Meromorphic continuation of Koba-Nielsen string amplitudes
- PDF / 644,062 Bytes
- 44 Pages / 595.276 x 841.89 pts (A4) Page_size
- 15 Downloads / 136 Views
Springer
Received: March Revised: August Accepted: August Published: September
10, 20, 21, 22,
2020 2020 2020 2020
M. Bocardo-Gaspar,a Willem Veysb and W.A. Z´ un ˜iga-Galindoc,1 a
Departamento de Matem´ aticas, CUCEI, Universidad de Guadalajara, Blvd. Marcelino Garc´ıa Barrag´ an #1421, Guadalajara, Jal. 44430, M´exico b Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3001 Leuven, Belgium c Departamento de Matem´ aticas, Unidad Quer´etaro, Centro de Investigaci´ on y de Estudios Avanzados del Instituto Polit´ecnico Nacional, Libramiento Norponiente #2000, Fracc. Real de Juriquilla. Santiago de Quer´etaro, Qro. 76230, M´exico
E-mail: [email protected], [email protected], [email protected] Abstract: In this article, we establish in a rigorous mathematical way that Koba-Nielsen amplitudes defined on any local field of characteristic zero are bona fide integrals that admit meromorphic continuations in the kinematic parameters. Our approach allows us to study in a uniform way open and closed Koba-Nielsen amplitudes over arbitrary local fields of characteristic zero. In the regularization process we use techniques of local zeta functions and embedded resolution of singularities. As an application we present the regularization of p-adic open string amplitudes with Chan-Paton factors and constant B-field. Finally, all the local zeta functions studied here are partition functions of certain 1D log-Coulomb gases, which shows an interesting connection between Koba-Nielsen amplitudes and statistical mechanics. Keywords: Bosonic Strings, D-branes, Differential and Algebraic Geometry ArXiv ePrint: 1905.10879
1
The second author was supported by KU Leuven grant C14/17/083. The third author was partially supported by Conacyt Grant No. 250845.
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)138
JHEP09(2020)138
Meromorphic continuation of Koba-Nielsen string amplitudes
Contents 1 Introduction
2
2 Discussion of the results 2.1 Open string tree amplitudes with Chan-Paton factors 2.2 Koba-Nielsen local zeta functions and 1D log-Coulomb gases
6 7 10
4 Local zeta functions of Koba-Nielsen type
13
5 Road map of the proof 5.1 Example 5.2 Example 5.3 Case I = {2, . . . , N − 2} 5.4 Case I 6= {2, . . . , N − 2} 5.5 Proof of Theorem 4.1 and precise description of the convergence domain 5.6 Example
16 17 17 19 23 26 27
6 Local zeta functions of Koba-Nielsen type over local fields 6.1 Local fields 6.2 Multivariate local zeta functions: general case 6.3 Meromorphic continuation of local zeta functions: general case 6.4 A result of Vanhove and Zerbini
28 28 28 30 31
7 Meromorphic continuation of Koba-Nielsen string amplitudes over local fields of characteristic zero 33 7.1 Convergence of the Koba-Nielsen amplitudes 33 7.2 Meromorphic continuation of Koba-Nielsen string amplitudes 34 7.3 Tachyon scattering 35 7.3.1 Example 37 8 Amplitudes and gamma functions 8.1 Veneziano amplitude (N ) 8.2 AR (k) as a sum of gamma
Data Loading...
