Inequivalence between the Euclidean and Lorentzian versions of the type IIB matrix model from Lefschetz thimble calculations
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arXiv
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| Natura: | Preprint |
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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 |