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 $O(6)$ $\sigma$-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

Digital equalization of time-delay array receivers on coherent laser communications

© [2017 Optical Society of America.]. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited.Field conjugation arrays use adaptive combining techniques on multi-aperture receivers to improve the performance of coherent laser communication links by mitigating the consequences of atmospheric turbulence on the down-converted coherent power. However, this motivates the use of complex receivers as optical signals collected by different apertures need to be adaptively processed, co-phased, and scaled before they are combined. Here, we show that multiple apertures, coupled with optical delay lines, combine retarded versions of a signal at a single coherent receiver, which uses digital equalization to obtain diversity gain against atmospheric fading. We found in our analysis that, instead of field conjugation arrays, digital equalization of time-delay multi-aperture receivers is a simpler and more versatile approach to accomplish reduction of atmospheric fading.Peer ReviewedPostprint (author's final draft

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

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

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

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