Abstract
We consider two-dimensional lattice SU(Nc) gauge theories with Nf real scalar fields transforming in the adjoint representation of the gauge group and with a global O(Nf) invariance. Focusing on systems with Nf≥ 3, we study their zero-temperature limit, to understand under which conditions a continuum limit exists, and to investigate the nature of the associated quantum field theory. Extending previous analyses, we address the role that the gauge-group representation and the quartic scalar potential play in determining the nature of the continuum limit (when it exists). Our results further corroborate the conjecture that the continuum limit of two-dimensional lattice gauge models with multiflavor scalar fields, when it exists, is associated with a σ model defined on a symmetric space that has the same global symmetry as the lattice model.
Highlights
Parameter, and they do not undergo phase transitions associated with the spontaneous breaking of the global symmetry
The above issues are investigated by scrutinizing the nature of the low-energy configurations that are relevant in the zero-temperature limit, and by performing numerical finite-size scaling (FSS) analyses of Monte Carlo (MC) results
According to the conjecture reported in the introduction, the critical behavior should be the same as that of the 2D σ models defined on the symmetric spaces with the same global symmetry, that is the models defined on [3, 16] O(Nf )/O(p)⊗O(Nf − p) for different values of p
Summary
Which satisfy Tr Bx = 1 and Tr Qx = 0, due to the fixed-length constraint. Assuming translation invariance, holding for finite-size systems with periodic boundary conditions, we define the two-point correlation function. The corresponding susceptibility χ = x G(x) and second-moment correlation length ξ2. Where G(p) = x eip·xG(x) is the Fourier transform of G(x), and pm = (2π/L, 0). We consider universal renormalization-group (RG) invariant quantities, such as the ratio
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