81 research outputs found
Tensionless strings: physical Fock space and higher spin fields
I study the physical Fock space of the tensionless string theory with
perimeter action, exploring its new gauge symmetry algebra. The cancellation of
conformal anomaly requires the space-time to be 13-dimensional. All particles
are massless and there are no tachyon states in the spectrum. The zero mode
conformal operator defines the levels of the physical Fock space. All levels
can be classified by the highest Casimir operator W of the little group E(11)
for massless particles in 11-dimensions. The ground state is infinitely
degenerated and contains massless gauge fields of arbitrary large integer spin,
realizing the irreducible representations of E(11) of fixed helicity. The
excitation levels realize CSR representations of little group E(11) with an
infinite number of helicities. After inspection of the first excitation level,
which, as I prove, is a physical null state, I conjecture that all excitation
levels are physical null states. In this theory the tensor field of the second
rank does not play any distinctive role and therefore one can suggest that in
this model there is no gravity.Comment: 22 pages, Latex, references adde
Type IIB tensionless superstrings in a pp-wave background
We solve the tensionless string in a constant plane wave background and
obtain a hugely degenerate spectrum. This is the case for a large class of
plane wave backgrounds. We show that the solution can also be derived as a
consistent limit of the quantized tensile theory of IIB strings in a pp-wave.
This is in contrast to the situation for several other backgrounds.Comment: 1+17 pages, LaTeX, minor corrections, added new reference
3-D Interacting CFTs and Generalized Higgs Phenomenon in Higher Spin Theories on AdS
We study a duality, recently conjectured by Klebanov and Polyakov, between
higher-spin theories on AdS_4 and O(N) vector models in 3-d. These theories are
free in the UV and interacting in the IR. At the UV fixed point, the O(N) model
has an infinite number of higher-spin conserved currents. In the IR, these
currents are no longer conserved for spin s>2. In this paper, we show that the
dual interpretation of this fact is that all fields of spin s>2 in AdS_4 become
massive by a Higgs mechanism, that leaves the spin-2 field massless. We
identify the Higgs field and show how it relates to the RG flow connecting the
two CFTs, which is induced by a double trace deformation.Comment: 8 pages, latex; v2 references adde
Analysis of Higher Spin Field Equations in Four Dimensions
The minimal bosonic higher spin gauge theory in four dimensions contains
massless particles of spin s=0,2,4,.. that arise in the symmetric product of
two spin 0 singletons. It is based on an infinite dimensional extension of the
AdS_4 algebra a la Vasiliev. We derive an expansion scheme in which the
gravitational gauge fields are treated exactly and the gravitational curvatures
and the higher spin gauge fields as weak perturbations. We also give the
details of an explicit iteration procedure for obtaining the field equations to
arbitrary order in curvatures. In particular, we highlight the structure of all
the quadratic terms in the field equations.Comment: Latex, 30 pages, several clarifications and few references adde
Random walks and the Hagedorn transition
We study details of the approach to the Hagedorn temperature in string theory
in various static spacetime backgrounds. We show that the partition function
for a {\it single} string at finite temperature is the torus amplitude
restricted to unit winding around Euclidean time. We use the worldsheet path
integral to derive the statement that the the sum over random walks of the
thermal scalar near the Hagedorn transition is precisely the image under a
modular transformation of the sum over spatial configurations of a single
highly excited string. We compute the radius of gyration of thermally excited
strings in . We show that the winding mode indicates an
instability despite the AdS curvature at large radius, and that the negative
mass squared decreases with decreasing AdS radius, much like the type 0
tachyon. We add further arguments to statements by Barbon and Rabinovici, and
by Adams {\it et. al.}, that the Euclidean AdS black hole can thought of as a
condensate of the thermal scalar. We use this to provide circumstantial
evidence that the condensation of the thermal scalar decouples closed string
modes.Comment: 34 pages (7 of references), 5 figures. v2: Reference added, grant
acknowledgement added, typos correcte
Scalar Field Corrections to AdS_4 Gravity from Higher Spin Gauge Theory
