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Seminar on Theoretical and Computational Physics:
TitleFinite N effect in the 1/D expansion for the one-dimensional large N gauge theory
SpeakerDr. Shingo Takeuchi
AffiliationVietnam National Space Center, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam
DateTuesday, 09-01-2018
Time10:00 AM
LocationMeeting room, 8th floor, 2H Building, 18 Hoang Quoc Viet, Hanoi
AbstractWe consider finite N BFSS matrix model with D scalar fields and a gauge field given by N x N Hermitian matrix on a one-dimensional circled space. BFSS matrix model has originally come up in the literature of the M-theory, but it is interesting to investigate the correspondence between the confinement/deconfinement transition in the matrix model and Gregory-Laflamme instability in black D0-brane geometry. As the black string/black hole transition shows similarity with the Rayleigh-Plateau instability, it is also interesting to investigate it. The interesting research objects are the regions where the perturbative analysis and numerical analysis with lattice cannot reach. The 1/D expansion in the bosonic BFSS has been performed in [1], which is non-perturbative expansion. This is because it is just that D is large but there is no expansion point. Actually, we can analyze the transition order using the 1/D expansion which numerical analysis cannot work out. In the usual analysis of the 1/D expansion, the Ginzburg-Landau type effective action with Wilson line as its dynamical variable obtained from the effective action up to one-loop order with regard to the scalar fields are considered. At this time, finite D corrections are be considered, but large-N limit is taken always. This is because finite N correction arises from the non-planer diagrams, which make analysis quite complicated. However, finite N effects are still interesting in terms of the string length and the quantum gravity effects. As such, I in this talk introduce my study [2] which focuses on some term remaining in the finite N in the one-loop effective action, and analyze confinement/deconfinemnt transition and the third-order phase transition with the finite N effect at large D. [1] G.Mandal, M.Mahato and T.Morita, "Phases of one dimensional large N gauge theory in a 1/D expansion,' JHEP {f 1002}, 034 (2010), [arXiv:0910.4526 [hep-th]]. [2] S.Takeuchi, "Finite N effect in the 1/D expansion for the one-dimensional large N gauge theory', arXiv:1712.xxxxx (To appear in arXiv soon).
Host personHoàng Ngọc Long