Phase structure of theO(2)ghost model with higher-order gradient term

Abstract

The phase structure and the infrared behaviour of the Euclidean 3-dimensional O(2) symmetric ghost scalar field model with higher-order derivative term has been investigated in Wegner and Houghton's renormalization group framework. The symmetric phase in which no ghost condensation occurs and the phase with restored symmetry but with a transient presence of a ghost condensate have been identified. Finiteness of the correlation length at the phase boundary hints to a phase transition of first order. The results are compared with those for the ordinary O(2) symmetric scalar field model.

Partially massless higher-spin theory II: one-loop effective actions

“…In [1], we presented evidence for a partially massless higher-spin theory which extends the Vasiliev theory [2][3][4][5] (see [4,[6][7][8][9][10] for reviews) to include additional partially massless states [11][12][13][14][15]. Furthermore, we presented evidence that the theory is dual to the 2 CFT which we studied in [16] (see also [17][18][19][20][21]).…”

Triple point in theO(2)ghost model with higher-order gradient term

“…In the LPA the wavefunction renormalization Z and the higher-derivative coupling Y do not acquire RG flow. The WH RG equation for the local potential is given as [10]…”

“…For scales k ≤ k c the resummation of the loop expansion by means of the WH equation is not any more possible. The IR behaviour can then be revealed by means of the tree-level renormalization (TLR) procedure [11] (see also its application to the O(2) model in our previous paper [10]). While in the case of the one-component (N = 1) real scalar field the vanishing of s + (k) governs the singularity, in cases with N ≥ 2 the vanishing of s − (k) does it.…”

“…Our numerical procedure for the determination of the RG trajectories is just the same as in our paper [10]. The WH RG equations are rewritten as a coupled set of ordinary differential equations for the dimensionless couplingsṽ n of the local potentialŨ k (Φ) and those solved with the truncation M = 10 with fourth-order Runge-Kutta method for scales k c < k ≤ Λ.…”

“…It corresponds to different approximations or RG schemes to keep either the dimensionful, or the dimensionless higher-derivative couplings constant. In our previous paper [10] we argued for keeping the dimensionful coupling Y constant and showed that the model exhibits two phases: besides the trivial symmetric phase there occurs a phase with restored symmetry characterized by a quasi-universal dimensionful effective potential. The existence of the latter is related with the occurrence of the ghost condensate at intermediate scales k. Now we shall take another point of view and keep the dimensionless couplingỸ = Y k −2 constant during the WH RG flow.…”