31 research outputs found
Constraining conformal field theories with a slightly broken higher spin symmetry
We consider three dimensional conformal field theories that have a higher
spin symmetry that is slightly broken. The theories have a large N limit, in
the sense that the operators separate into single trace and multitrace and obey
the usual large N factorization properties. We assume that the spectrum of
single trace operators is similar to the one that one gets in the Vasiliev
theories. Namely, the only single trace operators are the higher spin currents
plus an additional scalar. The anomalous dimensions of the higher spin currents
are of order 1/N. Using the slightly broken higher spin symmetry we constrain
the three point functions of the theories to leading order in N. We show that
there are two families of solutions. One family can be realized as a theory of
N fermions with an O(N) Chern-Simons gauge field, the other as a N bosons plus
the Chern-Simons gauge field. The family of solutions is parametrized by the 't
Hooft coupling. At special parity preserving points we get the critical O(N)
models, both the Wilson-Fisher one and the Gross-Neveu one. Our analysis also
fixes the on shell three point functions of Vasiliev's theory on AdS_4 or dS_4.Comment: 54 pages, 3 figure
Conformal invariance: from Weyl to SO(2,d)
The present work deals with two different but subtilely related kinds of
conformal mappings: Weyl rescaling in dimensional spaces and SO(2,d)
transformations. We express how the difference between the two can be
compensated by diffeomorphic transformations. This is well known in the
framework of String Theory but in the particular case of spaces. Indeed,
the Polyakov formalism describes world-sheets in terms of two-dimensional
conformal field theory. On the other hand, B. Zumino had shown that a classical
four-dimensional Weyl-invariant field theory restricted to live in Minkowski
space leads to an SO(2,4)-invariant field theory. We extend Zumino's result to
relate Weyl and SO(2,d) symmetries in arbitrary conformally flat spaces (CFS).
This allows us to assert that a classical -invariant field does not
distinguish, at least locally, between two different -dimensional CFSs.Comment: 5 pages, no figures. There are slight modifications to match with the
published versio
Mixed-symmetry tensor conserved currents and AdS/CFT correspondence
We present the full list of conserved currents built of two massless spinor
fields in Minkowski space and their derivatives multiplied by Clifford algebra
elements. The currents have particular mixed-symmetry type described by Young
diagrams with one row and one column of arbitrary lengths and heights. Along
with Yukawa-like totally antisymmetric currents the complete set of constructed
currents exactly matches the spectrum of AdS mixed-symmetry fields arising in
the generalized Flato-Fronsdal theorem for two spinor singletons. As a
by-product, we formulate and study general properties of primary fields and
conserved currents of mixed-symmetry type.Comment: 17 pages; v2: typos corrected, clarifications and refs added; v3:
more explanations and refs added; contribution to the J.Phys.A special volume
on "Higher Spin Theories and AdS/CFT" edited by Matthias Gaberdiel and
Mikhail Vasilie
Construction of Infrared Finite Observables in N=4 Super Yang-Mills Theory
In this paper we give all the details of the calculation that we presented in
our previous paper ArXiv:0908.0387 where the infrared structure of the MHV
gluon amplitudes in the planar limit for super Yang-Mills theory
was considered in the next-to-leading order of perturbation theory. Explicit
cancellation of the infrared divergencies in properly defined inclusive
cross-sections is demonstrated first in a toy model example of "conformal QED"
and then in the real SYM theory. We give the full-length details
both for the calculation of the real emission and for the diagrams with
splitting in initial and final states. The finite parts for some inclusive
differential cross-sections are presented in an analytical form. In general,
contrary to the virtual corrections, they do not reveal any simple structure.
An example of the finite part containing just the log functions is presented.
