Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSp(2) Renormalization
125
0
0.0
(
0
)
Authors
Peter M. Lavrov
Ask ChatGPT about the research
No Arabic abstract
The renormalization of general gauge theories on flat and curved space-time backgrounds is considered within the Sp(2)-covariant quantization method. We assume the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Sp(2)-covariant formalism one can show that the theory possesses gauge invariant and diffeomorphism invariant renormalizability to all orders in the loop expansion and the extended BRST symmetry after renormalization is preserved. The advantage of the Sp(2)-method compared to the standard Batalin-Vilkovisky approach is that, in reducible theories, the structure of ghosts and ghosts for ghosts and auxiliary fields is described in terms of irreducible representations of the Sp(2) group. This makes the presentation of solutions to the master equations in more simple and systematic way because they are Sp(2)- scalars.
rate research
Read More
In a previous paper it was shown how to calculate the ground-state energy density $E$ and the $p$-point Greens functions $G_p(x_1,x_2,...,x_p)$ for the $PT$-symmetric quantum field theory defined by the Hamiltonian density $H=frac{1}{2}( ablaphi)^2+frac{1}{2}phi^2(iphi)^varepsilon$ in $D$-dimensional Euclidean spacetime, where $phi$ is a pseudoscalar field. In this earlier paper $E$ and $G_p(x_1,x_2,...,x_p)$ were expressed as perturbation series in powers of $varepsilon$ and were calculated to first order in $varepsilon$. (The parameter $varepsilon$ is a measure of the nonlinearity of the interaction rather than a coupling constant.) This paper extends these perturbative calculations to the Euclidean Lagrangian $L= frac{1}{2}( ablaphi)^2+frac{1}{2}mu^2phi^2+frac{1}{2} gmu_0^2phi^2big(imu_0^{1-D/2}phibig)^varepsilon-ivphi$, which now includes renormalization counterterms that are linear and quadratic in the field $phi$. The parameter $g$ is a dimensionless coupling strength and $mu_0$ is a scaling factor having dimensions of mass. Expressions are given for the one-, two, and three-point Greens functions, and the renormalized mass, to higher-order in powers of $varepsilon$ in $D$ dimensions ($0leq Dleq2$). Renormalization is performed perturbatively to second order in $varepsilon$ and the structure of the Greens functions is analyzed in the limit $Dto 2$. A sum of the most divergent terms is performed to {it all} orders in $varepsilon$. Like the Cheng-Wu summation of leading logarithms in electrodynamics, it is found here that leading logarithmic divergences combine to become mildly algebraic in form. Future work that must be done to complete the perturbative renormalization procedure is discussed.
In this article, we extend the work of arXiv:0901.4744 to a Bethe/Gauge correspondence between 2d (or resp. 3d) SO/Sp gauge theories and open XXX (resp. XXZ) spin chains with diagonal boundary conditions. The case of linear quiver gauge theories is also considered.
This paper aims at presenting the first steps towards a formulation of the Exact Renormalization Group Equation in the Hopf algebra setting of Connes and Kreimer. It mostly deals with some algebraic preliminaries allowing to formulate perturbative renormalization within the theory of differential equations. The relation between renormalization, formulated as a change of boundary condition for a differential equation, and an algebraic Birkhoff decomposition for rooted trees is explicited.
The gauge dependence problem of alternative flow equation for the functional renormalization group is studied. It is shown that the effective two-particle irreducible effective action depends on gauges at any value of IR parameter $k$. The situation with gauge dependence is similar to the standard formulation based on the effective one-particle irreducible effective action.
We construct 4D $mathcal{N}=2$ theories on an infinite family of 4D toric manifolds with the topology of connected sums of $S^2 times S^2$. These theories are constructed through the dimensional reduction along a non-trivial $U(1)$-fiber of 5D theories on toric Sasaki-Einstein manifolds. We discuss the conditions under which such reductions can be carried out and give a partial classification result of the resulting 4D manifolds. We calculate the partition functions of these 4D theories and they involve both instanton and anti-instanton contributions, thus generalizing Pestuns famous result on $S^4$.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
