The equation of state of 3D U(1) lattice gauge theory is consistent with a single massive state below T_c and a free photon gas above T_c, with no Hagedorn tower of states.
Conformal field theory and the hot phase of three-dimensional U(1) gauge theory
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abstract
We study the high-temperature phase of compact U(1) gauge theory in 2+1 dimensions, comparing the results of lattice calculations with analytical predictions from the conformal-field-theory description of the low-temperature phase of the bidimensional XY model. We focus on the two-point correlation functions of probe charges and the field-strength operator, finding excellent quantitative agreement with the functional form and the continuously varying critical indices predicted by conformal field theory.
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On the equation of state of U(1) lattice gauge theory in three dimensions
The equation of state of 3D U(1) lattice gauge theory is consistent with a single massive state below T_c and a free photon gas above T_c, with no Hagedorn tower of states.