Related papers: On $\phi^3$ Theory Above Six Dimensions
We derive a set of relations among the thermal components of the 3-point function and its spectral representations at finite temperature in the real-time formalism. We then use these to explicitly calculate the 3-point spectral densities…
Three related analyses of $\phi^4$ theory with $O(N)$ symmetry are presented. In the first, we review the $O(N)$ model over the $p$-adic numbers and the discrete renormalization group transformations which can be understood as spin blocking…
Assuming triviality of the 4-dimensional $\lambda \phi ^4$-theory we compute the effective potential by means of a self consistent Feynman-Bogoliubov method. This potential $U_{eff}^{FB}$ depends on a UV-cutoff, which is fixed by a…
Let $F\in\mathbb{C}[x,y,s,t]$ be an irreducible constant-degree polynomial, and let $A,B,C,D\subset\mathbb{C}$ be finite sets of size $n$. We show that $F$ vanishes on at most $O(n^{8/3})$ points of the Cartesian product $A\times B\times…
We compute the $S^d$ partition function of the fixed point of non-abelian gauge theories in continuous $d$, using the $\epsilon$-expansion around $d=4$. We illustrate in detail the technical aspects of the calculation, including all the…
The positive zeros of [2|1], [1|2] and the most general possible [2|2] Pade approximants whose Maclaurin series reproduce the presently known terms in the three-flavour QCD beta-function are all shown to correspond to ultraviolet fixed…
We formulate the three dimensional Thirring model on a spacetime lattice and study it for various even numbers of fermion flavors N_f by Monte Carlo simulation. We find clear evidence for spontaneous chiral symmetry breaking at strong…
We investigate $\beta$-functions of quantum gravity using dimensional regularisation. In contrast to minimal subtraction, a non-minimal renormalisation scheme is employed which is sensitive to power-law divergences from mass terms or…
We consider the scenario where all the couplings in the theory are strong at the cut-off scale, in the context of higher dimensional grand unified field theories where the unified gauge symmetry is broken by an orbifold compactification. In…
To investigate the non-perturbative, electric sector of a deconfined gauge theory at nonzero temperature, we consider a SU(2) matrix model. We compute beta-functions to one loop order for the simplest extension of the O(4) nonlinear sigma…
I review the field-theoretic renomalization group approach to quantum gravity, built around the existence of a non-trivial ultraviolet fixed point in four dimensions. I discuss the implications of such a fixed point, found in three largely…
We reconsider critical properties of O(N) scalar models with cubic interactions in $d>4$ dimensions using functional renormalization group equations. Working at next-to-leading order in the derivative expansion, we find non-trivial IR fixed…
The Euclidean quantum field theory for the fields $\phi_{\Delta x}(x)$, which depend on both the position $x$ and the resolution $\Delta x$, constructed in SIGMA 2 (2006), 046, hep-th/0604170, on the base of the continuous wavelet…
Boundary conformal field theory (BCFT) provides a universal framework for critical phenomena in the presence of boundaries. We determine BCFT data for the normal and ordinary boundary universality classes of the $1+1$-dimensional boundaries…
We have carried out a Schrodinger-functional calculation for the Abelian gauge theory with Nf=2 four-component fermions in three dimensions. We find no fixed point in the beta function, meaning that the theory is confining rather than…
We show bounds on five- and six-dimensional universal extra dimension (UED) models from the latest results of the Higgs searches at the LHC and from the electroweak precision data for the S and T parameters. We consider the minimal UED…
A momentum dependent projection of the Wegner-Hougton equation is derived for a scalar theory coupled to an external field. This formalism is useful to discuss the phase diagram of the theory. In particular we study some properties of the…
We discuss the arbitrariness in the choice of cutoff scheme in calculations of beta functions. We define a class of "pure" cutoff schemes, in which the cutoff is completely independent of the parameters that appear in the action. In a sense…
The ``extended'' BF-Yang-Mills theory in 3 dimensions, which contains a minimally coupled scalar field, is shown to be ultraviolet finite. It obeys a trivial Callan-Symanzik equation, with all beta-functions and anomalous dimensions…
We present results from numerical simulations of three different 3d four-fermion models that exhibit Z_2, U(1), and SU(2) x SU(2) chiral symmetries, respectively. We performed the simulations by using the hybrid Monte Carlo algorithm. We…