Renormalization of the flavor-singlet axial-vector current and its anomaly in dimensional regularization

The renormalization constant ZJ of the flavor-singlet axial-vector current with a non-anticommuting γ5 in dimensional regularization is determined to order $$ {\alpha}_s^3 $$ α s 3 in QCD with massless quarks. The result is obtained by computing the matrix elements of the operators appearing in the axial-anomaly equation $$ {\left[{\partial}_{\mu }{J}_5^{\mu}\right]}_R=\frac{\alpha_s}{4\pi }{n}_f{\mathrm{T}}_F{\left[F\tilde{F}\right]}_R $$ ∂ μ J 5 μ R = α s 4 π n f T F F F ˜ R between the vacuum and a state of two (off-shell) gluons to 4-loop order. Furthermore, through this computation, the equality between the $$ \overline{\mathrm{MS}} $$ MS ¯ renormalization constant $$ {Z}_{F\tilde{F}} $$ Z F F ˜ associated with the operator $$ {\left[F\tilde{F}\right]}_R $$ F F ˜ R and that of αs is verified explicitly to hold true at 4-loop order. This equality automatically ensures a relation between the respective anomalous dimensions, $$ {\gamma}_J=\frac{\alpha_s}{4\pi }{n}_f{\mathrm{T}}_F{\gamma}_{FJ} $$ γ J = α s 4 π n f T F γ FJ , at order $$ {\alpha}_s^4 $$ α s 4 given the validity of the axial-anomaly equation which was used to determine the non-$$ \overline{\mathrm{MS}} $$ MS ¯ piece of ZJ for the particular γ5 prescription in use.

Renormalization of the bilocal sine-Gordon model

The functional renormalization group treatment is presented for the two-dimensional sine-Gordon model including a bilocal term in the potential, which contributes to the flow at the tree level. It is shown that the flow of the bilocal term can substitute the evolution of the wave function renormalization constant, since it can recover the Kosterlitz–Thouless type phase transition. The flows can also reveal the connection between the sine-Gordon and the noninteracting Thirring models at a special value of the wave number parameter.

High Energy Behavior in Maximally Supersymmetric Gauge Theories in Various Dimensions

Maximally supersymmetric field theories in various dimensions are believed to possess special properties due to extended supersymmetry. In four dimensions, they are free from UV divergences but are IR divergent on shell; in higher dimensions, on the contrary, they are IR finite but UV divergent. In what follows, we consider the four-point on-shell scattering amplitudes in D = 6 , 8 , 10 supersymmetric Yang–Mills theory in the planar limit within the spinor-helicity and on-shell supersymmetric formalism. We study the UV divergences and demonstrate how one can sum them over all orders of PT. Analyzing the R -operation, we obtain the recursive relations and derive differential equations that sum all leading, subleading, etc., divergences in all loops generalizing the standard RG formalism for the case of nonrenormalizable interactions. We then perform the renormalization procedure, which differs from the ordinary one in that the renormalization constant becomes the operator depending on kinematics. Solving the obtained RG equations for particular sets of diagrams analytically and for the general case numerically, we analyze their high energy behavior and find that, while each term of PT increases as a power of energy, the total sum behaves differently: in D = 6 two partial amplitudes decrease with energy and the third one increases exponentially, while in D = 8 and 10 the amplitudes possess an infinite number of periodic poles at finite energy.

Compositeness of hadron resonances in chiral dynamics

Recent experimental observations of many unconventional hadronic states stimulate an interest in the structure of hadrons. While various internal configurations have been proposed, it is a subtle problem to identify the structure of hadron resonances in a model independent manner. Here we discuss the composite/elementary nature of hadrons using the field renormalization constant Z. In particular, we show that the magnitude of the effective range parameter re is related to the structure of s-wave near-threshold resonances.

Renormalization of QED Near Decoupling Temperature

We study the effective parameters of QED near decoupling temperatures and show that the QED perturbative series is convergent, at temperatures below the decoupling temperature. The renormalization constant of QED acquires different values if a system cools down from a hotter system to the electron mass temperature or heats up from a cooler system to the same temperature. At T = m, the first order contribution to the electron self-mass, δm/m is 0.0076 for a heating system and 0.0115 for a cooling system and the difference between two values is equal to 1/3 of the low temperature value and 1/2 of the high temperature value around T~m. This difference is a measure of hot fermion background at high temperatures. With the increase in release of more fermions at hotter temperatures, the fermion background contribution dominates and weak interactions have to be incorporated to understand the background effects.

PROOF OF TRIVIALITY OF λϕ4 THEORY

We show that a recent analysis in the strong coupling limit of the λϕ4 theory proves that this theory is indeed trivial giving in this limit the expansion of a free quantum field theory. We can get in this way the propagator with the renormalization constant and the renormalized mass. As expected the theory in this limit has the same spectrum as a harmonic oscillator. Some comments about triviality of the Yang–Mills theory in the infrared are also given.