The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory

Using the method of maximal cuts, we construct the complete D-dimensional integrand of the five-loop four-point amplitude of N = 4 super-Yang-Mills theory, including nonplanar contributions. In the critical dimension where this amplitude becomes ultraviolet divergent, we present a compact explicit expression for the nonvanishing ultraviolet divergence in terms of three vacuum integrals. This construction provides a crucial step towards obtaining the corresponding amplitude of N = 8 supergravity useful for resolving the general ultraviolet behavior of supergravity theories.Comment: 5 pages, 4 figures, RevTex. Ancillary file included. v2 minor corrections, corrected references and overall phase in eq. (5), matching journal versio

Consumption and habits : evidence from panel data

The purpose of this paper is to test for the presence of habit formation in consumption decisions using household panel data. We use the test proposed by Meghir and Weber (1996) and estimate the within -period marginal rate of substitution between commodities, which is robust to the presence of liquidity constraints. To that end, we use a Spanish panel data set in which households are observed up to eight consecutive quarters. This temporal dimension is crucial, since it allows us to take into account time invariant unobserved heterogeneity across households ("fixed effects") and, therefore, to investigate if the relationship between current and past consumption reflects habits or heterogeneity. Our results conf irm the importance of accounting for fixed effects when analyzing intertemporal consumption decisions allowing for time non-separabilities. Once fixed effects are controlled for and a proper set of instruments is used, the results yield supporting evidence of habit formation in the demand system of food at home, transport and services