Related papers: Limit Cycles in Four Dimensions
The most general local, classically scale invariant, perturbatively renormalizable, globally $SU(N)$ invariant Lagrangian is constructed for spin-1 fields in 4 dimensions. The total number of independent couplings is 7 and the 1-loop…
We investigate whether the six-loop beta function of the $\lambda \phi^4_4$ theory exhibits evidence for an ultraviolet zero. As part of our analysis, we calculate and analyze Pad\'e approximants to this beta function. Extending our earlier…
In [8], the gradient conjecture of R. Thom was proven for gradient flows of analytic functions on Rn. This result means that the secant at a limit point converges, so that the flow cannot spiral forever. Once the trajectory becomes…
We study the renormalization group flow of higher derivative gravity, utilizing the functional renormalization group equation for the average action. Employing a recently proposed algorithm, termed the universal renormalization group…
We consider free higher derivative theories of scalars and Dirac fermions in the presence of a boundary in general dimension. We establish a method for finding consistent conformal boundary conditions in these theories by removing certain…
The generalized Wilson loop operator interpolating between the supersymmetric and the ordinary Wilson loop in ${\cal N}=4$ SYM theory provides an interesting example of renormalization group flow on a line defect: the scalar coupling…
In this paper we provide a method to generate a continuum of limit cycles using a single precomputed exponentially stable limit cycle designed within the Hybrid Zero Dynamics framework. Guarantees for existence and stability of these limit…
We determine complete one-loop beta functions of the multi-scalar four-point couplings in four-dimensional $SU(N)$ gauge theories with $M$ adjoint scalar multiplets. For adjoints scalars, the sign of the one loop gauge coupling beta…
In this paper, we consider the $\beta$ function at one-loop approximation for noncommutative scalar QED. The renormalization of the full theory, including the basic vertices, and the renormalization group equation are fully established.…
We find an upper bound to the maximal number of limit cycles, which bifurcate from a hamiltonian two-saddle loop of an analytic vector field, under an analytic deformation.
We studied SU(2) flux distributions on four dimensional euclidean lattices with one dimension very large. By choosing the time direction appropriately we can study physics in two cases: one is finite volume in the zero temperature limit,…
We establish conditions under which the worldsheet beta-functions of logarithmic conformal field theories can be derived as the gradient of some scalar function on the moduli space of running coupling constants. We derive a renormalization…
We compute template formulae of all four-loop $\beta$-functions and anomalous dimensions of arbitrary renormalisable quantum field theories with fermions and scalar fields in the $\overline{\text{MS}}$ scheme. Using these results, novel…
Gradient flow has proved useful in the definition and measurement of renormalized quantities on the lattice. Recently, the fact that it suppresses high-modes of the field has been used to construct new, continuous RG transformations both…
A supersymmetric gradient flow for four-dimensional N=1 supersymmetric QCD (SQCD) is proposed. The flow equation is given in both the superfield and component fields of the Wess-Zumino gauge. The superfield flow equation is defined for each…
We discuss the perturbative expansion of several one-loop improved renormalisation group equations. It is shown that in general the integrated renormalisation group flows fail to reproduce perturbation theory beyond one loop.
We employ the harmonic superspace methods to study a six-dimensional $\mathcal{N}=(1,0)$ supersymmetric gauge theory with higher derivatives coupled to a hypermultiplet in the adjoint representation. By introducing a novel non-minimal…
In this article we investigate a family of nonlinear evolutions of polygons in the plane called the $\beta$-polygon flow and obtain some results analogous to results for the smooth curve shortening flow: (1) any planar polygon shrinks to a…
In this paper, we study the limiting behavior of Riemann solutions to the Euler equations of one-dimensional compressible fluid flow as $\gamma$ tends to one. We show that the limit solution forms the delta wave to the pressureless Euler…
We investigate singly and doubly charged flux tubes in U(1) lattice gauge theory. By simulating the dually transformed path integral we are able to consider large flux tube lengths, low temperatures, and multiply charged systems without…