Related papers: Operator Coefficients for Composite Operators in t…
We propose an implicit regularisation scheme. The main advantage is that since no explicit use of a regulator is made, one can in principle avoid undesirable symmetry violations related to its choice. The divergent amplitudes are split into…
We consider the multiple products of relevant and marginal scalar composite operators at the Gaussian fixed-point in $D=4$ dimensions. This amounts to perturbative construction of the $\phi^4$ theory where the parameters of the theory are…
We present a self-consistent calculation of the finite temperature effective potential for $\lambda \phi^4$ theory, using the composite operator effective potential in which an infinite series of the leading diagrams is summed up. Our…
I derive a formula for the coupling-constant derivative of the coefficients of the operator product expansion (Wilson OPE coefficients) in an arbitrary curved space, as the natural extension of the quantum action principle. Expanding the…
We assess the accuracy of our previous Asymptotic Pad\'e predictions of the five-loop QCD $\beta$-function and quark mass anomalous dimension in the light of subsequent exact results. We find the low-order coefficients in an expansion in…
We give a detailed account of the theory of position space renormalization using graphical functions in the case of dimensionally regularized $\phi^4$ theory in four dimensions. In this theory we calculate the beta function, the mass gamma…
We compute the complete $Q$-dependence of anomalous dimensions of traceless symmetric tensor operator $\phi^Q$ in $O(N)$ scalar theory to five-loop. The renormalization factors are extracted from $\phi^Q\rightarrow Q\phi$ form factors, and…
We calculate the finite temperature effective potential of $\lambda\phi^4$ at the two loop order of the 2PPI expansion. This expansion contains all diagrams which remain connected when two lines meeting at the same point are cut and…
We consider $\phi^3$ theory in $6-2\epsilon$ with $F_4$ global symmetry. The beta function is calculated up to 3 loops, and a stable unitary IR fixed point is observed. The anomalous dimensions of operators quadratic or cubic in $\phi$ are…
The operator product expansion is used to compute the matrix elements of composite renormalized operators on the lattice. We study the product of two fundamental fields in the two-dimensional sigma-model and discuss the possible sources of…
We compute two-point functions of lowest weight operators at the next-to-leading order in the couplings for the beta-deformed N=4 SYM. In particular we focus on the CPO Tr(Phi_1^2) and the operator Tr(Phi_1 Phi_2) not presently listed as…
A technique of large-charge expansion provides a novel opportunity for calculation of critical dimensions of operators $\phi^Q$ with fixed charge $Q$. In the small-coupling regime the polynomial structure of the anomalous dimensions can be…
We analytically determine all the eigenvalues and eigenfunctions of the linearized Boltzmann collision operator in massless scalar $\lambda \phi^4$ theory in the high-temperature (classical) regime. This is used to exactly compute the shear…
We revisit scalar $\phi^4$ theory and construct a reorganized perturbative expansion in which the kinetic operator, rather than the quartic interaction, is treated as the perturbation. Starting from the exactly solvable $0$-dimensional…
We give a short account of recent advances in our understanding of the $\pi$-dependent terms in massless (Euclidean) 2-point functions as well as in generic anomalous dimensions (ADs) and $\beta$-functions. We extend the considerations of…
We study the effective potential for composite operators. Introducing a source coupled to the composite operator, we define the effective potential by a Legendre transformation. We find that in three or fewer dimensions, one can use the…
The critical exponent phi_c, derived from the anomalous dimension of the bilinear operator responsible for crossover behaviour in O(N) phi^4 theory, is calculated at O(1/N^2) in a large N expansion in arbitrary space-time dimension d = 4 -…
We compute four-point correlation functions of scalar composite operators in the N=4 supercurrent multiplet at order g^4 using the N=1 superfield formalism. We confirm the interpretation of short-distance logarithmic behaviours in terms of…
We study the correlation functions of a conformally coupled $\phi^4$-interacting theory in AdS$_3$ and its dual CFT$_2$. The one-loop diagram is not expressible in terms of known transcendental functions, but is shown to be expressible as…
Algebraic and analytic aspects of self-adjoint operators of order four or more with polynomial coefficients are investigated. As a consequence, a systematic way of constructing such operators is given. The procedure is applied to obtain…