1,201 research outputs found

### SU(2|2) for Theories with Sixteen Supercharges at Weak and Strong Coupling

We consider the dimensional reductions of N=4 Supersymmetric Yang-Mills
theory on R x S^3 to the three-dimensional theory on R x S^2, the orbifolded
theory on R x S^3/Z_k, and the plane-wave matrix model. With explicit emphasis
on the three-dimensional theory, we demonstrate the realization of the SU(2|3)
algebra in a radial Hamiltonian framework. Using this structure we constrain
the form of the spin chains, their S-matrices, and the corresponding one- and
two-loop Hamiltonian of the three dimensional theory and find putative signs of
integrability up to the two-loop order. The string duals of these theories
admit the IIA plane-wave geometry as their Penrose limit. Using known results
for strings quantized on this background, we explicitly construct the
strong-coupling dual extended SU(2|2) algebra and discuss its implications for
the gauge theories.Comment: 37 pages, 1 figure. v2 some minor improvements to the text, version
to appear in Phys.Rev.

### Review of AdS/CFT Integrability, Chapter I.3: Long-range spin chains

In this contribution we briefly review recent developments in the theory of
long-range integrable spin chains. These spin chains constitute a natural
generalisation of the well-studied integrable nearest-neighbour chains and are
of particular relevance to the integrability in the AdS/CFT correspondence
since the dilatation operator in the asymptotic region is conjectured to be a
Hamiltonian of an integrable long-range psu spin chain.Comment: 17 pages, see also overview article arXiv:1012.3982, v2: references
to other chapters updated, v3: minor typos corrected, references adde

### Matrix Reduction and the su(2|2) superalgebra in AdS/CFT

We study the supersymmetry generators Q, S on the 1-loop vectorless sector of
N=4 Super Yang-Mills, by reduction to the plane-wave matrix model. Using a
coherent basis in the su(2|2) sector, a comparison with the algebra given by
Beisert in nlin/0610017 is presented, and some parameters (up to one-loop) are
determined. We make a final comparison of these supercharges with the results
that can be obtained from the string action by working in the light-cone-gauge
and discretizing the string.Comment: 20 pages, no figures v2: Typos corrected, references adde

### The Complete One-Loop Dilation Operator of N=2 SuperConformal QCD

We evaluate the full planar one-loop dilation operator of N=2 SuperConformal
QCD, the SU(N_c) super Yang-Mills theory with N_f = 2 N_c fundamental
hypermultiplets, in the flavor-singlet sector. Remarkably, the spin-chain
Hamiltonian turns out to be completely fixed by superconformal symmetry, as in
N=4 SYM. We present a more general calculation, for the superconformal quiver
theory with SU(N_c)X SU(N_c) gauge group, which interpolates between N=2 SCQCD
and the Z_2 orbifold of N=4 SYM; here symmetry fixes the Hamiltonian up to a
single parameter, corresponding to the ratio of the two marginal gauge
couplings.Comment: v2: typo corrected, cosmetic changes. JHEP versio

### Higher-Loop Integrability in N=4 Gauge Theory

The dilatation operator measures scaling dimensions of local operator in a conformal field theory. Algebraic methods of constructing the dilatation operator in four-dimensional N=4 gauge theory are reviewed. These led to the discovery of novel integrable spin chain models in the planar limit. Making use of Bethe ansaetze, a superficial discrepancy in the AdS/CFT correspondence was found, we discuss this issue and give a possible resolution

### Fluctuations and Energy Shifts in the Bethe Ansatz

We study fluctuations and finite size corrections for the ferromagnetic
thermodynamic limit in the Bethe ansatz for the Heisenberg XXX1/2 spin chain,
which is the AdS/CFT dual of semiclassical spinning strings. For this system we
derive the standard quantum mechanical formula which expresses the energy shift
as a sum over fluctuation energies. As an example we apply our results to the
simplest, one-cut solution of this system and derive its spectrum of
fluctuations.Comment: 8 pages, 1 figure, v2: comparison to string theory improved,
reference adde

### Long-Range GL(n) Integrable Spin Chains and Plane-Wave Matrix Theory

Quantum spin chains arise naturally from perturbative large-N field theories
and matrix models. The Hamiltonian of such a model is a long-range deformation
of nearest-neighbor type interactions. Here, we study the most general
long-range integrable spin chain with spins transforming in the fundamental
representation of gl(n). We derive the Hamiltonian and the corresponding
asymptotic Bethe ansatz at the leading four perturbative orders with several
free parameters. Furthermore, we propose Bethe equations for all orders and
identify the moduli of the integrable system. We finally apply our results to
plane-wave matrix theory and show that the Hamiltonian in a closed sector is
not of this form and therefore not integrable beyond the first perturbative
order. This also implies that the complete model is not integrable.Comment: 22 pages, v2: reference adde

### The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure

In this paper we investigate the algebraic structure of AdS/CFT in the
strong-coupling limit. We propose an expression for the classical r-matrix with
(deformed) u(2|2) symmetry, which leads to a quasi-triangular Lie bialgebra as
the underlying symmetry algebra. On the fundamental representation our r-matrix
coincides with the classical limit of the quantum R-matrix.Comment: 31 pages, v2: added comment on classical double structure in 4.5. new
section 5 on relation to other algebras (from old appendix and new results).
fixed typos and mathematical inaccuracies, added references, v3: improved
mathematical presentation, to appear in CM

### On Quantum Corrections to Spinning Strings and Bethe Equations

Recently, it was demonstrated that one-loop energy shifts of spinning
superstrings on AdS5xS5 agree with certain Bethe equations for quantum strings
at small effective coupling. However, the string result required artificial
regularization by zeta-function. Here we show that this matching is indeed
correct up to fourth order in effective coupling; beyond, we find new
contributions at odd powers. We show that these are reproduced by quantum
corrections within the Bethe ansatz. They might also identify the "three-loop
discrepancy" between string and gauge theory as an order-of-limits effect.Comment: 12 pages, v2, v3: minor corrections, footnotes and references added,
v3: to appear in Phys. Lett.

### Landau-Lifshitz sigma-models, fermions and the AdS/CFT correspondence

We define Landau-Lifshitz sigma models on general coset space $G/H$, with $H$
a maximal stability sub-group of $G$. These are non-relativistic models that
have $G$-valued N\"other charges, local $H$ invariance and are classically
integrable. Using this definition, we construct the $PSU(2,2|4)/PS(U(2|2)^2)$
Landau-Lifshitz sigma-model. This sigma model describes the thermodynamic limit
of the spin-chain Hamiltonian obtained from the complete one-loop dilatation
operator of the N=4 super Yang-Mills (SYM) theory. In the second part of the
paper, we identify a number of consistent truncations of the Type IIB
Green-Schwarz action on $AdS_5\times S^5$ whose field content consists of two
real bosons and 4,8 or 16 real fermions. We show that $\kappa$-symmetry acts
trivially in these sub-sectors. In the context of the large spin limit of the
AdS/CFT correspondence, we map the Lagrangians of these sub-sectors to
corresponding truncations of the $PSU(2,2|4)/PS(U(2|2)^2)$ Landau-Lifshitz
sigma-model.Comment: 42 page

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