Year: 2021
Type: dissertation
Abstract: provides a non-perturbative evidence of the WZ/minimal-model correspondence.In this thesis, we numerically study the 2D N = 2 WZ model, by using the formulation by Kamata and Suzuki.This formulation is based on the Nicolai map and the momentum cutoff regularization; allowing the action to be non-local, the theory preserves the full set of SUSY even with a finite cutoff, as well as the translational invariance.We focus on the following three numerical studies: (A) the numerical simulation of the ADE-type theories and verification of the theoretical conjecture; (B) the continuum limit analysis of the scaling dimension based on the finite-size scaling; (C) the application to the torus compactification of superstring theory.(A) We apply the SUSY-preserving formulation to the following various ADE-type theories: the A 2 , A 3 , D 3 , D 4 , E 6 ( ∼ = A 2 ⊗ A 3 ), and E 7 models.In some aspects, we extend and improve the theoretical and numerical analyses in the preceding works.First, to study the DE minimal models and further applications, the method is generalized to one with multiple superfields and more complicated superpotentials.Second, for the A 2 minimal model, numerical accuracy is quite improved.Third, we numerically measure the scaling dimension, by using the two-point function of the scalar field in the momentum space.Also we numerically measure the central charge, by using the two-point function of the supercurrent and that of the energy-momentum tensor.Our results are consistent with the conjectured WZ/minimal-model correspondence.(B) We develop an extrapolation method to take the continuum and infinite-volume limit, while any extrapolation has been not done in the preceding numerical studies.Then, we perform a precision measurement of the scaling dimension in the A 2 -type theory.This result implies the restoration of the locality in the continuum limit.(C) We apply the above method to non-minimal SCFTs.For simplicity we consider the complex one-dimensional torus compactification.This theory may be simply described by the A 2 ⊗ A 2 ⊗ A 2 minimal model.To deform the geometry of the compactification, we add a would-be marginal operator to the superpotential; then, the central charge is believed not to depend on this deformation.We numerically observe the central charge being constant under this deformation, which provides the non-perturbative evidence of the conjecture.These studies show a coherence picture which is consistent with the conjecture of the LG description of SCFT, and support the validity of our formulation.This kind of numerical approach, when further developed, will come in useful to study superstring theory.This thesis is based on the following papers:• O. Morikawa and H. Suzuki, "Numerical study of the N = 2 Landau-Ginzburg model," PTEP 2018 no.8, (2018) 083B05,
Author: 森川, 億人
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7155665723