65 research outputs found
Quantization in Ads and the Ads/CFT Correspondence
The quantization of a scalar field in AdS leads to two kinds of normalizable
modes, usually called regular and irregular modes. The regular one is easily
taken into account in the standard prescription for the AdS/CFT correspondence.
The irregular mode requires a modified prescription which we argue is not
completely satisfactory. We discuss an alternative quantization in AdS which
incorporates boundary terms in a natural way. Within this quantization scheme
we present an improved prescription for the AdS/CFT correspondence which can be
applied to both, regular and irregular modes. Boundary conditions other than
Dirichlet are naturally treated in this new improved setting.Comment: 8 pages. Contribution to the Proceedings of the Second Londrina
Winter School "Mathematical Methods in Physics", August 25-30, 2002,
Londrina, PR, Brazil; v2: typos correcte
Multi-Trace Operators and the Generalized AdS/CFT Prescription
We show that multi-trace interactions can be consistently incorporated into
an extended AdS/CFT prescription involving the inclusion of generalized
boundary conditions and a modified Legendre transform prescription. We find new
and consistent results by considering a self-contained formulation which
relates the quantization of the bulk theory to the AdS/CFT correspondence and
the perturbation at the boundary by double-trace interactions. We show that
there exist particular double-trace perturbations for which irregular modes are
allowed to propagate as well as the regular ones. We perform a detailed
analysis of many different possible situations, for both minimally and
non-minimally coupled cases. In all situations, we make use of a new constraint
which is found by requiring consistence. In the particular non-minimally
coupled case, the natural extension of the Gibbons-Hawking surface term is
generated.Comment: 27 pages, LaTeX, v.2:minor changes, v.3:comments added, v.4:several
new results, discussions, references and a section of Conclusions added.
Previous results unchanged, v.5: minor changes. Final version to be published
in Phys.Rev.
Energy and the AdS/CFT Correspondence
We consider a scalar field theory on AdS in both minimally and non-minimally coupled cases. We show that there exist constraints which arise in the quantization of the scalar field theory on AdS which cannot be reproduced through the usual AdS/CFT prescription. We argue that the usual energy, defined through the stress-energy tensor, is not the natural one to be considered in the context of the AdS/CFT correspondence. We analyze a new definition of the energy which makes use of the Noether current corresponding to time displacements in global coordinates. We compute the new energy for Dirichlet, Neumann and mixed boundary conditions on the scalar field and for both the minimally and non-minimally coupled cases. Then, we perform the quantization of the scalar field theory on AdS showing that, for `regular' and `irregular' modes, the new energy is conserved, positive and finite. We show that the quantization gives rise, in a natural way, to a generalized AdS/CFT prescription which maps to the boundary all the information contained in the bulk. In particular, we show that the divergent local terms of the on-shell action contain information about the Legendre transformed generating functional, and that the new constraints for which the irregular modes propagate in the bulk are the same constraints for which such divergent local terms cancel out. In this situation, the addition of counterterms is not required. We also show that there exist particular cases for which the unitarity bound is reached, and the conformal dimension becomes independent of the effective mass. This phenomenon has no bulk counterpart
Bound States in the AdS/CFT Correspondence
We consider a massive scalar field theory in anti-de Sitter space, in both
minimally and non-minimally coupled cases. We introduce a relevant double-trace
perturbation at the boundary, by carefully identifying the correct source and
generating functional for the corresponding conformal operator. We show that
such relevant double-trace perturbation introduces changes in the coefficients
in the boundary terms of the action, which in turn govern the existence of a
bound state in the bulk. For instance, we show that the usual action,
containing no additional boundary terms, gives rise to a bound state, which can
be avoided only through the addition of a proper boundary term. Another
notorious example is that of a conformally coupled scalar field, supplemented
by a Gibbons-Hawking term, for which there is no associated bound state. In
general, in both minimally and non-minimally coupled cases, we explicitly
compute the boundary terms which give rise to a bound state, and which ones do
not. In the non-minimally coupled case, and when the action is supplemented by
a Gibbons-Hawking term, this also fixes allowed values of the coupling
coefficient to the metric. We interpret our results as the fact that the
requirement to satisfy the Breitenlohner-Freedman bound does not suffice to
prevent tachyonic behavior from existing in the bulk, as it must be
supplemented by additional conditions on the coefficients in the boundary terms
of the action.Comment: 32 pages, Latex. v2: added comments and clarifications, minor
changes. v3: corrected wrong result in the non-minimally coupled case, added
reference, minor changes. v4: Added new results and discussions, parts of the
paper are rewritten. Final version to be published in Phys.Rev.
