54 research outputs found
An A_r threesome: Matrix models, 2d CFTs and 4d N=2 gauge theories
We explore the connections between three classes of theories: A_r quiver
matrix models, d=2 conformal A_r Toda field theories and d=4 N=2 supersymmetric
conformal A_r quiver gauge theories. In particular, we analyse the quiver
matrix models recently introduced by Dijkgraaf and Vafa and make detailed
comparisons with the corresponding quantities in the Toda field theories and
the N=2 quiver gauge theories. We also make a speculative proposal for how the
matrix models should be modified in order for them to reproduce the instanton
partition functions in quiver gauge theories in five dimensions.Comment: 43 pages; v2: minor typos corrected, reference added. v3: Added
clarifying discussions in sections 4.1 and 5.1; typos correcte
The Dynamics of Knotted Strings Attached to D-Branes
We extend the general solution to the Cauchy problem for the relativistic
closed string (Phys. Lett. B404 (1997) 57-65, hep-th/9704084) to the case of
open strings attached to Dp-branes, including the cases where the initial data
has a knotlike topology. We use this extended solution to derive intrinsic
dynamical properties of open and closed relativistic strings attached to
Dp-branes. We also study the singularity structure and the oscillating periods
of this extended solution.Comment: 9 pages, 4 figures, Plain Te
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
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
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
Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP2
The holomorphic anomaly equations describe B-model closed topological strings
in Calabi-Yau geometries. Having been used to construct perturbative
expansions, it was recently shown that they can also be extended past
perturbation theory by making use of resurgent transseries. These yield formal
nonperturbative solutions, showing integrability of the holomorphic anomaly
equations at the nonperturbative level. This paper takes such constructions one
step further by working out in great detail the specific example of topological
strings in the mirror of the local CP2 toric Calabi-Yau background, and by
addressing the associated (resurgent) large-order analysis of both perturbative
and multi-instanton sectors. In particular, analyzing the asymptotic growth of
the perturbative free energies, one finds contributions from three different
instanton actions related by Z_3 symmetry, alongside another action related to
the Kahler parameter. Resurgent transseries methods then compute, from the
extended holomorphic anomaly equations, higher instanton sectors and it is
shown that these precisely control the asymptotic behavior of the perturbative
free energies, as dictated by resurgence. The asymptotic large-order growth of
the one-instanton sector unveils the presence of resonance, i.e., each
instanton action is necessarily joined by its symmetric contribution. The
structure of different resurgence relations is extensively checked at the
numerical level, both in the holomorphic limit and in the general
nonholomorphic case, always showing excellent agreement with transseries data
computed out of the nonperturbative holomorphic anomaly equations. The
resurgence relations further imply that the string free energy displays an
intricate multi-branched Borel structure, and that resonance must be properly
taken into account in order to describe the full transseries solution.Comment: 63 pages, 54 images in 24 figures, jheppub-nosort.sty; v2: corrected
figure, minor changes, final version for CM
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