The Conformal Window and Walking Technicolor

Abstract

I discuss recent progress in the uncovering of the phase diagram of non-supersymmetric gauge theories. The nature of the conformal window for higher dimensional representations suggests a possible way to construct realistic technicolor models. I then explicitly provide two such theories. One of these models also has a natural cold Dark Matter candidate.The origin of electroweak symmetry breaking is one of the most outstanding problems of today in high energy physics. In the past many different ideas have been proposed to explain the mass generation of the electroweak gauge bosons with technicolor [1] being one of the best motivated extensions beyond the Standard Model (SM). Despite the elegance of the technicolor proposal it is only very recent that viable specific models not at odds with experiments have been constructed (for a review see [2]).Typically one is faced with the problem of constructing a technicolor theory that does not give a too large contribution to the S parameter [3] while at the same time exhibits walking dynamics [4]. In the original technicolor proposal the fermions were taken to be in the fundamental representation and hence one was at odds with the Electroweak Precision Tests since a large number of fermions was needed in order to obtain the desired dynamics.However, with recent advances in the understanding of the phase diagram of gauge theories involving fermions in arbitrary representations of the gauge group [5,6,7,8] new directions and possibilities for model building have been opened and envisioned [5,9]. Already a large amount of work has been done ranging from the study of Beyond SM phenomenology [10], Unification [11] and the finite temperature phase transition [12] together with Cosmology [13]. Also the lattice is starting to probe the (near) conformal dynamics of the simplest models [14]. THE PHASE DIAGRAMLet us first set the notation by denoting the generators of the gauge group in the representation r by T a r , a = 1 . . . N 2 − 1. They are normalized according to Tr T a r T b r = T(r)δ ab while the quadratic Casimir C 2 (r) is given by T a r T a r = C 2 (r)I. The trace normalization factor T(r) and the quadratic Casimir are connected via C 2 (r)d(r) = T(r)d(G) where d(r) is the dimension of the representation r. The adjoint representation is denoted by G.Let us first consider an SU(N) gauge theory with N f (r i ) Dirac fermions in the representation r i , i = 1, . . . , k of the gauge group. To estimate the conformal window we shall employ the recently conjectured all-orders beta function for non-supersymmetric theories [8] β(g) = − g 3 (4π) 2with