On Symmetry Enhancement in the psu(1,1|2) Sector of N=4 SYM

Strong evidence indicates that the spectrum of planar anomalous dimensions of N=4 super Yang-Mills theory is given asymptotically by Bethe equations. A curious observation is that the Bethe equations for the psu(1,1|2) subsector lead to very large degeneracies of 2^M multiplets, which apparently do not follow from conventional integrable structures. In this article, we explain such degeneracies by constructing suitable conserved nonlocal generators acting on the spin chain. We propose that they generate a subalgebra of the loop algebra for the su(2) automorphism of psu(1,1|2). Then the degenerate multiplets of size 2^M transform in irreducible tensor products of M two-dimensional evaluation representations of the loop algebra.Comment: 35 pages, v2: references added, sign inconsistency resolved in (5.5,5.6), v3: Section 3.4 on Hamiltonian added, minor improvements, to appear in JHE

Two-loop Integrability of Planar N=6 Superconformal Chern-Simons Theory

Bethe ansatz equations have been proposed for the asymptotic spectral problem of AdS_4/CFT_3. This proposal assumes integrability, but the previous verification of weak-coupling integrability covered only the su(4) sector of the ABJM gauge theory. Here we derive the complete planar two-loop dilatation generator of N=6 superconformal Chern-Simons theory from osp(6|4) superconformal symmetry. For the osp(4|2) sector, we prove integrability through a Yangian construction. We argue that integrability extends to the full planar two-loop dilatation generator, confirming the applicability of the Bethe equations at weak coupling. Further confirmation follows from an analytic computation of the two-loop twist-one spectrum.Comment: 45 pages, v2: typos in (D.9) fixed, reference added, many small change

From Scattering Amplitudes to the Dilatation Generator in N=4 SYM

The complete spin chain representation of the planar N=4 SYM dilatation generator has long been known at one loop, where it involves leading nearest-neighbor 2 -> 2 interactions. In this work we use superconformal symmetry to derive the unique solution for the leading L -> 2 interactions of the planar dilatation generator for arbitrarily large L. We then propose that these interactions are given by the scattering operator that has N=4 SYM tree-level scattering amplitudes as matrix elements. We provide compelling evidence for this proposal, including explicit checks for L=2,3 and a proof of consistency with superconformal symmetry.Comment: 39 pages, v2: reference added and minor changes, published versio

Yangian Symmetry at Two Loops for the su(2|1) Sector of N=4 SYM

We present the perturbative Yangian symmetry at next-to-leading order in the su(2|1) sector of planar N=4 SYM. Just like the ordinary symmetry generators, the bi-local Yangian charges receive corrections acting on several neighboring sites. We confirm that the bi-local Yangian charges satisfy the necessary conditions: they transform in the adjoint of su(2|1), they commute with the dilatation generator, and they satisfy the Serre relations. This proves that the sector is integrable at two loops.Comment: 13 pages, v2: minor correction

N=4 SYM to Two Loops: Compact Expressions for the Non-Compact Symmetry Algebra of the su(1,1|2) Sector

We begin a study of higher-loop corrections to the dilatation generator of N=4 SYM in non-compact sectors. In these sectors, the dilatation generator contains infinitely many interactions, and therefore one expects very complicated higher-loop corrections. Remarkably, we find a short and simple expression for the two-loop dilatation generator. Our solution for the non-compact su(1,1|2) sector consists of nested commutators of four O(g) generators and one simple auxiliary generator. Moreover, the solution does not require the planar limit; we conjecture that it is valid for any gauge group. To obtain the two-loop dilatation generator, we find the complete O(g^3) symmetry algebra for this sector, which is also given by concise expressions. We check our solution using published results of direct field theory calculations. By applying the expression for the two-loop dilatation generator to compute selected anomalous dimensions and the bosonic sl(2) sector internal S-matrix, we confirm recent conjectures of the higher-loop Bethe ansatz of hep-th/0412188.Comment: 28 pages, v2: additional checks against direct field theory calculations, references added, minor corrections, v3: additional minor correction

Charging the Superconformal Index

The superconformal index is an important invariant of superconformal field theories. In this note we refine the superconformal index by inserting the charge conjugation operator C. We construct a matrix integral for this charged index for N=4 SYM with SU(N) gauge group. The key ingredient for the construction is a "charged character," which reduces to Tr(C) for singlet representations of the gauge group. For each irreducible real SU(N) representation, we conjecture that this charged character is equal to the standard character for a corresponding representation of SO(N+1) or SP(N-1), for N even or odd respectively. The matrix integral for the charged index passes tests for small N and for N -> infinity. Like the ordinary superconformal index, for N=4 SYM the charged index is independent of N in the large-N limit.Comment: 31 pages, v2: minor changes, published versio

ENIGMA-anxiety working group : Rationale for and organization of large-scale neuroimaging studies of anxiety disorders

Altres ajuts: Anxiety Disorders Research Network European College of Neuropsychopharmacology; Claude Leon Postdoctoral Fellowship; Deutsche Forschungsgemeinschaft (DFG, German Research Foundation, 44541416-TRR58); EU7th Frame Work Marie Curie Actions International Staff Exchange Scheme grant 'European and South African Research Network in Anxiety Disorders' (EUSARNAD); Geestkracht programme of the Netherlands Organization for Health Research and Development (ZonMw, 10-000-1002); Intramural Research Training Award (IRTA) program within the National Institute of Mental Health under the Intramural Research Program (NIMH-IRP, MH002781); National Institute of Mental Health under the Intramural Research Program (NIMH-IRP, ZIA-MH-002782); SA Medical Research Council; U.S. National Institutes of Health grants (P01 AG026572, P01 AG055367, P41 EB015922, R01 AG060610, R56 AG058854, RF1 AG051710, U54 EB020403).Anxiety disorders are highly prevalent and disabling but seem particularly tractable to investigation with translational neuroscience methodologies. Neuroimaging has informed our understanding of the neurobiology of anxiety disorders, but research has been limited by small sample sizes and low statistical power, as well as heterogenous imaging methodology. The ENIGMA-Anxiety Working Group has brought together researchers from around the world, in a harmonized and coordinated effort to address these challenges and generate more robust and reproducible findings. This paper elaborates on the concepts and methods informing the work of the working group to date, and describes the initial approach of the four subgroups studying generalized anxiety disorder, panic disorder, social anxiety disorder, and specific phobia. At present, the ENIGMA-Anxiety database contains information about more than 100 unique samples, from 16 countries and 59 institutes. Future directions include examining additional imaging modalities, integrating imaging and genetic data, and collaborating with other ENIGMA working groups. The ENIGMA consortium creates synergy at the intersection of global mental health and clinical neuroscience, and the ENIGMA-Anxiety Working Group extends the promise of this approach to neuroimaging research on anxiety disorders