257 research outputs found
Four-point functions of all-different-weight chiral primary operators in the supergravity approximation
Recently a Mellin-space formula was conjectured for the form of correlation
functions of BPS operators in planar SYM in the strong 't
Hooft coupling limit. In this work we report on the computation of two
previously unknown four-point functions of operators with weights and , from the effective type-IIB supergravity
action using AdS/CFT. These correlators are novel: they are the first
correlators with all-different weights and in particular
is the first next-next-next-to-extremal correlator to ever have been computed.
We also present simplifications of the known algorithm, without which these
computations could not have been executed without considerable computer power.
The main simplifications we found are present in the computation of the
exchange Lagrangian and in the computation of tensors. After bringing our
results in the appropriate form we successfully corroborate the recently
conjectured formula.Comment: 20+23 pages, 3 figures; v2: published versio
Quantum Spectral Curve for the eta-deformed AdS_5xS^5 superstring
The spectral problem for the superstring and
its dual planar maximally supersymmetric Yang-Mills theory can be efficiently
solved through a set of functional equations known as the quantum spectral
curve. We discuss how the same concepts apply to the -deformed superstring, an integrable deformation of the superstring with quantum group symmetry. This model can
be viewed as a trigonometric version of the
superstring, like the relation between the XXZ and XXX spin chains, or the
sausage and the sigma models for instance. We derive the quantum
spectral curve for the -deformed string by reformulating the
corresponding ground-state thermodynamic Bethe ansatz equations as an analytic
system, and map this to an analytic system which upon suitable gauge
fixing leads to a system -- the quantum spectral curve. We
then discuss constraints on the asymptotics of this system to single out
particular excited states. At the spectral level the -deformed string and
its quantum spectral curve interpolate between the superstring and a superstring on "mirror" ,
reflecting a more general relationship between the spectral and thermodynamic
data of the -deformed string. In particular, the spectral problem of the
mirror string, and the thermodynamics of the
undeformed string, are described by a second
rational limit of our trigonometric quantum spectral curve, distinct from the
regular undeformed limit.Comment: 32+37 pages; 6 figures. v2: added reference
Four-point functions of 1/2-BPS operators of any weights in the supergravity approximation
We present the computation of all the correlators of 1/2-BPS operators in
SYM with weights up to 8 as well as some very high-weight
correlation functions from the effective supergravity action. The computation
is done by implementing the recently developed simplified algorithm in
combination with the harmonic polynomial formalism. We provide a database of
these results attached to this publication and additionally check for almost
all of the functions in this database that they agree with the conjecture on
their Mellin-space form.Comment: 6 pages, database included; v2: database extended, appendix adde
Towards 4-point correlation functions of any 1/2-BPS operators from supergravity
The quartic effective action for Kaluza-Klein modes that arises upon
compactification of type IIB supergravity on the five-sphere S^5 is a starting
point for computing the four-point correlation functions of arbitrary weight
1/2-BPS operators in N=4 super Yang-Mills theory in the supergravity
approximation. The apparent structure of this action is rather involved, in
particular it contains quartic terms with four derivatives which cannot be
removed by field redefinitions. By exhibiting intricate identities between
certain integrals involving spherical harmonics of S^5 we show that the net
contribution of these four-derivative terms to the effective action vanishes.
Our result is in agreement with and provides further support to the recent
conjecture on the Mellin space representation of the four-point correlation
function of any 1/2-BPS operators in the supergravity approximation.Comment: 12 page
The deformed Inozemtsev spin chain
We present two new quantum-integrable models with long-range spin
interactions. First, a partially isotropic (xxz-type) spin chain that unifies
the Inozemtsev and partially isotropic Haldane-Shastry chains. Its short-range
limit is a variant of the twisted Heisenberg xxz chain. Second, a quantum
many-body system that generalises the elliptic Ruijsenaars model by including
spins with interactions mediated by dynamical R-matrices. It unifies the
elliptic Calogero-Sutherland and trigonometric Ruijsenaars-Macdonald models
with spins, and gives our spin chain by 'freezing'.Comment: 8 pages, 1 figur
Periodic solutions of the non-chiral intermediate Heisenberg ferromagnet equation described by elliptic spin Calogero-Moser dynamics
We present a class of periodic solutions of the non-chiral intermediate
Heisenberg ferromagnet (ncIHF) equation, which was recently introduced by the
authors together with Langmann as a classical, continuum limit of an
Inozemtsev-type spin chain. These exact analytic solutions are constructed via
a spin-pole ansatz written in terms of certain elliptic functions. The
dynamical parameters in our solutions solve an elliptic spin Calogero-Moser
(CM) system subject to certain constraints. In the course of our construction,
we establish a novel B\"acklund transformation for this constrained elliptic
spin CM system.Comment: 37 pages, 3 figure
Quantum Trace Formulae for the Integrals of the Hyperbolic Ruijsenaars-Schneider model
We conjecture the quantum analogue of the classical trace formulae for the
integrals of motion of the quantum hyperbolic Ruijsenaars-Schneider model. This
is done by departing from the classical construction where the corresponding
model is obtained from the Heisenberg double by the Poisson reduction
procedure. We also discuss some algebraic structures associated to the Lax
matrix in the classical and quantum theory which arise upon introduction of the
spectral parameter.Comment: 35 pages, v2 as accepted by JHE
Regge spectroscopy of higher twist states in supersymmetric Yang-Mills theory
We study a family of higher-twist Regge trajectories in
supersymmetric Yang-Mills theory using the Quantum Spectral Curve. We explore
the many-sheeted Riemann surface connecting the different trajectories and show
the interplay between the degenerate non-local operators known as horizontal
trajectories. We resolve their degeneracy analytically by computing the first
non-trivial order of the Regge intercept at weak coupling, which exhibits new
behaviour: it depends linearly on the coupling. This is consistent with our
numerics, which interpolate all the way to strong coupling.Comment: main text: 6 pages, 5 figures; supplemental material: 17 pages, 3
figures, 3 table
- …