Abstract
We compute the free energy in the presence of a chemical potential coupled to a conserved charge in the effective SU(N)xSU(N) scalar field theory to third order for asymmetric volumes in general d-dimensions, using dimensional regularization. We also compute the mass gap in a finite box with periodic boundary conditions.
Highlights
In a previous paper [6] we computed the change in the free energy due to a chemical potential coupled to a conserved charge in the non-linear O(n) sigma model with two regularizations, lattice regularization and dimensional regularization (DR) in a general d-dimensional asymmetric volume with periodic boundary conditions in all directions
In particular we could convert the computation of the mass gap in a periodic box, by Niedermayer and Weiermann [7] using lattice regularization to a result involving parameters of the dimensionally regularized effective theory, and we verified this result by a direct computation [6]
Matzelle and Tiburzi [10] have studied the effect of small symmetry breaking in the quantum mechanical (QM) rotator picture (Nf = 2), and extended the results to small non-zero temperatures
Summary
The dynamical fields are matrices U (x) ∈ SU(N ). In the chiral limit the action is invariant under global SU(N )L × SU(N )R transformations of the fields. In this limit the leading order effective Lagrangian is given by [1]:. For N ≥ 4 there are four linearly independent four-derivative terms in the effective Lagrangian [1]. Note the absence of the 4-derivative term tr( U † U ) in the above list; As explained in [12], this term can be eliminated by redefinition of the field U. In (2.3) one can restrict the summation to i = 1, 2 for N = 2 and to i = 1, 2, 3 for N = 3 From these relations it follows that the results obtained for general N should at N = 2 be invariant under the transformation. These and the relations (2.10), (2.11) can serve as checks on the final results
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