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

Weakly coupled N=4 Super Yang-Mills and N=6 Chern-Simons theories from u(2|2) Yangian symmetry

In this paper we derive the universal R-matrix for the Yangian Y(u(2|2)), which is an abstract algebraic object leading to rational solutions of the Yang-Baxter equation on representations. We find that on the fundamental representation the universal R-matrix reduces to the standard rational R-matrix R = R_0(1 + P/u), where the scalar prefactor is surprisingly simple compared to prefactors one finds e.g. for sl(n) R-matrices. This leads precisely to the S-matrix giving the Bethe Ansatz of one-loop N = 4 Super Yang-Mills theory and two-loop N = 6 Chern-Simons theory.Comment: 16 page

The Morphology of N=6 Chern-Simons Theory

We tabulate various properties of the language of N=6 Chern-Simons Theory, in the sense of Polyakov. Specifically we enumerate and compute character formulas for all syllables of up to four letters, i.e. all irreducible representations of OSp(6|4) built from up to four fundamental fields of the ABJM theory. We also present all tensor product decompositions for up to four singletons and list the (cyclically invariant) four-letter words, which correspond to single-trace operators of length four. As an application of these results we use the two-loop dilatation operator to compute the leading correction to the Hagedorn temperature of the weakly-coupled planar ABJM theory on R \times S^2.Comment: 41 pages, 1 figure; 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

Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory

Tree-level scattering amplitudes in N=4 super Yang-Mills theory have recently been shown to transform covariantly with respect to a 'dual' superconformal symmetry algebra, thus extending the conventional superconformal symmetry algebra psu(2,2|4) of the theory. In this paper we derive the action of the dual superconformal generators in on-shell superspace and extend the dual generators suitably to leave scattering amplitudes invariant. We then study the algebra of standard and dual symmetry generators and show that the inclusion of the dual superconformal generators lifts the psu(2,2|4) symmetry algebra to a Yangian. The non-local Yangian generators acting on amplitudes turn out to be cyclically invariant due to special properties of psu(2,2|4). The representation of the Yangian generators takes the same form as in the case of local operators, suggesting that the Yangian symmetry is an intrinsic property of planar N=4 super Yang-Mills, at least at tree level.Comment: 23 pages, no figures; v2: typos corrected, references added; v3: minor changes, references adde

Factorized Tree-level Scattering in AdS_4 x CP^3

AdS_4/CFT_3 duality relating IIA string theory on AdS_4 x CP^3 to N=6 superconformal Chern-Simons theory provides an arena for studying aspects of integrability in a new potentially exactly solvable system. In this paper we explore the tree-level worldsheet scattering for strings on AdS_4 x CP^3. We compute all bosonic four-, five- and six-point amplitudes in the gauge-fixed action and demonstrate the absence of particle production.Comment: 23 pages, v2. references adde

QCD properties of twist operators in the N=6 Chern-Simons theory

We consider twist-1, 2 operators in planar N=6 superconformal Chern-Simons ABJM theory. We derive higher order anomalous dimensions from integrability and test various QCD-inspired predictions known to hold in N=4 SYM. In particular, we show that the asymptotic anomalous dimensions display intriguing remnants of Gribov-Lipatov reciprocity and Low-Burnett-Kroll logarithmic cancellations. Wrapping effects are also discussed and shown to be subleading at large spin.Comment: 22 pages, expanded reference

Anomalous dimensions at twist-3 in the sl(2) sector of N=4 SYM

We consider twist-3 operators in the sl(2) sector of N=4 SYM built out of three scalar fields with derivatives. We extract from the Bethe Ansatz equations of this sector the exact lowest anomalous dimension gamma(s) of scaling fields for several values of the operator spin s. We propose compact closed expressions for the spin dependence of gamma(s) up to the four loop level and show that they obey a simple new twist-3 transcendentality principle. As a check, we reproduce the four loop universal cusp anomalous dimension governing the logarithmic large spin limit of gamma(s).Comment: 26 pages, JHEP styl

Simplifying superstring and D-brane actions in AdS(4) x CP(3) superbackground

By making an appropriate choice for gauge fixing kappa-symmetry we obtain a relatively simple form of the actions for a D=11 superparticle in AdS(4) x S(7)/Z_k, and for a D0-brane, fundamental string and D2-branes in the AdS(4) x CP(3) superbackground. They can be used to study various problems of string theory and the AdS4/CFT3 correspondence, especially in regions of the theory which are not reachable by the OSp(6|4)/U(3) x SO(1,3) supercoset sigma-model. In particular, we present a simple form of the gauge-fixed superstring action in AdS(4) x CP(3) and briefly discuss issues of its T-dualization.Comment: 1+36 pages, v2,v3 clarifications and references adde

Planar N=4 Gauge Theory and the Hubbard Model

Recently it was established that a certain integrable long-range spin chain describes the dilatation operator of N=4 gauge theory in the su(2) sector to at least three-loop order, while exhibiting BMN scaling to all orders in perturbation theory. Here we identify this spin chain as an approximation to an integrable short-ranged model of strongly correlated electrons: The Hubbard model.Comment: 35 pages, 2 figures; v2: typos and references fixed, published versio