33 research outputs found
The Resurgence of the Cusp Anomalous Dimension
This work addresses the resurgent properties of the cusp anomalous
dimension's strong coupling expansion, obtained from the integral
Beisert-Eden-Staudacher (BES) equation. This expansion is factorially
divergent, and its first nonperturbative corrections are related to the mass
gap of the -model. The factorial divergence can also be analysed
from a resurgence perspective. Building on the work of Basso and Korchemsky, a
transseries ansatz for the cusp anomalous dimension is proposed and the
corresponding expected large-order behaviour studied. One finds
non-perturbative phenomena in both the positive and negative real coupling
directions, which need to be included to address the analyticity conditions
coming from the BES equation. After checking the resurgence structure of the
proposed transseries, it is shown that it naturally leads to an unambiguous
resummation procedure, furthermore allowing for a strong/weak coupling
interpolation.Comment: 12 pages, 5 figure
Nonperturbative Ambiguities and the Reality of Resurgent Transseries
In a wide range of quantum theoretical settings -- from quantum mechanics to
quantum field theory, from gauge theory to string theory -- singularities in
the complex Borel plane, usually associated to instantons or renormalons,
render perturbation theory ill-defined as they give rise to nonperturbative
ambiguities. These ambiguities are associated to choices of an integration
contour in the resummation of perturbation theory, along (singular) Stokes
directions in the complex Borel plane (rendering perturbative expansions
non-Borel summable along any Stokes line). More recently, it has been shown
that the proper framework to address these issues is that of resurgent analysis
and transseries. In this context, the cancelation of all nonperturbative
ambiguities is shown to be a consequence of choosing the transseries median
resummation as the appropriate family of unambiguous real solutions along the
coupling-constant real axis. While the median resummation is easily implemented
for one-parameter transseries, once one considers more general multi-parameter
transseries the procedure becomes highly dependent upon properly understanding
Stokes transitions in the complex Borel plane. In particular, all Stokes
coefficients must now be known in order to explicitly implement multi-parameter
median resummations. In the cases where quantum-theoretical physical
observables are described by resurgent functions and transseries, the methods
described herein show how one may cancel nonperturbative ambiguities, and
define these observables nonperturbatively starting out from perturbation
theory. Along the way, structural results concerning resurgent transseries are
also obtained.Comment: 62 pages, 4 figures; v2: corrected typos, added small discussion on
topological sectors, two new figure
Notes on Collective Field Theory of Matrix and Spin Calogero Models
Matrix models and related Spin-Calogero-Sutherland models are of major
relevance in a variety of subjects, ranging from condensed matter physics to
QCD and low dimensional string theory. They are characterized by integrability
and exact solvability. Their continuum, field theoretic representations are
likewise of definite interest. In this paper we describe various continuum,
field theoretic representations of these models based on bosonization and
collective field theory techniques. We compare various known representations
and describe some nontrivial applications.Comment: 36 pages, no figures v2: references added, a version to appear in the
special issue of JPhysA (edited by G Dunne, J Feinberg and P Dorey)
v3:comments changed, paper identical to v
Massless L\"uscher Terms and the Limitations of the AdS3 Asymptotic Bethe Ansatz
In AdS5/CFT4 integrability the Bethe ansatz gives the spectrum of long
strings, accurate up to exponentially small corrections. This is no longer true
in AdS3, as we demonstrate here by studying Luscher F-terms with a massless
particle running in the loop. We apply this to the classic test of Hernandez &
Lopez, in which the su(2) sector Bethe equations (including one-loop dressing
phase) should match the semiclassical string theory result for a circular
spinning string. These calculations did not agree in AdS3xS3xT4, and we show
that the sum of all massless Luscher F-terms can reproduce the difference.Comment: 15 pages, 1 figure; v2:references, typos and clarification
An improved AFS phase for AdS3 string integrability
We propose a number of modifications to the classical term in the dressing
phase for integrable strings in AdS3 x S3 x S3 x S1, and check these against
existing perturbative calculations, crossing symmetry, and the semiclassical
limit of the Bethe equations. The principal change is that the phase for
different masses should start with a term Q_1 Q_2, like the one-loop AdS3
dressing phase, rather than Q_2 Q_3 as for the original AdS5 AFS phase.Comment: 7 page
The Resurgence of Instantons in String Theory
Nonperturbative effects in string theory are usually associated to D-branes.
In many cases it can be explicitly shown that D-brane instantons control the
large-order behavior of string perturbation theory, leading to the well-known
(2g)! growth of the genus expansion. This paper presents a detailed treatment
of nonperturbative solutions in string theory, and their relation to the
large-order behavior of perturbation theory, making use of transseries and
resurgent analysis. These are powerful techniques addressing general
nonperturbative contributions within non-linear systems, which are developed at
length herein as they apply to string theory. The cases of topological strings,
the Painleve I equation describing 2d quantum gravity, and the quartic matrix
model, are explicitly addressed. These results generalize to minimal strings
and general matrix models. It is shown that, in order to completely understand
string theory at a fully nonperturbative level, new sectors are required beyond
the standard D-brane sector.Comment: 108 pages; v2,v3: references added; v4: improved pedagogical content,
final version for CNTP; v5: typos correcte
Quantum Strings and the AdS4/CFT3 Interpolating Function
The existence of a nontrivial interpolating function h(\lambda) is one of the
novel features of the new AdS4/CFT3 correspondence involving ABJM theory. At
strong coupling, most of the investigation of semiclassical effects so far has
been for strings in the AdS4 sector. Several cutoff prescriptions have been
proposed, leading to different predictions for the constant term in the
expansion h(\lambda)=\sqrt{\lambda/2} + c + ... . We calculate quantum
corrections for giant magnons, using the algebraic curve, and show by comparing
to the dispersion relation that the same prescriptions lead to the same values
of c in this CP3 sector. We then turn to finite-J effects, where a comparison
with the Luescher F-term correction shows a mismatch for one of the three sum
prescriptions. We also compute some dyonic and higher F-terms for future
comparisons.Comment: 30 pages, 1 figure, 1 table. v2 has minor improvements to the text,
and extra references. v3 has further textual changes, version to appear in
JHE
Vibrating giant spikes and the large-winding sector
The single spike is a rigidly rotating classical string configuration closely
related to the giant magnon. We calculate bosonic and fermionic modes of this
solution, from which we see that it is not supersymmetric. It can be viewed as
an excitation above a hoop of string wound around the equator, in the same
sense that the magnon is an excitation above an orbiting point particle. We
find the operator which plays the role of the Hamiltonian for this sector,
which compared to the magnon's E-J has the angular momentum replaced by a
winding charge. The single spike solution is unstable, and we use the modes to
attempt a semi-classical computation of its lifetime.Comment: 30 pages, 5 figures. v2 has extra references and thank
Poisson Structures of Calogero-Moser and Ruijsenaars-Schneider Models
We examine the Hamiltonian structures of some Calogero-Moser and
Ruijsenaars-Schneider N-body integrable models. We propose explicit
formulations of the bihamiltonian structures for the discrete models, and
field-theoretical realizations of these structures. We discuss the relevance of
these realizations as collective-field theory for the discrete models.Comment: 15 pages, no figures; v2 references added, typos correcte