标题： 格点上的强耦合't Hooft模型 显示英文标题

标题： The Strongly Coupled 't Hooft Model on the Lattice

摘要： 我们研究了一味和两味无质量't Hooft模型在格点上的强耦合极限，即$large-{\cal N}_c$-色$QCD_2$模型。我们使用交错费米子和哈密顿量方法来处理格点规范理论。我们证明一味模型可以有效地用反铁磁Ising模型描述，在无穷大耦合极限下其基态即为规范模型的真空；围绕这个基态展开我们推导了强耦合展开，并计算了最低激发的强子质量和规范理论的手征凝聚量。我们的格点计算很好地再现了连续理论的结果。在无穷大耦合极限下，重子是无质量的；它们在强耦合展开的二阶就获得了质量，这与Witten提出的重子是$QCD$孤立子的论断一致。两味模型的谱和手征凝聚量可以用量子反铁磁Heisenberg模型的可观测量来有效描述。我们明确地用自旋模型基态上的自旋-自旋关联函数表示了最低激发的强子质量和手征凝聚量。我们证明了规范模型的平面极限（${\cal N}_c\longrightarrow \infty$）对应于反铁磁体的大自旋极限（$S\longrightarrow \infty$），并在该极限下计算了强子的质量谱，发现即使在这个模型中，格点上的手征对称性破缺模式也很好地再现了连续理论的结果。 显示英文摘要

摘要： We study the strong coupling limit of the one-flavor and two-flavor massless 't Hooft models, $large-{\cal N}_c$-color $QCD_2$, on a lattice. We use staggered fermions and the Hamiltonian approach to lattice gauge theories. We show that the one-flavor model is effectively described by the antiferromagnetic Ising model, whose ground state is the vacuum of the gauge model in the infinite coupling limit; expanding around this ground state we derive a strong coupling expansion and compute the lowest lying hadron masses as well as the chiral condensate of the gauge theory. Our lattice computation well reproduces the results of the continuum theory. Baryons are massless in the infinite coupling limit; they acquire a mass already at the second order in the strong coupling expansion in agreement with the Witten argument that baryons are the $QCD$ solitons. The spectrum and chiral condensate of the two-flavor model are effectively described in terms of observables of the quantum antiferromagnetic Heisenberg model. We explicitly write the lowest lying hadron masses and chiral condensate in terms of spin-spin correlators on the ground state of the spin model. We show that the planar limit (${\cal N}_c\longrightarrow \infty$) of the gauge model corresponds to the large spin limit ($S\longrightarrow \infty$) of the antiferromagnet and compute the hadron mass spectrum in this limit finding that, also in this model, the pattern of chiral symmetry breaking of the continuum theory is well reproduced on the lattice.