Structure Of UV Divergences Research Articles

On genus-one string amplitudes on AdS5 \xd7 S5

We study non-planar correlators in mathcal{N} = 4 super-Yang-Mills in Mellin space. We focus in the stress tensor four-point correlator to order 1/N4 and in a strong coupling expansion. This can be regarded as the genus-one four-point graviton amplitude of type IIB string theory on AdS5× S5 in a low energy expansion. Both the loop supergravity result as well as the tower of stringy corrections have a remarkable simple structure in Mellin space, making manifest important properties such as the correct flat space limit and the structure of UV divergences.

Structure of UV divergences in maximally supersymmetric gauge theories

We consider the UV divergences up to sub-subleading order for the four-point on-shell scattering amplitudes in $D=8$ supersymmetric Yang-Mills theory in the planar limit. We trace how the leading, subleading, etc divergences appear in all orders of perturbation theory. The structure of these divergences is typical for any local quantum field theory independently on renormalizability. We show how the generalized renormalization group equations allow one to evaluate the leading, subleading, etc. contributions in all orders of perturbation theory starting from one-, two-, etc. loop diagrams respectively. We focus then on subtraction scheme dependence of the results and show that in full analogy with renormalizable theories the scheme dependence can be absorbed into the redefinition of the couplings. The only difference is that the role of the couplings play dimensionless combinations like ${g}^{2}{s}^{2}$ or ${g}^{2}{t}^{2}$, where $s$ and $t$ are the Mandelstam variables.

The bispectrum in the Effective Field Theory of Large Scale Structure

We study the bispectrum in the Effective Field Theory of Large Scale Structure, consistently accounting for the effects of short-scale dynamics. We begin by proving that, as long as the theory is perturbative, it can be formulated to arbitrary order using only operators that are local in time. We then derive all the new operators required to cancel the UV-divergences and obtain a physically meaningful prediction for the one-loop bispectrum. In addition to new, subleading stochastic noises and the viscosity term needed for the one-loop power spectrum, we find three new effective operators. The three new parameters can be constrained by comparing with N-body simulations. The best fit is precisely what is suggested by the structure of UV-divergences, hence justifying a formula for the EFTofLSS bispectrum whose only fitting parameter is already fixed by the power spectrum. This result predicts the bispectrum of N-body simulations up to kmax≈0.22 h Mpc−1 at 0z=, an improvement by nearly a factor of two as compared to one-loop standard perturbation theory.

The structure of UV divergences in SS YM theories

Using the background-field method, covariant supergraphs and infrared subtraction techniques we analyse the structure of the higher-loop ultraviolet divergences in supersymmetric Yang-Mills theories. We show that in regularization by dimensional reduction they are given by a specific gauge invariant term constructed outof the vector connection and that they can be obtained by analyzing a special subset of all possible supergraphs. From the structure of the divergences we are able to conclude that in supersymmetric theories if the self-energies of the quantum fields in the presence of the background are finite up to L loops the YM background effective action is finite at ( L + 1) loops.