732 research outputs found
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
From counting to construction of BPS states in N=4 SYM
We describe a universal element in the group algebra of symmetric groups,
whose characters provides the counting of quarter and eighth BPS states at weak
coupling in N=4 SYM, refined according to representations of the global
symmetry group. A related projector acting on the Hilbert space of the free
theory is used to construct the matrix of two-point functions of the states
annihilated by the one-loop dilatation operator, at finite N or in the large N
limit. The matrix is given simply in terms of Clebsch-Gordan coefficients of
symmetric groups and dimensions of U(N) representations. It is expected, by
non-renormalization theorems, to contain observables at strong coupling. Using
the stringy exclusion principle, we interpret a class of its eigenvalues and
eigenvectors in terms of giant gravitons. We also give a formula for the action
of the one-loop dilatation operator on the orthogonal basis of the free theory,
which is manifestly covariant under the global symmetry.Comment: 41 pages + Appendices, 4 figures; v2 - refs and acknowledgments adde
d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories
We study three dimensional O(N)_k and U(N)_k Chern-Simons theories coupled to
a scalar field in the fundamental representation, in the large N limit. For
infinite k this is just the singlet sector of the O(N) (U(N)) vector model,
which is conjectured to be dual to Vasiliev's higher spin gravity theory on
AdS_4. For large k and N we obtain a parity-breaking deformation of this
theory, controlled by the 't Hooft coupling lambda = 4 \pi N / k. For infinite
N we argue (and show explicitly at two-loop order) that the theories with
finite lambda are conformally invariant, and also have an exactly marginal
(\phi^2)^3 deformation.
For large but finite N and small 't Hooft coupling lambda, we show that there
is still a line of fixed points parameterized by the 't Hooft coupling lambda.
We show that, at infinite N, the interacting non-parity-invariant theory with
finite lambda has the same spectrum of primary operators as the free theory,
consisting of an infinite tower of conserved higher-spin currents and a scalar
operator with scaling dimension \Delta=1; however, the correlation functions of
these operators do depend on lambda. Our results suggest that there should
exist a family of higher spin gravity theories, parameterized by lambda, and
continuously connected to Vasiliev's theory. For finite N the higher spin
currents are not conserved.Comment: 34 pages, 29 figures. v2: added reference
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
Flavour singlets in gauge theory as permutations
50 pages, v2: typos corrected, v3: to appear in JHEPJHEP is an open-access journal funded by SCOAP3 and licensed under CC BY 4.
Higher Spin Gravity with Matter in AdS_3 and Its CFT Dual
We study Vasiliev's system of higher spin gauge fields coupled to massive
scalars in AdS_3, and compute the tree level two and three point functions.
These are compared to the large N limit of the W_N minimal model, and
nontrivial agreements are found. We propose a modified version of the
conjecture of Gaberdiel and Gopakumar, under which the bulk theory is
perturbatively dual to a subsector of the CFT that closes on the sphere.Comment: 58 pages; typos corrected, references adde
Thresholds of large N factorization in CFT4: exploring bulk spacetime in AdS(5)
52 pages, 6 figures52 pages, 6 figure
Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions
We consider the conformal field theory of N complex massless scalars in 2+1
dimensions, coupled to a U(N) Chern-Simons theory at level k. This theory has a
't Hooft large N limit, keeping fixed \lambda = N/k. We compute some
correlation functions in this theory exactly as a function of \lambda, in the
large N (planar) limit. We show that the results match with the general
predictions of Maldacena and Zhiboedov for the correlators of theories that
have high-spin symmetries in the large N limit. It has been suggested in the
past that this theory is dual (in the large N limit) to the Legendre transform
of the theory of fermions coupled to a Chern-Simons gauge field, and our
results allow us to find the precise mapping between the two theories. We find
that in the large N limit the theory of N scalars coupled to a U(N)_k
Chern-Simons theory is equivalent to the Legendre transform of the theory of k
fermions coupled to a U(k)_N Chern-Simons theory, thus providing a bosonization
of the latter theory. We conjecture that perhaps this duality is valid also for
finite values of N and k, where on the fermionic side we should now have (for
N_f flavors) a U(k)_{N-N_f/2} theory. Similar results hold for real scalars
(fermions) coupled to the O(N)_k Chern-Simons theory.Comment: 49 pages, 16 figures. v2: added reference
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