42 research outputs found
Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c=1 Matrix Models
We address the nonperturbative structure of topological strings and c=1
matrix models, focusing on understanding the nature of instanton effects
alongside with exploring their relation to the large-order behavior of the 1/N
expansion. We consider the Gaussian, Penner and Chern-Simons matrix models,
together with their holographic duals, the c=1 minimal string at self-dual
radius and topological string theory on the resolved conifold. We employ Borel
analysis to obtain the exact all-loop multi-instanton corrections to the free
energies of the aforementioned models, and show that the leading poles in the
Borel plane control the large-order behavior of perturbation theory. We
understand the nonperturbative effects in terms of the Schwinger effect and
provide a semiclassical picture in terms of eigenvalue tunneling between
critical points of the multi-sheeted matrix model effective potentials. In
particular, we relate instantons to Stokes phenomena via a hyperasymptotic
analysis, providing a smoothing of the nonperturbative ambiguity. Our
predictions for the multi-instanton expansions are confirmed within the
trans-series set-up, which in the double-scaling limit describes
nonperturbative corrections to the Toda equation. Finally, we provide a
spacetime realization of our nonperturbative corrections in terms of toric
D-brane instantons which, in the double-scaling limit, precisely match
D-instanton contributions to c=1 minimal strings.Comment: 71 pages, 14 figures, JHEP3.cls; v2: added refs, minor change
Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
We study the S-matrix of planar supersymmetric Yang-Mills
theory when external momenta are restricted to a two-dimensional subspace of
Minkowski space. We find significant simplifications and new, interesting
structures for tree and loop amplitudes in two-dimensional kinematics; in
particular, the higher-point amplitudes we consider can be obtained from those
with lowest-points by a collinear uplifting. Based on a compact formula for
one-loop NMHV amplitudes, we use an equation proposed previously to
compute, for the first time, the complete two-loop NMHV and three-loop MHV
octagons, which we conjecture to uplift to give the full -point amplitudes
up to simpler logarithmic terms or dilogarithmic terms.Comment: v2: important typos fixed. 38 pages, 4 figures. An ancillary file
with two-loop NMHV "remainders" for n=10,12 can be found at
http://www.nbi.dk/~schuot/nmhvremainders.zi
Non-factorizable corrections to W-pair production: methods and analytic results
In this paper we present two methods to evaluate non-factorizable corrections
to pair-production of unstable particles. The methods are illustrated in detail
for W-pair-mediated four-fermion production. The results are valid a few widths
above threshold, but not at threshold. One method uses the decomposition of
-point scalar functions for virtual and real photons, and can therefore be
generalized to more complicated final states than four fermions. The other
technique is an elaboration on a method known from the literature and serves as
a useful check. Applications to other processes than W-pair production are
briefly mentioned.Comment: 45 pages, LaTeX2e, 4 postscript figures, uses axodraw.st
On the finite size corrections of anti-ferromagnetic anomalous dimensions in SYM
Non-linear integral equations derived from Bethe Ansatz are used to evaluate
finite size corrections to the highest (i.e. {\it anti-ferromagnetic}) and
immediately lower anomalous dimensions of scalar operators in SYM.
In specific, multi-loop corrections are computed in the SU(2) operator
subspace, whereas in the general SO(6) case only one loop calculations have
been finalised. In these cases, the leading finite size corrections are given
by means of explicit formul\ae and compared with the exact numerical
evaluation. In addition, the method here proposed is quite general and
especially suitable for numerical evaluations.Comment: 38 pages, Latex revised version: draft formulae indicator deleted,
one reference added, typos corrected, few minor text modification
Groundstate finite-size corrections and dilogarithm identities for the twisted , and models
We consider the -systems satisfied by the , , vertex and loop models at roots of unity with twisted boundary conditions on the cylinder. The vertex models are the 6-, 15- and Izergin-Korepin 19-vertex models respectively. The corresponding loop models are the dense, fully packed and dilute Temperley-Lieb loop models respectively. For all three models, our focus is on roots of unity values of with the crossing parameter corresponding to the principal and dual series of these models. Converting the known functional equations to nonlinear integral equations in the form of Thermodynamic Bethe Ansatz (TBA) equations, we solve the -systems for the finite-size corrections to the groundstate eigenvalue following the methods of Kl\"umper and Pearce. The resulting expressions for , where is the central charge and is the conformal weight associated with the groundstate, are simplified using various dilogarithm identities. Our analytic results are in agreement with previous results obtained by different methods and are new for the dual series of the model