10 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
Non-planar ABJM Theory and Integrability
Using an effective vertex method we explicitly derive the two-loop dilatation
generator of ABJM theory in its SU(2)xSU(2) sector, including all non-planar
corrections. Subsequently, we apply this generator to a series of finite length
operators as well as to two different types of BMN operators. As in N=4 SYM, at
the planar level the finite length operators are found to exhibit a degeneracy
between certain pairs of operators with opposite parity - a degeneracy which
can be attributed to the existence of an extra conserved charge and thus to the
integrability of the planar theory. When non-planar corrections are taken into
account the degeneracies between parity pairs disappear hinting the absence of
higher conserved charges. The analysis of the BMN operators resembles that of
N=4 SYM. Additional non-planar terms appear for BMN operators of finite length
but once the strict BMN limit is taken these terms disappear.Comment: 1+26 pages, uses axodraw.sty. v2: typos fixed, references added. v3:
more typos fixed, minor correction
Anomalous dimensions of finite size field strength operators in N=4 SYM
In the N=4 super Yang-Mills theory, we consider the higher order anomalous
dimensions gamma_L(g) of purely gluonic operators Tr(F^L) where F is a
component of the self-dual field strength. We propose compact closed
expressions depending parametrically on L that reproduce the prediction of
Bethe Ansatz equations up to five loop order, including transcendental dressing
corrections. The size dependence follows a simple pattern as the perturbative
order is increased and suggests hidden relations for these special operators.Comment: 26 pages, 3 eps figures. v2: published version, minor changes,
references adde
Matching gauge theory and string theory in a decoupling limit of AdS/CFT
We identify a regime of the AdS/CFT correspondence in which we can
quantitatively match N=4 super Yang-Mills (SYM) for small 't Hooft coupling
with weakly coupled type IIB string theory on AdS_5 x S^5. We approach this
regime by taking the same decoupling limit on both sides of the correspondence.
On the gauge theory side only the states in the SU(2) sector survive, and in
the planar limit the Hamiltonian is given by the XXX_{1/2} Heisenberg spin
chain. On the string theory side we show that the decoupling limit corresponds
to a non-relativistic limit. In this limit some of the bosonic modes and all of
the fermionic modes of the string become infinitely heavy and decouple. We
first take the decoupling limit of the string sigma-model classically. This
enables us to identify a semi-classical regime with semi-classical string
states even though we are in a regime corresponding to small 't Hooft coupling.
We furthermore analyze the quantum corrections that enter in taking the limit.
From this we infer that gauge theory and string theory match, both in terms
of the action and the spectrum, for the leading part and the first correction
away from the semi-classical regime. Finally we consider the implications for
the hitherto unexplained matching of the one-loop contribution to the energy of
certain gauge theory and string theory states, and we explain how our results
give a firm basis for the matching of the Hagedorn temperature in
hep-th/0608115.Comment: 29 pages, 1 figure. v2: Version published in JHEP, section 4 improve
Serre Relation and Higher Grade Generators of the AdS/CFT Yangian Symmetry
It was shown that the spin chain model coming from AdS/CFT correspondence
satisfies the Yangian symmetry if we assume evaluation representation, though
so far there is no explicit proof that the evaluation representation satisfies
the Serre relation, which is one of the defining equations of the Yangian
algebra imposing constraints on the whole algebraic structure. We prove
completely that the evaluation representation adopted in the model satisfies
the Serre relation by introducing a three-dimensional gamma matrix. After
studying the Serre relation, we proceed to the whole Yangian algebraic
structure, where we find that the conventional construction of higher grade
generators is singular and we propose an alternative construction. In the
discussion of the higher grade generators, a great simplification for the proof
of the Serre relation is found. Using this expression, we further show that the
proof is lifted to the exceptional superalgebra, which is a non-degenerate
deformation of the original superalgebra.Comment: 24 pages, 1 figure, v2: on exceptional superalgebra, previous
incorrect comments removed and new sections added, v3: clarifications adde
Review of AdS/CFT Integrability, Chapter II.2: Quantum Strings in AdS5xS5
We review the semiclassical analysis of strings in AdS5xS5 with a focus on
the relationship to the underlying integrable structures. We discuss the
perturbative calculation of energies for strings with large charges, using the
folded string spinning in an AdS3 subset of AdS5 as our main example.
Furthermore, we review the perturbative light-cone quantization of the string
theory and the calculation of the worldsheet S-matrix.Comment: 20 pages, see also overview article arXiv:1012.3982, v2: references
to other chapters update
Review of AdS/CFT Integrability, Chapter III.3: The dressing factor
We review the construction of the AdS/CFT dressing factor, its analytic
properties and several checks of its validity.Comment: 22 pages, see also overview article arXiv:1012.3982, v2: references
to other chapters update