A Note on Scalar Field Theory in AdS_3/CFT_2
We consider a scalar field theory in AdS_{d+1}, and introduce a formalism on
surfaces at equal values of the radial coordinate. In particular, we define the
corresponding conjugate momentum. We compute the Noether currents for
isometries in the bulk, and perform the asymptotic limit on the corresponding
charges. We then introduce Poisson brackets at the border, and show that the
asymptotic values of the bulk scalar field and the conjugate momentum transform
as conformal fields of scaling dimensions \Delta_{-} and \Delta_{+},
respectively, where \Delta_{\pm} are the standard parameters giving the
asymptotic behavior of the scalar field in AdS. Then we consider the case d=2,
where we obtain two copies of the Virasoro algebra, with vanishing central
charge at the classical level. An AdS_3/CFT_2 prescription, giving the
commutators of the boundary CFT in terms of the Poisson brackets at the border,
arises in a natural way. We find that the boundary CFT is similar to a
generalized ghost system. We introduce two different ground states, and then
compute the normal ordering constants and quantum central charges, which depend
on the mass of the scalar field and the AdS radius. We discuss certain
implications of the results.Comment: 24 pages. v2: added minor clarification. v3: added several comments
and discussions, abstract sligthly changed. Version to be publishe
AdS/CFT, Multitrace Deformations and New Instabilities of Nonlocal String Theories
We study "multitrace" deformations of large N master fields in models with a
mass gap. In particular, we determine the conditions for the multitrace
couplings to drive tachyonic instabilities. These tachyons represent new local
instabilities of the associated nonlocal string theories. In the particular
case of Dp-branes at finite temperature, we consider topology-changing phase
transitions and the effect of multitrace perturbations on the corresponding
phase diagrams.Comment: harvmac. 28 pages. 9 eps figure
Duality in Noncommutative Topologically Massive Gauge Field Theory Revisited
We introduce a master action in noncommutative space, out of which we obtain
the action of the noncommutative Maxwell-Chern-Simons theory. Then, we look for
the corresponding dual theory at both first and second orders in the
noncommutative parameter. At the first order, the dual theory happens to be,
precisely, the action obtained from the usual commutative Self-Dual model by
generalizing the Chern-Simons term to its noncommutative version, including a
cubic term. Since this resulting theory is also equivalent to the
noncommutative massive Thirring model in the large fermion mass limit, we
remove, as a byproduct, the obstacles arising in the generalization to
noncommutative space, and to the first nontrivial order in the noncommutative
parameter, of the bosonization in three dimensions. Then, performing
calculations at the second order in the noncommutative parameter, we explicitly
compute a new dual theory which differs from the noncommutative Self-Dual
model, and further, differs also from other previous results, and involves a
very simple expression in terms of ordinary fields. In addition, a remarkable
feature of our results is that the dual theory is local, unlike what happens in
the non-Abelian, but commutative case. We also conclude that the generalization
to noncommutative space of bosonization in three dimensions is possible only
when considering the first non-trivial corrections over ordinary space.Comment: 14 pages, Latex. v2: comments and references added, minor changes.
v3: analysis extended to the second order in the noncommutative parameter,
references and discussions added. v4: added discussion on higher order
corrections, minor change
Multitrace deformations, Gamow states, and Stability of AdS/CFT
We analyze the effect of multitrace deformations in conformal field theories
at leading order in a large N approximation. These theories admit a description
in terms of a weakly coupled gravity dual. We show how the deformations can be
mapped into boundary terms of the gravity theory and how to reproduce the RG
equations found in field theory. In the case of doubletrace deformations, and
for bulk scalars with masses in the range , the deformed
theory flows between two fixed points of the renormalization group, manifesting
a resonant behavior at the scale characterizing the transition between the two
CFT's. On the gravity side the resonance is mapped into an IR non-normalizable
mode (Gamow state) whose overlap with the UV region increases as the dual
operator approaches the free field limit. We argue that this resonant behavior
is a generic property of large N theories in the conformal window, and
associate it to a remnant of the Nambu-Goldstone mode of dilatation invariance.
We emphasize the role of nonminimal couplings to gravity and establish a
stability theorem for scalar/gravity systems with AdS boundary conditions in
the presence of arbitrary boundary potentials and nonminimal coupling.Comment: 14 pages, references added, introduction change
(2,0) Chern-Simons Supergravity Plus Matter Near the Boundary of AdS_3
We examine the boundary behaviour of the gauged N=(2,0) supergravity in D=3
coupled to an arbitrary number of scalar supermultiplets which parametrize a
Kahler manifold. In addition to the gravitational coupling constant, the model
depends on two parameters, namely the cosmological constant and the size of the
Kahler manifold. It is shown that regular and irregular boundary conditions can
be imposed on the matter fields depending on the size of the sigma model
manifold. It is also shown that the super AdS transformations in the bulk
produce the transformations of the N=(2,0) conformal supergravity and scalar
multiplets on the boundary, containing fields with nonvanishing Weyl weights
determined by the ratio of the sigma model and the gravitational coupling
constants. Various types of (2,0) superconformal multiplets are found on the
boundary and in one case the superconformal symmetry is shown to be realized in
an unconventional way.Comment: 28 pages, latex, references adde
Boundary multi-trace deformations and OPEs in AdS/CFT correspondence
We argue that multi-trace deformations of the boundary CFT in AdS/CFT
correspondence can arise through the OPE of single-trace operators. We work out
the example of a scalar field in AdS_5 with cubic self interaction. By an
appropriate reparametrization of the boundary data we are able to deform the
boundary CFT by a marginal operator that couples to the conformal anomaly. Our
method can be used in the analysis of multi-trace deformations in N=4 SYM where
the OPEs of various single-trace operators are known.Comment: 18 pages, v2 refinements and acknowledgements adde
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