Inequivalence between the Euclidean and Lorentzian versions of the type IIB matrix model from Lefschetz thimble calculations

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Autori principali: Chou, Chien-Yu, Nishimura, Jun, Tripathi, Ashutosh
Natura: Preprint
Pubblicazione: 2025
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author Chou, Chien-Yu
Nishimura, Jun
Tripathi, Ashutosh
author_facet Chou, Chien-Yu
Nishimura, Jun
Tripathi, Ashutosh
contents The type IIB matrix model is conjectured to describe superstring theory nonperturbatively in terms of ten $N \times N$ bosonic traceless Hermitian matrices $A_μ$ ($μ=0, \ldots , 9$), whose eigenvalues correspond to $(9+1)$-dimensional space-time. Quite often, this model has been investigated in its Euclidean version, which is well defined although the ${\rm SO}(9,1)$ Lorentz symmetry of the original model is replaced by the ${\rm SO}(10)$ rotational symmetry. Recently, a well-defined model respecting the Lorentz symmetry has been proposed by gauge-fixing the Lorentz symmetry nonperturbatively using the Faddeev-Popov procedure. Here we investigate the two models by Monte Carlo simulations, overcoming the severe sign problem by the Lefschetz thimble method, in the case of matrix size $N=2$ omitting fermionic contributions. We add a quadratic term $γ\, \mathrm{tr} (A_μA^μ)$ in the action and calculate the expectation values of rotationally symmetric (or Lorentz symmetric) observables as a function of the coefficient $γ$. Our results exhibit striking differences between the two models around $γ=0$ and in the $γ>0$ region, associated with the appearance of different saddle points, clearly demonstrating their inequivalence against naive expectations from quantum field theory.
format Preprint
id arxiv_https___arxiv_org_abs_2501_17798
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Inequivalence between the Euclidean and Lorentzian versions of the type IIB matrix model from Lefschetz thimble calculations
Chou, Chien-Yu
Nishimura, Jun
Tripathi, Ashutosh
High Energy Physics - Theory
General Relativity and Quantum Cosmology
High Energy Physics - Lattice
High Energy Physics - Phenomenology
The type IIB matrix model is conjectured to describe superstring theory nonperturbatively in terms of ten $N \times N$ bosonic traceless Hermitian matrices $A_μ$ ($μ=0, \ldots , 9$), whose eigenvalues correspond to $(9+1)$-dimensional space-time. Quite often, this model has been investigated in its Euclidean version, which is well defined although the ${\rm SO}(9,1)$ Lorentz symmetry of the original model is replaced by the ${\rm SO}(10)$ rotational symmetry. Recently, a well-defined model respecting the Lorentz symmetry has been proposed by gauge-fixing the Lorentz symmetry nonperturbatively using the Faddeev-Popov procedure. Here we investigate the two models by Monte Carlo simulations, overcoming the severe sign problem by the Lefschetz thimble method, in the case of matrix size $N=2$ omitting fermionic contributions. We add a quadratic term $γ\, \mathrm{tr} (A_μA^μ)$ in the action and calculate the expectation values of rotationally symmetric (or Lorentz symmetric) observables as a function of the coefficient $γ$. Our results exhibit striking differences between the two models around $γ=0$ and in the $γ>0$ region, associated with the appearance of different saddle points, clearly demonstrating their inequivalence against naive expectations from quantum field theory.
title Inequivalence between the Euclidean and Lorentzian versions of the type IIB matrix model from Lefschetz thimble calculations
topic High Energy Physics - Theory
General Relativity and Quantum Cosmology
High Energy Physics - Lattice
High Energy Physics - Phenomenology
url https://arxiv.org/abs/2501.17798