1,519 research outputs found
Nonplanar integrability at two loops
In this article we compute the action of the two loop dilatation operator on
restricted Schur polynomials that belong to the su(2) sector, in the displaced
corners approximation. In this non-planar large N limit, operators that
diagonalize the one loop dilatation operator are not corrected at two loops.
The resulting spectrum of anomalous dimensions is related to a set of decoupled
harmonic oscillators, indicating integrability in this sector of the theory at
two loops. The anomalous dimensions are a non-trivial function of the 't Hooft
coupling, with a spectrum that is continuous and starting at zero at large N,
but discrete at finite N.Comment: version to appear in JHE
A double coset ansatz for integrability in AdS/CFT
We give a proof that the expected counting of strings attached to giant
graviton branes in AdS_5 x S^5, as constrained by the Gauss Law, matches the
dimension spanned by the expected dual operators in the gauge theory. The
counting of string-brane configurations is formulated as a graph counting
problem, which can be expressed as the number of points on a double coset
involving permutation groups. Fourier transformation on the double coset
suggests an ansatz for the diagonalization of the one-loop dilatation operator
in this sector of strings attached to giant graviton branes. The ansatz agrees
with and extends recent results which have found the dynamics of open string
excitations of giants to be given by harmonic oscillators. We prove that it
provides the conjectured diagonalization leading to harmonic oscillators.Comment: 33 pages, 3 figures; v2: references adde
Ceramides: a new player in the inflammation-insulin resistance paradigm?
No abstract available
Correlators of Giant Gravitons from dual ABJ(M) Theory
We generalize the operators of ABJM theory, given by Schur polynomials, in
ABJ theory by computing the two point functions in the free field and at finite
limits. These polynomials are then identified with the states of
the dual gravity theory. Further, we compute correlators among giant gravitons
as well as between giant gravitons and ordinary gravitons through the
corresponding correlators of ABJ(M) theory. Finally, we consider a particular
non-trivial background produced by an operator with an -charge of
and find, in presence of this background, due to the contribution of
the non-planar corrections, the large expansion is replaced by
and respectively.Comment: Latex, 32+1 pages, 2 figures, journal versio
ABJM Dibaryon Spectroscopy
We extend the proposal for a detailed map between wrapped D-branes in Anti-de
Sitter space and baryon-like operators in the associated dual conformal field
theory provided in hep-th/0202150 to the recently formulated AdS_4 \times
CP^3/ABJM correspondence. In this example, the role of the dibaryon operator of
the 3-dimensional CFT is played by a D4-brane wrapping a CP^2 \subset CP^3.
This topologically stable D-brane in the AdS_4 \times CP^3 is nothing but
one-half of the maximal giant graviton on CP^3.Comment: 26 page
Surprisingly Simple Spectra
The large N limit of the anomalous dimensions of operators in
super Yang-Mills theory described by restricted Schur polynomials, are studied.
We focus on operators labeled by Young diagrams that have two columns (both
long) so that the classical dimension of these operators is O(N). At large N
these two column operators mix with each other but are decoupled from operators
with columns. The planar approximation does not capture the large N
dynamics. For operators built with 2, 3 or 4 impurities the dilatation operator
is explicitly evaluated. In all three cases, in a certain limit, the dilatation
operator is a lattice version of a second derivative, with the lattice emerging
from the Young diagram itself. The one loop dilatation operator is diagonalized
numerically. All eigenvalues are an integer multiple of and there
are interesting degeneracies in the spectrum. The spectrum we obtain for the
one loop anomalous dimension operator is reproduced by a collection of harmonic
oscillators. This equivalence to harmonic oscillators generalizes giant
graviton results known for the BPS sector and further implies that the
Hamiltonian defined by the one loop large dilatation operator is
integrable. This is an example of an integrable dilatation operator, obtained
by summing both planar and non-planar diagrams.Comment: 34 page
Gauge invariant perturbation theory and non-critical string models of Yang-Mills theories
We carry out a gauge invariant analysis of certain perturbations of
-branes solutions of low energy string theories. We get generically a
system of second order coupled differential equations, and show that only in
very particular cases it is possible to reduce it to just one differential
equation. Later, we apply it to a multi-parameter, generically singular family
of constant dilaton solutions of non-critical string theories in
dimensions, a generalization of that recently found in arXiv:0709.0471[hep-th].
According to arguments coming from the holographic gauge theory-gravity
correspondence, and at least in some region of the parameters space, we obtain
glue-ball spectra of Yang-Mills theories in diverse dimensions, putting special
emphasis in the scalar metric perturbations not considered previously in the
literature in the non critical setup. We compare our numerical results to those
studied previously and to lattice results, finding qualitative and in some
cases, tuning properly the parameters, quantitative agreement. These results
seem to show some kind of universality of the models, as well as an irrelevance
of the singular character of the solutions. We also develop the analysis for
the T-dual, non trivial dilaton family of solutions, showing perfect agreement
between them.Comment: A new reference added
Quivers, words and fundamentals
40 pages + Appendices, 9 figures40 pages + Appendices, 9 figure
Bi-local Construction of Sp(2N)/dS Higher Spin Correspondence
We derive a collective field theory of the singlet sector of the Sp(2N) sigma
model. Interestingly the hamiltonian for the bilocal collective field is the
same as that of the O(N) model. However, the large-N saddle points of the two
models differ by a sign. This leads to a fluctuation hamiltonian with a
negative quadratic term and alternating signs in the nonlinear terms which
correctly reproduces the correlation functions of the singlet sector. Assuming
the validity of the connection between O(N) collective fields and higher spin
fields in AdS, we argue that a natural interpretation of this theory is by a
double analytic continuation, leading to the dS/CFT correspondence proposed by
Anninos, Hartman and Strominger. The bi-local construction gives a map into the
bulk of de Sitter space-time. Its geometric pseudospin-representation provides
a framework for quantization and definition of the Hilbert space. We argue that
this is consistent with finite N grassmanian constraints, establishing the
bi-local representation as a nonperturbative framework for quantization of
Higher Spin Gravity in de Sitter space.Comment: 1 figur
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