42 research outputs found

    Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c=1 Matrix Models

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    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

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    We study the S-matrix of planar N=4\mathcal{N}=4 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 N2{}^2MHV 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 nn-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

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    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 nn-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 N=4{\cal N}=4 SYM

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    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 N=4{\cal N}=4 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 A1(1)A_1^{(1)}, A2(1)A_2^{(1)} and A2(2)A_2^{(2)} models

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    We consider the YY-systems satisfied by the A1(1)A_1^{(1)}, A2(1)A_2^{(1)}, A2(2)A_2^{(2)} 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 eiλe^{i\lambda} with the crossing parameter λ\lambda 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 YY-systems for the finite-size 1N\frac 1N corrections to the groundstate eigenvalue following the methods of Kl\"umper and Pearce. The resulting expressions for c−24Δc-24\Delta, where cc is the central charge and Δ\Delta 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 A2(1)A_2^{(1)} model
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