64 research outputs found
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.
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
States and Boundary Terms: Subtleties of Lorentzian AdS/CFT
We complete the project of specifying the Lorentzian AdS/CFT correspondence
and its approximation by bulk semi-classical methods begun by earlier authors.
At the end, the Lorentzian treatment is self-contained and requires no analytic
continuation from the Euclidean. The new features involve a careful study of
boundary terms associated with an initial time and a final time .
These boundary terms are determined by a choice of quantum states. The main
results in the semi-classical approximation are 1) The times may be
finite, and need only label Cauchy surfaces respectively to the past and future
of the points at which one wishes to obtain CFT correlators. Subject to this
condition on , we provide a bulk computation of CFT correlators that is
manifestly independent of . 2) As a result of (1), all CFT correlators
can be expressed in terms of a path integral over regions of spacetime {\it
outside} of any black hole horizons. 3) The details of the boundary terms at
serve to guarrantee that, at leading order in this approximation, any
CFT one-point function is given by a simple boundary value of the classical
bulk solution at null infinity, . This work is dedicated to the memory of
Bryce S. DeWitt. The remarks in this paper largely study the relation of the
AdS/CFT dictionary to the Schwinger variational principle, which the author
first learned from DeWitt as a Ph.D. student.Comment: 31 pages, JHEP style, various typos correcte
Spectral Flow in AdS(3)/CFT(2)
We study the spectral flowed sectors of the H3 WZW model in the context of
the holographic duality between type IIB string theory in AdS(3)x S^3 x T^4
with NSNS flux and the symmetric product orbifold of T^4. We construct
explicitly the physical vertex operators in the flowed sectors that belong to
short representations of the superalgebra, thus completing the bulk-to-boundary
dictionary for 1/2 BPS states. We perform a partial calculation of the string
three-point functions of these operators. A complete calculation would require
the three-point couplings of non-extremal flowed operators in the H3 WZW model,
which are at present unavailable. In the unflowed sector, perfect agreement has
recently been found between the bulk and boundary three-point functions of 1/2
BPS operators. Assuming that this agreement persists in the flowed sectors, we
determine certain unknown three-point couplings in the H3 WZW model in terms of
three-point couplings of affine descendants in the SU(2) WZW model.Comment: 50 pages, 2 figure
Geometry of Schroedinger Space-Times II: Particle and Field Probes of the Causal Structure
We continue our study of the global properties of the z=2 Schroedinger
space-time. In particular, we provide a codimension 2 isometric embedding which
naturally gives rise to the previously introduced global coordinates.
Furthermore, we study the causal structure by probing the space-time with point
particles as well as with scalar fields. We show that, even though there is no
global time function in the technical sense (Schroedinger space-time being
non-distinguishing), the time coordinate of the global Schroedinger coordinate
system is, in a precise way, the closest one can get to having such a time
function. In spite of this and the corresponding strongly Galilean and almost
pathological causal structure of this space-time, it is nevertheless possible
to define a Hilbert space of normalisable scalar modes with a well-defined
time-evolution. We also discuss how the Galilean causal structure is reflected
and encoded in the scalar Wightman functions and the bulk-to-bulk propagator.Comment: 32 page
Mixed RG Flows and Hydrodynamics at Finite Holographic Screen
We consider quark-gluon plasma with chemical potential and study
renormalization group flows of transport coefficients in the framework of
gauge/gravity duality. We first study them using the flow equations and compare
the results with hydrodynamic results by calculating the Green functions on the
arbitrary slice. Two results match exactly. Transport coefficients at arbitrary
scale is ontained by calculating hydrodynamics Green functions. When either
momentum or charge vanishes, transport coefficients decouple from each other.Comment: 22 pages, 6 figure
A Field-theoretical Interpretation of the Holographic Renormalization Group
A quantum-field theoretical interpretation is given to the holographic RG
equation by relating it to a field-theoretical local RG equation which
determines how Weyl invariance is broken in a quantized field theory. Using
this approach we determine the relation between the holographic C theorem and
the C theorem in two-dimensional quantum field theory which relies on the
Zamolodchikov metric. Similarly we discuss how in four dimensions the
holographic C function is related to a conjectured field-theoretical C
function. The scheme dependence of the holographic RG due to the possible
presence of finite local counterterms is discussed in detail, as well as its
implications for the holographic C function. We also discuss issues special to
the situation when mass deformations are present. Furthermore we suggest that
the holographic RG equation may also be obtained from a bulk diffeomorphism
which reduces to a Weyl transformation on the boundary.Comment: 24 pages, LaTeX, no figures; references added, typos corrected,
paragraph added to section
Clean Time-Dependent String Backgrounds from Bubble Baths
We consider the set of controlled time-dependent backgrounds of general
relativity and string theory describing ``bubbles of nothing'', obtained via
double analytic continuation of black hole solutions. We analyze their quantum
stability, uncover some novel features of their dynamics, identify their causal
structure and observables, and compute their particle production spectrum. We
present a general relation between squeezed states, such as those arising in
cosmological particle creation, and nonlocal theories on the string worldsheet.
The bubble backgrounds have various aspects in common with de Sitter space,
Rindler space, and moving mirror systems, but constitute controlled solutions
of general relativity and string theory with no external forces. They provide a
useful theoretical laboratory for studying issues of observables in systems
with cosmological horizons, particle creation, and time-dependent string
perturbation theory.Comment: 38 pages, harvmac big, 6 figure
Affine sl(N) conformal blocks from N=2 SU(N) gauge theories
Recently Alday and Tachikawa proposed a relation between conformal blocks in
a two-dimensional theory with affine sl(2) symmetry and instanton partition
functions in four-dimensional conformal N=2 SU(2) quiver gauge theories in the
presence of a certain surface operator. In this paper we extend this proposal
to a relation between conformal blocks in theories with affine sl(N) symmetry
and instanton partition functions in conformal N=2 SU(N) quiver gauge theories
in the presence of a surface operator. We also discuss the extension to
non-conformal N=2 SU(N) theories.Comment: 40 pages. v2: minor changes and clarification
Holographic and Wilsonian Renormalization Groups
We develop parallels between the holographic renormalization group in the
bulk and the Wilsonian renormalization group in the dual field theory. Our
philosophy differs from most previous work on the holographic RG; the most
notable feature is the key role of multi-trace operators. We work out the forms
of various single- and double-trace flows. The key question, `what cutoff on
the field theory corresponds to a radial cutoff in the bulk?' is left
unanswered, but by sharpening the analogy between the two sides we identify
possible directions.Comment: 31 pages, 3 figures. v2: Minor clarifications. Added reference
- âŠ