Related papers: Dual formulations of Polyakov loop lattice models
Non-abelian lattice spin models with symmetry group SU(N) or U(N) can be formulated in terms of link variables which are subject to the Bianchi constraints. Using this representation we derive exact and local dual formulation for the…
Dual formulations of Abelian U(1) and Z(N) LGT with a static fermion determinant are constructed at finite temperatures and non-zero chemical potential. The dual form is valid for a broad class of lattice gauge actions, for arbitrary number…
Various approaches to construction of dual formulations of non-abelian lattice gauge theories are reviewed. In the case of U(N) LGT we use a theory of the Weingarten functions to construct a dual formulation. In particular, the dual…
Non-Abelian Lattice Gauge Theory in Euclidean space-time of dimension d>=2 whose gauge group is any compact Lie group is related to a Spin Foam Model by an exact strong-weak duality transformation. The group degrees of freedom are…
We derive an exact duality transformation for pure non-Abelian gauge theory regularized on a lattice. The duality transformation can be applied to gauge theory with an arbitrary compact Lie group G as the gauge group and on Euclidean…
We develop a general theory of a boson decomposition for both local and non-local interactions in lattice fermion models which allows us to describe fermionic degrees of freedom and collective charge and spin excitations on equal footing.…
Many Polyakov loop models can be written in a dual formulation which is free of sign problem even when a non-vanishing baryon chemical potential is introduced in the action. Here, results of numerical simulations of a dual representation of…
In this work we introduce the concept of Cartan-Polyakov loops, a special subset of Polyakov loops in the fundamental representation of the $\mathrm{SU}(N_c)$ group, with charges $k=1,\ldots,(N_c-1)/2$. It constitutes a sufficient set of…
We derive dual representations for O(N) and CP(N-1) models on the lattice. In terms of the dual variables the partition sums have only real and positive contributions also at finite chemical potential. Thus the complex action problem of the…
The strong-coupling expansion of the lattice gauge action leads to Polyakov-loop models that effectively describe gluodynamics at low temperatures, and together with the hopping expansion of the fermion determinant provides insight into the…
The effective action of the SU(N) Polyakov loop model in the strong coupling region and in the static limit for the quark determinant can be mapped onto the Ising model in any dimensions, with the Ising variables attached on the links of…
In any Abelian gauge theory with an action periodic in the link variables one can perform a duality transformation not only in the partition function, but also in correlation functions including Polyakov loops. The calculation of…
In this series of three papers, we generalize the derivation of dual photons and monopoles by Polyakov, and Banks, Myerson and Kogut, to obtain approximative models of SU(2) lattice gauge theory. Our approach is based on stationary phase…
We show that the Polyakov loop approaches its asymptotic value at high temperatures {\it from below} in any strongly-coupled gauge theory at large $N_c$ with a dual supergravity description. In these theories the Polyakov loop can be used…
We introduce the basics of the nonabelian duality transformation of SU(N) or U(N) vector-field models defined on a lattice. The dual degrees of freedom are certain species of the integer-valued fields complemented by the symmetric groups'…
We compare SU(2) Polyakov loop models with different effective actions with data from full two-color QCD simulations around and above the critical temperature. We then apply the effective theories at finite temperature and density to…
In the past several decades there have been a number of proposals for computing with dual forms of non-abelian Yang-Mills theories on the lattice. Motivated by the gauge-invariant, geometric picture offered by dual models and successful…
In this series of three papers, we generalize the derivation of dual photons and monopoles by Polyakov, and Banks, Myerson and Kogut, to obtain approximative models of SU(2) lattice gauge theory. The papers take three different…
The (discrete) Gross-Neveu model is studied in a lattice realization with an N-component Majorana Wilson fermion field. It has an internal O(N) symmetry in addition to the euclidean lattice symmetries. The discrete chiral symmetry for…
We derive the spin Boltzmann equations for spin-1/2 fermions in a non-relativistic model with four-fermion contact interaction which conserves spin degrees of freedom. A great advantage of the model is that the spin matrix elements in…