Order 1/N3{\bf 1/N^3} corrections to the conformal anomaly of the (2,0) theory in six dimensions

Using Supergravity on $AdS_7\times S^4$ we calculate the bulk one-loop contribution to the conformal anomaly of the (2,0) theory describing $N$ coincident M5 branes. When this is added to the tree-level result, and an additional subleading order contribution calculated by Tseytlin, it gives an expression for the anomaly that interpolates correctly between the large $N$ theory and the free (2,0) tensor theory corresponding to N=1. Thus we can argue that we have identified the exact $N$-dependence of the anomaly, which may have a simple protected form valid away from the large $N$ limit.Comment: LaTeX, 9 page

Providence and democracy

"Alexis de Tocqueville was a liberal, but, as he once wrote, a “new kind of liberal.” For us, no feature of his new liberalism is more remarkable than the alliance between religion and liberty that he saw in America and proposed to be imitated, wherever it can, in every free society. In liberalism today, there is a debate over whether liberal theory needs— or should avoid—a “foundation.” Tocqueville seems to take the anti-foundational side: lie never mentions the “state of nature,” which was the standard foundation of 17th-century liberalism, and in Democracy in America he omits any reference to the Declaration of Independence with its ringing foundational assertion that “all men are created equal.” Yet, if he avoids laying a foundation in reason, he also thinks that religion is essential to political liberty because of the “certain fixed ideas” that it offers to ground the practice of self-government. These are doctrines of faith, since for Tocqueville “religion” means revealed religion, not a rational or natural religion."(...

Liberty and Yirtue in the American Founding

"Liberty and virtue are not a likely pair. At first sight they seem to be contraries, for liberty appears to mean living as you please and virtue to mean living not as you please but as you ought. It does not seem likely that a society dedicated to liberty could make much of virtue, nor that one resolved to have virtue could pride itself on liberty. Yet liberty and virtue also seem necessary to each other. A free people, with greater opportunity to misbehave than a people in shackles, needs the guidance of an inner force to replace the lack of external restraint. And virtue cannot come from within, or truly be virtue, unless it is voluntary and people are free to choose it. Americans are, and think themselves to be, a free people first of all. Whatever virtue they have, and however much, is a counterpoint to the theme of liberty. But how do they manage to make virtue and liberty harmonious?"(...

Boundary fermion currents and subleading order chiral anomaly in the AdS/CFT correspondence

We construct a wave-functional whose argument couples to boundary fermion currents in the AdS/CFT correspondence. Using this we calculate the contributions from bulk fermions to the chiral anomaly that give the subleading order term in the exact $N$-dependence of the chiral anomaly of ${\cal N}=4$ SYM. The result agrees with the calculation of Bilal & Chu.Comment: 6 page

What Tocqueville Says to Liberals and Conservatives Today

"Russell Baker once said that in our time people cite Tocqueville without reading him even more than they do the Bibie and Shakespeare. Every American president sińce Eisenhower has ąuoted him, no doubt without reading him, and some of our professors, to say nothing of other citizens, have picked up their habit of fishing for what they like, and throwing back the rest, in Tocqueville’s great work Democracy in America."(...