Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
- PDF / 1,219,201 Bytes
- 29 Pages / 595.276 x 841.89 pts (A4) Page_size
- 72 Downloads / 140 Views
Springer
Received: February 26, 2020 Accepted: May 9, 2020 Published: June 9, 2020
Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
a
Physics Department, National Technical University, Zografou Campus, GR-15780 Athens, Greece b Institute for Fundamental Sciences, Setsunan University, 17-8 Ikeda Nakamachi, Neyagawa, Osaka, 572-8508, Japan c National Institute of Technology, Tokuyama College, Gakuendai, Shunan, Yamaguchi 745-8585, Japan d KEK Theory Center, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan e Graduate University for Advanced Studies (SOKENDAI), 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan f Faculty of Science and Technology, Meijo University, Nagoya, 468-8502, Japan
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: The IKKT matrix model is a promising candidate for a nonperturbative formulation of superstring theory. In this model, spacetime is conjectured to emerge dynamically from the microscopic matrix degrees of freedom in the large-N limit. Indeed in the Lorentzian version, Monte Carlo studies suggested the emergence of (3+1)-dimensional expanding spacetime. Here we study the Euclidean version instead, and investigate an alternative scenario for dynamical compactification of extra dimensions via the spontaneous symmetry breaking (SSB) of 10D rotational symmetry. We perform numerical simulations based on the complex Langevin method (CLM) in order to avoid a severe sign problem. Furthermore, in order to avoid the singular-drift problem in the CLM, we deform the model and determine the SSB pattern as we vary the deformation parameter. From these results, we conclude that the original model has an SO(3) symmetric vacuum, which is consistent with previous results obtained by the Gaussian expansion method (GEM). We also apply the GEM to the deformed matrix model and find consistency with the results obtained by the CLM. Keywords: 1/N Expansion, Matrix Models ArXiv ePrint: 2002.07410
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP06(2020)069
JHEP06(2020)069
Konstantinos N. Anagnostopoulos,a Takehiro Azuma,b Yuta Ito,c,d Jun Nishimura,d,e Toshiyuki Okubof and Stratos Kovalkov Papadoudisa
Contents 1 Introduction
1
2 Brief review of the IKKT matrix model 2.1 The Lorentzian version 2.2 The Euclidean version
4 4 7 9 9 10 10 12
4 Consistency check based on the GEM 4.1 Applying the GEM to the deformed model 4.2 Results of the GEM
15 15 17
5 Summary and discussions
19
A The singular-drift problem vanishing at large N
20
1
Introduction
Superstring theory has been studied intensively as a unified theory that includes quantum gravity. The theory is defined in ten spacetime dimensions and the connection to the real world, where only four dimensions are macroscopic, is realized via compactification of the extra dimensions. How this can actually occur ha
Data Loading...
