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Register a new userRenormalization-Group Behavior of $phi^3$ Theories in $d=6$ Dimensions
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We investigate possible renormalization-group fixed points at nonzero coupling in $phi^3$ theories in six spacetime dimensions, using beta functions calculated to the four-loop level. We analyze three theories of this type, with (a) a one-component scalar, (b) a scalar transforming as the fundamental representation of a global ${rm SU}(N)$ symmetry group, and (c) a scalar transforming as a bi-adjoint representation of a global ${rm SU}(N) otimes {rm SU}(N)$ symmetry. We do not find robust evidence for such fixed points in theories (a) or (b). Theory (c) has the special feature that the one-loop term in the beta function is zero; implications of this are discussed.
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Recently it was shown that the scaling dimension of the operator $phi^n$ in scale-invariant $d=3$ theory may be computed semiclassically, and this was verified to leading order (two loops) in perturbation theory at leading and subleading $n$. Here we extend this verification to six loops, once again at leading and subleading $n$. We then perform a similar exercise for a theory with a multiplet of real scalars and an $O(N)$ invariant hexic interaction. We also investigate the strong-coupling regime for this example.
In this work, we report on the possibility of occurrence of oscillon configurations in the fourth state of matter. Oscillons are extremely long-lived, time-periodic, spatially-localised scalar field structures. Starting from a scalar field theory in 1+1 space-time dimensions, we find out that small-amplitude oscillons can be obtained in the framework of a $phi^6$ self-interacting potential. A connection between our results and ideal MHD theory is established. Perspectives for a development of the present work are pointed out.
We discuss some general aspects of renormalization group flows in four dimensions. Every such flow can be reinterpreted in terms of a spontaneously broken conformal symmetry. We analyze in detail the consequences of trace anomalies for the effective action of the Nambu-Goldstone boson of broken conformal symmetry. While the c-anomaly is algebraically trivial, the a-anomaly is non-Abelian, and leads to a positive-definite universal contribution to the S-matrix of 2->2 dilaton scattering. Unitarity of the S-matrix results in a monotonically decreasing function that interpolates between the Euler anomalies in the ultraviolet and the infrared, thereby establishing the a-theorem.
We calculate the next to the leading order Casimir effect for a real scalar field, within $phi^4$ theory, confined between two parallel plates in three spatial dimensions with the Dirichlet boundary condition. In this paper we introduce a systematic perturbation expansion in which the counterterms automatically turn out to be consistent with the boundary conditions. This will inevitably lead to nontrivial position dependence for physical quantities, as a manifestation of the breaking of the translational invariance. This is in contrast to the usual usage of the counterterms in problems with nontrivial boundary conditions, which are either completely derived from the free cases or at most supplemented with the addition of counterterms only at the boundaries. Our results for the massive and massless cases are different from those reported elsewhere. Secondly, and probably less importantly, we use a supplementary renormalization procedure, which makes the usage of any analytic continuation techniques unnecessary.
Holographic renormalization group flows can be interpreted in terms of effective field theory. Based on such an interpretation, a formula for the running scaling dimensions of gauge-invariant operators along such flows is proposed. The formula is checked for some simple examples from the AdS/CFT correspondence, but can be applied also in non-AdS/non-CFT cases.
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