New insight in the 2-flavor Schwinger model based on lattice simulations

Authors

  • Jaime Fabián Nieto Castellanos Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México
  • Wolfgang Bietenholz Instituto de Ciencias Nucleares, UNAM
  • Ivan Hip Faculty of Geotechnical Engineering, University of Zagreb, Croatia

DOI:

https://doi.org/10.31349/SuplRevMexFis.3.020707

Keywords:

Schwinger model, lattice gauge theory, finite temperature, chiral condensate, ±-regime, pion decay constant

Abstract

We consider the Schwinger model with two degenerate, light fermion flavors by means of lattice simulations. At finite temperature, we probe the viability of a bosonization method by Hosotani {\it et al.} Next we explore an analogue to the pion decay constant, which agrees for independent formulations based on the Gell-Mann--Oakes--Renner relation, the 2-dimensional Witten--Veneziano formula and the $\delta$-regime. Finally we confront several conjectures about the chiral condensate with lattice results.

References

J. Schwinger, Gauge Invariance and Mass. 2., Phys. Rev. 128 (1962) 2425, https://doi.org/10.1103/PhysRev. 128.2425.

L. V. Belvedere, K. D. Rothe, B. Schroer and J. Swieca, Generalized Two-dimensional Abelian Gauge Theories and Confinement, Nucl. Phys. B 153 (1979) 112, https://doi.org/10.1016/0550-3213(79)90594-7.

I. Hip, J. F. Nieto Castellanos and W. Bietenholz, Finite temperature and δ-regime in the 2-flavor Schwinger model, https://arxiv.org/abs/2109.13468.

Y. Hosotani, More about the massive multiflavor Schwinger model, in Nihon University Workshop on Fundamental Problems in Particle Physics (1995) 64, https://arxiv.org/abs/hep-th/9505168; Y. Hosotani and R. Rodriguez, Bosonized massive N-flavor Schwinger model, J. Phys. A 31 (1998) 9925, https://doi.org/10.1088/0305-4470/31/49/013.

J. F. Nieto Castellanos, The 2-flavor Schwinger model at finite temperature and in the delta-regime, B.Sc. thesis, Universidad Nacional Autonoma de Mexico, 2021.

A. V. Smilga, Critical amplitudes in two-dimensional theories, Phys. Rev. D 55 (1997) R443, https://doi.org/10.1103/PhysRevD.55.R443.

K. Harada, T. Sugihara, M. Taniguchi and M. Yahiro, The massive Schwinger model with SU(2)f on the light cone, Phys. Rev. D 49 (1994) 4226, https://doi.org/10.1103/PhysRevD.49.4226.

A. Smilga and J. J. M. Verbaarschot, Scalar susceptibility in QCD and the multiflavor Schwinger model, Phys. Rev. D 54 (1996) 1087, https://doi.org/10.1103/PhysRevD.54.1087.

A. Smilga, On the fermion condensate in the Schwinger model, Phys. Lett. B 278 (1992) 371, https://doi.org/10.1016/0370-2693(92)90209-M.

J. E. Hetrick, Y. Hosotani and S. Iso, The massive multiflavor Schwinger model, Phys. Lett. B 350 (1995) 92, https://doi.org/10.1016/0370-2693(95)00310-H.

E. Witten, Current Algebra Theorems for the U(1) Goldstone Boson, Nucl. Phys. B 156 (1979) 269, https://doi.org/10.1016/0550-3213(79)90031-2. G. Veneziano, U(1) Without Instatons, Nucl. Phys. B 159 (1979) 213, https://doi.org/10.1016/0550-3213(79)90332-8.

C. Gattringer and E. Seiler, Functional integral approach to the N flavor Schwinger model, Annals Phys. 233 (1994) 97, https://doi.org/10.1006/aphy.1994.1062

E. Seiler and I. O. Stamatescu, Some remarks on the Witten-Veneziano formula for the η 0 mass, Preprint (1987) https://lib-extopc.kek.jp/preprints/PDF/1987/8705/8705403.pdf.

W. A. Bardeen, A. Duncan, E. Eichten and H. Thacker, Quenched approximation artifacts: A study in two-dimensional QED, Phys. Rev. D 57 (1998) 3890, https://doi.org/10.1103/PhysRevD.57.3890. S. Durr and C. Hoel-bling, Staggered versus overlap fermions: A Study in the Schwinger model with Nf = 0, 1, 2, Phys. Rev. D 69 (2004) 034503, https://doi.org/10.1103/PhysRevD.69.034503. C. Bonati and P. Rossi, Topological susceptibility of two-dimensional U(N) gauge theories, Phys. Rev. D 99 (2019) 054503, https://doi.org/10.1103/PhysRevD.99.054503.

H. Leutwyler, Energy Levels of Light Quarks Confined to a Box, Phys. Lett. B 189 (1987) 197, https://doi.org/10.1016/0370-2693(87)91296-2

P. Hasenfratz and F. Niedermayer, Finite size and temperature effects in the AF Heisenberg model, Z. Phys. B 92 (1993) 91, https://doi.org/10.1007/BF01309171

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Published

2022-03-31

How to Cite

1.
Nieto Castellanos JF, Bietenholz W, Hip I. New insight in the 2-flavor Schwinger model based on lattice simulations. Supl. Rev. Mex. Fis. [Internet]. 2022 Mar. 31 [cited 2022 Jul. 2];3(2):020707 1-5. Available from: https://rmf.smf.mx/ojs/index.php/rmf-s/article/view/6124