50 research outputs found
TASI lectures on AdS/CFT
We introduce the AdS/CFT correspondence as a natural extension of QFT in a
fixed AdS background. We start by reviewing some general concepts of CFT,
including the embedding space formalism. We then consider QFT in a fixed AdS
background and show that one can define boundary operators that enjoy very
similar properties as in a CFT, except for the lack of a stress tensor.
Including a dynamical metric in AdS generates a boundary stress tensor and
completes the CFT axioms. We also discuss some applications of the bulk
geometric intuition to strongly coupled QFT. Finally, we end with a review of
the main properties of Mellin amplitudes for CFT correlation functions and
their uses in the context of AdS/CFT.Comment: 63 pages, 7 figure
String scattering in flat space and a scaling limit of Yang-Mills correlators
We use the flat space limit of the AdS/CFT correspondence to derive a simple
relation between the 2 to 2 scattering amplitude of massless string states in
type IIB superstring theory on ten-dimensional Minkowski space and a scaling
limit of the N=4 super Yang-Mills four point functions. We conjecture that this
relation holds non-perturbatively and at arbitrarily high energy.Comment: 13 page
Colliders and conformal interfaces
We set up a scattering experiment of matter against an impurity which
separates two generic one-dimensional critical quantum systems. We compute the
flux of reflected and transmitted energy, thus defining a precise measure of
the transparency of the interface between the related two-dimensional conformal
field theories. If the largest symmetry algebra is Virasoro, we find that the
reflection and transmission coefficients are independent of the details of the
initial state, and are fixed in terms of the central charges and of the
two-point function of the displacement operator. The situation is more
elaborate when extended symmetries are present. Positivity of the total energy
flux at infinity imposes bounds on the coefficient of the two-point function of
the displacement operator, which controls the free-energy cost of a small
deformation of the interface. Finally, we study out-of-equilibrium steady
states of a critical system connecting two reservoirs at different
temperatures. In the absence of extended symmetries, our result implies that
the energy flux across an impurity is proportional to the difference of the
squared temperatures and controlled by the reflection coefficient.Comment: 32+10 pages, 14 figures, a discussion on non-equilibrium steady
states adde
Bootstrapping QCD: the Lake, the Peninsula and the Kink
We consider the S-matrix bootstrap of four dimensional scattering amplitudes
with symmetry and no bound-states. We explore the allowed space of
scattering lengths which parametrize the interaction strength at threshold of
the various scattering channels. Next we consider an application of this
formalism to pion physics. A signature of pions is that they are derivatively
coupled leading to (chiral) zeros in their scattering amplitudes. In this work
we explore the multi-dimensional space of chiral zeros positions, scattering
length values and resonance mass values. Interestingly, we encounter lakes,
peninsulas and kinks depending on which sections of this intricate
multi-dimensional space we consider. We discuss the remarkable location where
QCD seems to lie in these plots, based on various experimental and theoretical
expectations.Comment: 6 pages, 7 figure
Spinning AdS Propagators
We develop the embedding formalism to describe symmetric traceless tensors in
Anti-de Sitter space. We use this formalism to construct the bulk-to-bulk
propagator of massive spin J fields and check that it has the expected short
distance and massless limits. We also and a split representation for the
bulk-to-bulk propagator, by writing it as an integral over the boundary of the
product of two bulk-to-boundary propagators. We exemplify the use of this
representation with the computation of the conformal partial wave decomposition
of Witten diagrams. In particular, we determine the Mellin amplitude associated
to AdS graviton exchange between minimally coupled scalars of general
dimension, including the regular part of the amplitude.Comment: 48 pages, 6 figure
The role of leading twist operators in the Regge and Lorentzian OPE limits
We study two kinematical limits, the Regge limit and the Lorentzian OPE
limit, of the four-point function of the stress-tensor multiplet in Super
Yang-Mills at weak coupling. We explain how both kinematical limits are
controlled by the leading twist operators. We use the known expression of the
four-point function up to three loops, to extract the pomeron residue at
next-to-leading order. Using this data and the known form of pomeron spin up to
next-to-leading order, we predict the behaviour of the four-point function in
the Regge limit at higher loops. Specifically, we determine the leading log
behaviour at any loop order and the next-to-leading log at four loops. Finally,
we check the consistency of our results with conformal Regge theory. This leads
us to predict the behaviour around of the OPE coefficient of the spin
leading twist operator in the OPE of two chiral primary operators.Comment: 22+14 page