Casimir Effect in Yang-Mills Theory in $D=2+1$

We study, for the first time, the Casimir effect in non-Abelian gauge theory using first-principles numerical simulations. Working in two spatial dimensions at zero temperature, we find that closely spaced perfect chromoelectric conductors attract each other with a small anomalous scaling dimension. At large separation between the conductors, the attraction is exponentially suppressed by a new massive quantity, the Casimir mass, which is surprisingly different from the lowest glueball mass. The apparent emergence of the new massive scale may be a result of the backreaction of the vacuum to the presence of the plates as sufficiently close chromoelectric conductors induce, in a space between them, a smooth crossover transition to a color deconfinement phase.

Figure 1

The Casimir potential $V_{\mathrm{Cas}}$ for a nearly perfect wire (${\lambda }_w=50$) as the function of the distance $R$ between the wires in units of the string tension $\sigma$ at various bulk couplings $\beta$.

Figure 2

The Casimir mass $M_{\mathrm{Cas}}$ and the anomalous dimension $\nu$ (in the inset) for the best fit (15) as a function of the strength of the wire ${\lambda }_w$. The thick dashed lines denote the best fit by function (16), and the short-dashed horizontal lines show the asymptotic values (17) and (19), respectively. The dotted-dashed line in the inset marks the tree-level power $\nu =0$.

Figure 3

A typical expectation value of the absolute value of the mean Polyakov line in the spaces in between and outside the wires vs the interwire separation $R$.