The dependence of inclusive cross-section on the external scale related to the
definition of asymptotic states is discussed.Comment: 49 pages, LATEX, 6 eps figures; Minor changes, Refs adde
The Higher Spin/Vector Model Duality
This paper is mainly a review of the dualities between Vasiliev's higher spin
gauge theories in AdS4 and three dimensional large N vector models, with focus
on the holographic calculation of correlation functions of higher spin
currents. We also present some new results in the computation of parity odd
structures in the three point functions in parity violating Vasiliev theories.Comment: 55 pages, 1 figure. Contribution to J. Phys. A special volume on
"Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasiliev.
v2: references adde
Black holes in three dimensional higher spin gravity: A review
We review recent progress in the construction of black holes in three
dimensional higher spin gravity theories. Starting from spin-3 gravity and
working our way toward the theory of an infinite tower of higher spins coupled
to matter, we show how to harness higher spin gauge invariance to consistently
generalize familiar notions of black holes. We review the construction of black
holes with conserved higher spin charges and the computation of their partition
functions to leading asymptotic order. In view of the AdS/CFT correspondence as
applied to certain vector-like conformal field theories with extended conformal
symmetry, we successfully compare to CFT calculations in a generalized Cardy
regime. A brief recollection of pertinent aspects of ordinary gravity is also
given.Comment: 49 pages, harvmac, invited contribution to J. Phys. A special volume
on "Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M.
Vasilie
Holography, Unfolding and Higher-Spin Theory
Holographic duality is argued to relate classes of models that have
equivalent unfolded formulation, hence exhibiting different space-time
visualizations for the same theory. This general phenomenon is illustrated by
the higher-spin gauge theory shown to be dual to the theory of 3d
conformal currents of all spins interacting with 3d conformal higher-spin
fields of Chern-Simons type. Generally, the resulting 3d boundary conformal
theory is nonlinear, providing an interacting version of the 3d boundary sigma
model conjectured by Klebanov and Polyakov to be dual to the HS theory
in the large limit. Being a gauge theory it escapes the conditions of the
theorem of Maldacena and Zhiboedov, which force a 3d boundary conformal theory
to be free. Two reductions of particular higher-spin gauge theories where
boundary higher-spin gauge fields decouple from the currents and which have
free boundary duals are identified. Higher-spin holographic duality is also
discussed for the cases of and duality between higher-spin
theories and nonrelativistic quantum mechanics. In the latter case it is shown
in particular that () geometry in the higher-spin setup is dual to
the (inverted) harmonic potential in the quantum-mechanical setup.Comment: 57 pages, V2: Acknowledgements, references, comments, clarifications
and new section on reductions of particular HS theories associated with free
boundary theories are added. Typos corrected, V3. Minor corrections:
clarification in section 9 is added and typos correcte
Form factors at strong coupling via a Y-system
We compute form factors in planar N=4 Super Yang-Mills at strong coupling.
Namely we consider the overlap between an operator insertion and 2n gluons.
Through the gauge/string duality these are given by minimal surfaces in AdS
space. The surfaces end on an infinite periodic sequence of null segments at
the boundary of AdS. We consider surfaces that can be embedded in AdS_3. We
derive set of functional equations for the cross ratios as functions of the
spectral parameter. These equations are of the form of a Y-system. The integral
form of the Y-system has Thermodynamics Bethe Ansatz form. The area is given by
the free energy of the TBA system or critical value of Yang-Yang functional. We
consider a restricted set of operators which have small conformal dimension
Minimal Model Holography
We review the duality relating 2d W_N minimal model CFTs, in a large N 't
Hooft like limit, to higher spin gravitational theories on AdS_3.Comment: 54 pages, 1 figure; Contribution to J. Phys. A special volume on
"Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasiliev.
v2. minor change
T-systems and Y-systems in integrable systems
The T and Y-systems are ubiquitous structures in classical and quantum
integrable systems. They are difference equations having a variety of aspects
related to commuting transfer matrices in solvable lattice models, q-characters
of Kirillov-Reshetikhin modules of quantum affine algebras, cluster algebras
with coefficients, periodicity conjectures of Zamolodchikov and others,
dilogarithm identities in conformal field theory, difference analogue of
L-operators in KP hierarchy, Stokes phenomena in 1d Schr\"odinger problem,
AdS/CFT correspondence, Toda field equations on discrete space-time, Laplace
sequence in discrete geometry, Fermionic character formulas and combinatorial
completeness of Bethe ansatz, Q-system and ideal gas with exclusion statistics,
analytic and thermodynamic Bethe ans\"atze, quantum transfer matrix method and
so forth. This review article is a collection of short reviews on these topics
which can be read more or less independently.Comment: 156 pages. Minor corrections including the last paragraph of sec.3.5,
eqs.(4.1), (5.28), (9.37) and (13.54). The published version (JPA topical
review) also needs these correction