187 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
Fusion Rules in N=1 Superconformal Minimal Models
The generalization to N=1 superconformal minimal models of the relation
between the modular transformation matrix and the fusion rules in rational
conformal field theories, the Verlinde theorem, is shown to provide complete
information about the fusion rules, including their fermionic parity. The
results for the superconformal Tricritical Ising and Ashkin-Teller models agree
with the known rational conformal formulation. The Coulomb gas description of
correlation functions in the Ramond sector of N=1 minimal models is also
discussed and a previous formulation is completed.Comment: 13 pages, latex, to appear in Phys. Lett.
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.
Scalar Field Theory in the AdS/CFT Correspondence Revisited
We consider the role of boundary conditions in the
correspondence for the scalar field theory. Also a careful analysis of some
limiting cases is presented. We study three possible types of boundary
conditions, Dirichlet, Neumann and mixed. We compute the two-point functions of
the conformal operators on the boundary for each type of boundary condition. We
show how particular choices of the mass require different treatments. In the
Dirichlet case we find that there is no double zero in the two-point function
of the operator with conformal dimension . The Neumann case leads
to new normalizations for the boundary two-point functions. In the massless
case we show that the conformal dimension of the boundary conformal operator is
precisely the unitarity bound for scalar operators. We find a one-parameter
family of boundary conditions in the mixed case. There are again new
normalizations for the boundary two-point functions. For a particular choice of
the mixed boundary condition and with the mass squared in the range
the boundary operator has conformal dimension comprised
in the interval . For mass squared
the same choice of mixed boundary condition leads to a boundary operator whose
conformal dimension is the unitarity bound.Comment: 22 pages, LaTeX, minor errors corrected, Conclusions and one
reference added, final version to be published in Nucl. Phys.
A note on causality in the bulk and stability on the boundary
By carefully analyzing the radial part of the wave-equation for a scalar
field in AdS, we show that for a particular range of boundary conditions on the
scalar field, the radial spectrum contains a bound state. Using the AdS/CFT
correspondence, we interpret this peculiar phenomenon as being dual to an
unstable double trace deformation of the boundary conformal field theory. We
thus show how the bulk theory holographically detects whether a boundary
perturbation is stable.Comment: 7 pages; v2: reference added, PLB versio
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.
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
Four Point Functions in the SL(2,R) WZW Model
We consider winding conserving four point functions in the SL(2,R) WZW model
for states in arbitrary spectral flow sectors. We compute the leading order
contribution to the expansion of the amplitudes in powers of the cross ratio of
the four points on the worldsheet, both in the m- and x-basis, with at least
one state in the spectral flow image of the highest weight discrete
representation. We also perform certain consistency check on the winding
conserving three point functions.Comment: 15 pages, Late
Winding Strings in AdS_3
Correlation functions of one unit spectral flowed states in string theory on
AdS_3 are considered. We present the modified Knizhnik-Zamolodchikov and null
vector equations to be satisfied by amplitudes containing states in winding
sector one and study their solution corresponding to the four point function
including one w=1 field. We compute the three point function involving two one
unit spectral flowed operators and find expressions for amplitudes of three w=1
states satisfying certain particular relations among the spins of the fields.
Several consistency checks are performed.Comment: 35 pages. v2. Important additions: one more author, complete results
for the 3-point function with two w=1 states and new section with computation
of 4-point function with one w=1 state. Acknowledgments and references
modifie
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
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