29 research outputs found
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