514 research outputs found
Sum rules and three point functions
Sum rules constraining the R-current spectral densities are derived
holographically for the case of D3-branes, M2-branes and M5-branes all at
finite chemical potentials. In each of the cases the sum rule relates a certain
integral of the spectral density over the frequency to terms which depend both
on long distance physics, hydrodynamics and short distance physics of the
theory. The terms which which depend on the short distance physics result from
the presence of certain chiral primaries in the OPE of two R-currents which are
turned on at finite chemical potential. Since these sum rules contain
information of the OPE they provide an alternate method to obtain the structure
constants of the two R-currents and the chiral primary. As a consistency check
we show that the 3 point function derived from the sum rule precisely matches
with that obtained using Witten diagrams.Comment: 41 page
E7(7) invariant Lagrangian of d=4 N=8 supergravity
We present an E7(7) invariant Lagrangian that leads to the equations of
motion of d=4 N=8 supergravity without using Lagrange multipliers. The
superinvariance of this new action and the closure of the supersymmetry algebra
are proved explicitly for the terms that differ from the Cremmer--Julia
formulation. Since the diffeomorphism symmetry is not realized in the standard
way on the vector fields, we switch to the Hamiltonian formulation in order to
prove the invariance of the E7(7) invariant action under general coordinate
transformations. We also construct the conserved E7(7)-Noether current of
maximal supergravity and we conclude with comments on the implications of this
manifest off-shell E7(7)-symmetry for quantizing d=4 N=8 supergravity, in
particular on the E7(7)-action on phase space.Comment: 45 pages, references adde
Counterterms vs. Dualities
We investigate and clarify the mutual compatibility of the higher order
corrections arising in supergravity and string theory effective actions and the
non-linear duality symmetries of these theories. Starting from a conventional
tree level action leading to duality invariant equations of motion, we show how
to accommodate duality invariant counterterms given as functionals of both
electric and magnetic fields in a perturbative expansion, and to deduce from
them a non-polynomial bona fide action satisfying the Gaillard-Zumino
constraint. There exists a corresponding consistency constraint in the
non-covariant Henneaux-Teitelboim formalism which ensures that one can always
restore diffeomorphism invariance by perturbatively solving this functional
identity. We illustrate how this procedure works for the R^2 \nabla F \nabla F
and F^4 counterterms in Maxwell theory.Comment: 15 page
Holography for chiral scale-invariant models
Deformation of any d-dimensional conformal field theory by a constant null
source for a vector operator of dimension (d + z -1) is exactly marginal with
respect to anisotropic scale invariance, of dynamical exponent z. The
holographic duals to such deformations are AdS plane waves, with z=2 being the
Schrodinger geometry. In this paper we explore holography for such chiral
scale-invariant models. The special case of z=0 can be realized with gravity
coupled to a scalar, and is of particular interest since it is related to a
Lifshitz theory with dynamical exponent two upon dimensional reduction. We show
however that the corresponding reduction of the dual field theory is along a
null circle, and thus the Lifshitz theory arises upon discrete light cone
quantization of an anisotropic scale invariant field theory.Comment: 62 pages; v2, published version, minor improvements and references
adde
Gravity duals of supersymmetric gauge theories on three-manifolds
We study gravity duals to a broad class of N=2 supersymmetric gauge theories
defined on a general class of three-manifold geometries. The gravity
backgrounds are based on Euclidean self-dual solutions to four-dimensional
gauged supergravity. As well as constructing new examples, we prove in general
that for solutions defined on the four-ball the gravitational free energy
depends only on the supersymmetric Killing vector, finding a simple closed
formula when the solution has U(1) x U(1) symmetry. Our result agrees with the
large N limit of the free energy of the dual gauge theory, computed using
localization. This constitutes an exact check of the gauge/gravity
correspondence for a very broad class of gauge theories with a large N limit,
defined on a general class of background three-manifold geometries.Comment: 74 pages, 2 figures; v2: minor change
Anomalous Dimensions of Non-Chiral Operators from AdS/CFT
Non-chiral operators with positive anomalous dimensions can have interesting
applications to supersymmetric model building. Motivated by this, we develop a
new method for obtaining the anomalous dimensions of non-chiral double-trace
operators in N=1 superconformal field theories (SCFTs) with weakly-coupled AdS
duals. Via the Hamiltonian formulation of AdS/CFT, we show how to directly
compute the anomalous dimension as a bound state energy in the gravity dual.
This simplifies previous approaches based on the four-point function and the
OPE. We apply our method to a class of effective AdS5 supergravity models, and
we find that the binding energy can have either sign. If such models can be UV
completed, they will provide the first calculable examples of SCFTs with
positive anomalous dimensions.Comment: 38 pages, 2 figures, refs adde
An overview of new supersymmetric gauge theories with 2-form gauge potentials
An overview of new 4d supersymmetric gauge theories with 2-form gauge
potentials constructed by various authors during the past five years is given.
The key role of three particular types of interaction vertices is emphasized.
These vertices are used to develop a connecting perspective on the new models
and to distinguish between them. One example is presented in detail to
illustrate characteristic features of the models. A new result on couplings of
2-form gauge potentials to Chern-Simons forms is presented.Comment: 11 pages; to appear in the proceedings of NATO ARW "Noncommutative
structures in mathematics and physics" (Kiev 09/00); table in section 3
correcte
Correlation Functions in 2-Dimensional Integrable Quantum Field Theories
In this talk I discuss the form factor approach used to compute correlation
functions of integrable models in two dimensions. The Sinh-Gordon model is our
basic example. Using Watson's and the recursive equations satisfied by matrix
elements of local operators, I present the computation of the form factors of
the elementary field and the stress-energy tensor of
the theory.Comment: 19pp, LATEX version, (talk at Como Conference on ``Integrable Quantum
Field Theories''
N=8 Counterterms and E7(7) Current Conservation
We examine conservation of the E7(7) Noether-Gaillard-Zumino current in the
presence of N=8 supergravity counterterms using the momentum space helicity
formalism, which significantly simplifies the calculations. The main result is
that the 4-point counterterms at any loop order L are forbidden by the E7(7)
current conservation identity. We also clarify the relation between linearized
and full non-linear superinvariants as candidate counterterms. This enables us
to show that all n-point counterterms at L=7, 8 are forbidden since they
provide a non-linear completions of the 4-point ones. This supports and
exemplifies our general proof in arXiv:1103.4115 of perturbative UV finiteness
of N=8 supergravity.Comment: 18 page
Writing CFT correlation functions as AdS scattering amplitudes
We explore the Mellin representation of conformal correlation functions
recently proposed by Mack. Examples in the AdS/CFT context reinforce the
analogy between Mellin amplitudes and scattering amplitudes. We conjecture a
simple formula relating the bulk scattering amplitudes to the asymptotic
behavior of Mellin amplitudes and show that previous results on the flat space
limit of AdS follow from our new formula. We find that the Mellin amplitudes
are particularly useful in the case of conformal gauge theories in the planar
limit. In this case, the four point Mellin amplitudes are meromorphic functions
whose poles and their residues are entirely determined by two and three point
functions of single-trace operators. This makes the Mellin amplitudes the ideal
objects to attempt the conformal bootstrap program in higher dimensions.Comment: 23 pages + appendice
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