Permanent Confinement in the CompactQED3with Fermionic Matter

Abstract

We argue that the compact three dimensional electrodynamics with massless relativistic fermions is always in the confined phase, in spite of the bare interaction between the magnetic monopoles being rendered logarithmic by fermions. The effect is caused by screening by other dipoles, which transforms the logarithmic back into the Coulomb interaction at large distances. Possible implications for the chiral symmetry breaking for fermions are discussed, and the global phase diagram of the theory is proposed.

Topological order and the deconfinement transition in the(2+1)-dimensional compact Abelian Higgs model

“…(21), and the correlation length exponent ν, for q = 2. With an appropriate choice of ν the data for different sizes should collapse onto a single scaling function.…”

“…It should be noted that a realistic theory of the high-T c cuprates would require also the inclusion of gapless nodal quasiparticles, which are here neglected. 19,20,21,22,23 We thus consider a (2+1)D compact U (1) gauge theory minimally coupled to a charge-q bosonic matter field, with an Euclidean action S = −J rµ cos(∇ µ θ r − qA rµ ) − 1 g rµ cos(B rµ ), (1) where θ r and A rµ are compact phases ∈ [0, 2π) living on the sites and links of a 3D simple cubic lattice, respectively. B rµ = ǫ µνλ ∇ ν A rλ is the dual field strength, with the lattice difference operators defined by ∇ µ f r = ∇ µ f r+eµ = f r+eµ − f r .…”

Massless fermions and the instanton dipole liquid in compact QED3

“…iv) On the other hand, according to our discussion in subsection 3.1, when the effect of massless fermions is studied by means of the anomalous sine-Gordon model with global Z 2 , given in [5,6], a destabilization of the area law is obtained, instead of the perimeter law characterizing deconfinement.…”

“…In this case, when disregarding the source terms in (65), the anomalous sine-Gordon model considered in [5,6] (cf. (4)) is obtained.…”

“…In [5,6], the effect of massless fermions was taken into account by keeping just the quadratic part of their contribution to the effective action, a procedure which is justified by invoking an IR fixed point argument. As it is well known, when parity is not broken, the quadratic part of the fermionic effective action contributes a nonlocal Maxwell term S nl to the effective action,…”