Deriving confinement via RG decimations
نویسنده
چکیده
We present the general framework and building blocks of a recent derivation of the fact that the SU(2) LGT is in a confining phase for all values of the coupling 0 < β < ∞, for space-time dimension d ≤ 4. The method employs approximate but explicitly computable RG decimations that are shown to constrain the exact partition function and order parameters from above and below, and flow from the weak to the strong coupling regime without encountering a fixed point.
منابع مشابه
Rg Decimations and Confinement *
We outline the steps in a derivation of the statement that the SU(2) gauge theory is in a confining phase for all values of the coupling, 0 < β < ∞, defined at lattice spacing a. The approach employed is to obtain both upper and lower bounds for the partition function and the ‘twisted’ partition function in terms of approximate decimation transformations. The behavior of the exact quantities is...
متن کاملRG decimation-based approach to confinement and computation on coarser lattices
A systematic procedure is presented for connecting short to long scales in LGT. Approximate decimations are used which can provide both upper and lower bounds on the partition function. Its exact value is then obtained by interpolation between the bounds. By iterating the procedure representations of the partition function as well as other physical quantities can be obtained on progressively co...
متن کاملConnecting Short to Long Scales in the Confining Vacuum
We study approximate decimations in SU(N) LGT that connect the short to long distance regimes. Simple ‘bond-moving’ decimations turn out to provide both upper and lower bounds on the exact partition function. This leads to a representation of the exact partition function in terms of successive decimations whose effective couplings flows are related to those of the easily computable bond-moving ...
متن کامل/ 0 60 90 47 v 2 2 7 Se p 20 06 RG decimation study of SU ( 2 ) gauge theory
We report on numerical studies of RG decimations in SU(2) gauge theory. We study in particular a class of plaquette actions involving sums of group representations. We measure a number of observables representative of different length scales in order to investigate the transformation of the system under different choices of spin blocking, and examine the flow of the effective action couplings. ...
متن کاملConfinement for all values of the coupling in four-dimensional SU(2) gauge theory
A derivation is given from first principles of the fact that the SU(2) gauge theory is in a confining phase for all values of the coupling 0 < g < ∞ defined at lattice spacing (UV regulator) a, and space-time dimension d ≤ 4. The strategy is to employ approximate RG decimation transformations of the potential moving type which give both upper and lower bounds on the partition function at each s...
متن کامل