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We construct a D2-D8-$\bar{D8}$ configuration in string theory, it can bedescribed at low energy by two dimensional field theory. In the weak couplingregion, the low energy theory is a nonlocal generalization of Gross-Neveu(GN)model which dynamically breaks the chiral flavor symmetry $U(N_f)_L \timesU(N_f)_R$ at large $N_c$ and finite $N_f$. However, in the strong couplingregion, we can use the SUGRA/Born-Infeld approximation to describe the lowenergy dynamics of the system. Also, we analyze the low energy dynamics aboutthe configuration of wrapping the one direction of D2 brane on a circle withanti-periodic boundary condition of fermions. The fermions and scalars on D2branes get mass and decouple from the low energy theory. The IR dynamics isdescribed by the $QCD_2$ at weak coupling. In the opposite region, the dynamicshas a holographic dual description. And we have discussed the phase transitionof chiral symmetry breaking at finite temperature. Finally, after performingT-duality, this configuration is related to some other brane configurations.Comment: 30 pages, 3 figures, minor change

NGN, QCD2and chiral phase transition from string theory

NGN, QCD₂and chiral phase transition from string theory