We compute the complete contribution to the stress-energy tensor in the
minimal bosonic higher spin theory in D=4 that is quadratic in the scalar
field. We find arbitrarily high derivative terms, and that the total sign of
the stress-energy tensor depends on the parity of the scalar field.Comment: 15 pages + appendix (30 pages
On the worldsheet theories of strings dual to free large N gauge theories
We analyze in detail some properties of the worldsheet of the closed string
theories suggested by Gopakumar to be dual to free large N SU(N) gauge theories
(with adjoint matter fields). We use Gopakumar's prescription to translate the
computation of space-time correlation functions to worldsheet correlation
functions for several classes of Feynman diagrams, by explicit computations of
Strebel differentials. We compute the worldsheet operator product expansion in
several cases and find that it is consistent with general worldsheet conformal
field theory expectations. A peculiar property of the construction is that in
several cases the resulting worldsheet correlation functions are non-vanishing
only on a sub-space of the moduli space (say, for specific relations between
vertex positions). Another strange property we find is that for a conformally
invariant space-time theory, the mapping to the worldsheet does not preserve
the special conformal symmetries, so that the full conformal group is not
realized as a global symmetry on the worldsheet (even though it is, by
construction, a symmetry of all integrated correlation functions).Comment: 60 pages, 17 figures, latex. v2: Added references and a minor
correctio
Evaluating the AdS dual of the critical O(N) vector model
We argue that the AdS dual of the three dimensional critical O(N) vector
model can be evaluated using the Legendre transform that relates the generating
functionals of the free UV and the interacting IR fixed points of the boundary
theory. As an example, we use our proposal to evaluate the minimal bulk action
of the scalar field that it is dual to the spin-zero ``current'' of the O(N)
vector model. We find that the cubic bulk self interaction coupling vanishes.
We briefly discuss the implications of our results for higher spin theories and
comment on the bulk-boundary duality for subleading N.Comment: 17 pages, 1 figure, v2 references added, JHEP versio
Large-N Collective Fields and Holography
We propose that the euclidean bilocal collective field theory of critical
large-N vector models provides a complete definition of the proposed dual
theory of higher spin fields in anti de-Sitter spaces. We show how this bilocal
field can be decomposed into an infinite number of even spin fields in one more
dimension. The collective field has a nontrivial classical solution which leads
to a O(N) thermodynamic entropy characteristic of the lower dimensional theory,
as required by general considerations of holography. A subtle cancellation of
the entropy coming from the bulk fields in one higher dimension with O(1)
contributions from the classical solution ensures that the subleading terms in
thermodynamic quantities are of the expected form. While the spin components of
the collective field transform properly under dilatational, translational and
rotational isometries of , special conformal transformations mix fields of
different spins indicating a need for a nonlocal map between the two sets of
fields. We discuss the nature of the propagating degrees of freedom through a
hamiltonian form of collective field theory and argue that nonsinglet states
which are present in an euclidean version are related to nontrivial
backgrounds.Comment: 27 pages, harvmac. v2: references adde
Supersymmetric non-linear sigma-models with boundaries revisited
We study two-dimensional supersymmetric non-linear sigma-models with
boundaries. We derive the most general family of boundary conditions in the
non-supersymmetric case. Next we show that no further conditions arise when
passing to the N=1 model. We present a manifest N=1 off-shell formulation. The
analysis is greatly simplified compared to previous studies and there is no
need to introduce non-local superspaces nor to go (partially) on-shell. Whether
or not torsion is present does not modify the discussion. Subsequently, we
determine under which conditions a second supersymmetry exists. As for the case
without boundaries, two covariantly constant complex structures are needed.
However, because of the presence of the boundary, one gets expressed in terms
of the other one and the remainder of the geometric data. Finally we recast
some of our results in N=2 superspace and discuss applications.Comment: LaTeX, 23 page
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