
| Recommended Citation GB/T 7714 | Arkani-Hamed, Nima,He, Song,Lam, Thomas. Stringy canonical forms[J]. JOURNAL OF HIGH ENERGY PHYSICS,2021(2):69. |
| APA | Arkani-Hamed, Nima,He, Song,&Lam, Thomas.(2021).Stringy canonical forms.JOURNAL OF HIGH ENERGY PHYSICS(2),69. |
| MLA | Arkani-Hamed, Nima,et al."Stringy canonical forms".JOURNAL OF HIGH ENERGY PHYSICS .2(2021):69. |
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| Stringy canonical fo（897KB） | 期刊论文 | 出版稿 | 开放获取 | CC BY-NC-SA | Application Full Text | |
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