Resummation of non-global logarithms and the BFKL equation

We consider a `color density matrix' in gauge theory. We argue that it systematically resums large logarithms originating from wide-angle soft radiation, sometimes referred to as non-global logarithms, to all logarithmic orders. We calculate its anomalous dimension at leading- and next-to-leading order. Combined with a conformal transformation known to relate this problem to shockwave scattering in the Regge limit, this is used to rederive the next-to-leading order Balitsky-Fadin-Kuraev-Lipatov equation (including its nonlinear generalization, the so-called Balitsky-JIMWLK equation), finding perfect agreement with the literature. Exponentiation of divergences to all logarithmic orders is demonstrated. The possibility of obtaining the evolution equation (and BFKL) to three-loop is discussed.Comment: 29 pages, 32 including appendix, 7 figures. v2 presentation improved thanks to helpful refere

Hard thermal loops in the real-time formalism

We present a systematic discussion of Braaten and Pisarski's hard thermal loop (HTL) effective theory within the framework of the real-time (Schwinger-Keldysh) formalism. As is well known, the standard imaginary-time HTL amplitudes for hot gauge theory express the polarization of a medium made out of nonabelian charged point-particles; we show that the complete real-time HTL theory includes, in addition, a second set of amplitudes which account for Gaussian fluctuations in the charge distributions, but nothing else. We give a concise set of graphical rules which generate both set of functions, and discuss its relation to classical plasma physics.Comment: 14 pages, 6 figure

Quantum channels as a categorical completion

We propose a categorical foundation for the connection between pure and mixed states in quantum information and quantum computation. The foundation is based on distributive monoidal categories. First, we prove that the category of all quantum channels is a canonical completion of the category of pure quantum operations (with ancilla preparations). More precisely, we prove that the category of completely positive trace-preserving maps between finite-dimensional C*-algebras is a canonical completion of the category of finite-dimensional vector spaces and isometries. Second, we extend our result to give a foundation to the topological relationships between quantum channels. We do this by generalizing our categorical foundation to the topologically-enriched setting. In particular, we show that the operator norm topology on quantum channels is the canonical topology induced by the norm topology on isometries.Comment: 12 pages + ref, accepted at LICS 201

Warts and all: using student portfolio outcomes to facilitate a faculty development workshop

In 2004, the Department of Writing Studies at Roger Williams University in Bristol, Rhode Island, the U.S., began an assessment of student outcomes for two first-year writing courses (Fall 04 to Fall 05) to evaluate performance on previously established criteria. A study of the students’ Portfolio Assessment Sheets concluded that one pervasive problem was “Development” as determined partly by low A grades in the two courses. To engage the faculty (full-time and adjunct), the grades from Fall 04, Spring 05, and Fall 05 were presented during a SummerWorkshop in June 2006. After analyzing a sample student essay, the 28 faculty participants discussed the implications of “Development” and evaluated the presentation itself. This case study of one college’s participatory exercise in improving writing found some faculty resistance and some unintended results

Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory

We study the S-matrix of planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory when external momenta are restricted to a two-dimensional subspace of Minkowski space. We find significant simplifications and new, interesting structures for tree and loop amplitudes in two-dimensional kinematics; in particular, the higher-point amplitudes we consider can be obtained from those with lowest-points by a collinear uplifting. Based on a compact formula for one-loop N${}^2$MHV amplitudes, we use an equation proposed previously to compute, for the first time, the complete two-loop NMHV and three-loop MHV octagons, which we conjecture to uplift to give the full $n$-point amplitudes up to simpler logarithmic terms or dilogarithmic terms.Comment: v2: important typos fixed. 38 pages, 4 figures. An ancillary file with two-loop NMHV "remainders" for n=10,12 can be found at http://www.nbi.dk/~schuot/nmhvremainders.zi

Renormalization group coefficients and the S-matrix

We show how to use on-shell unitarity methods to calculate renormalization group coefficients such as beta functions and anomalous dimensions. The central objects are the form factors of composite operators. Their discontinuities can be calculated via phase-space integrals and are related to corresponding anomalous dimensions. In particular, we find that the dilatation operator, which measures the anomalous dimensions, is given by minus the phase of the S-matrix divided by pi. We illustrate our method using several examples from Yang-Mills theory, perturbative QCD and Yukawa theory at one-loop level and beyond.Comment: 25 pages, 4 figures; v2: explanations improved, references added, matches journal versio