Resumming perturbative series in the presence of monopole bubbling effects

Honda, Masazumi; Yokoyama, Daisuke

doi:10.1103/physrevd.100.025012

Cited by 13 publications

(15 citation statements)

References 73 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Do notice that this caveat is very much attached to any renormalization needs. In quantum field theoretic contexts where such needs do not arise, the transseries structures addressed so far are certainly enough; see, e.g., [14,[148][149][150]152] for supersymmetric gauge theories, e.g., [179,175,180,163,97,16,205,80] for large N gauge theories, and, e.g., [174,195,178,130,77,135,78,76,79,65,66] for string theories.…”

Section: Evaluation Of the Asymptotic Expansionmentioning

confidence: 99%

A primer on resurgent transseries and their asymptotics

2019

View full text Add to dashboard Cite

The computation of observables in general interacting theories, be them quantum mechanical, field, gauge or string theories, is a non-trivial problem which in many cases can only be addressed by resorting to perturbative methods. In most physically interesting problems these perturbative expansions result in asymptotic series with zero radius of convergence. These asymptotic series then require the use of resurgence and transseries in order for the associated observables to become nonperturbatively well-defined. Resurgence encodes the complete largeorder asymptotic behaviour of the coefficients from a perturbative expansion, generically in terms of (multi) instanton sectors and for each problem in terms of its Stokes constants. Some observables arise from linear problems, and have a finite number of instanton sectors and associated Stokes constants; some other observables arise from nonlinear problems, and have an infinite number of instanton sectors and Stokes constants. By means of two very explicit examples, and with emphasis on a pedagogical style of presentation, this work aims at serving as a primer on the aforementioned resurgent, large-order asymptotics of general perturbative expansions. This includes discussions of transseries, Stokes phenomena, generalized steepest-descent methods, Borel transforms, nonlinear resonance, and alien calculus. Furthermore, resurgent properties of transseries-usually described mathematically via alien calculus-are recast in equivalent physical languages: either a "statistical mechanical" language, as motions in chains and lattices; or a "conformal field theoretical" language, with underlying Virasoro-like algebraic structures.

show abstract

Section: Evaluation Of the Asymptotic Expansionmentioning

confidence: 99%

A primer on resurgent transseries and their asymptotics

2019

View full text Add to dashboard Cite

show abstract

“…In fact, even in calculation of nonsupersymmetric quantities in (1.1), the Nicolai mapping is available reflecting the existence of supersymmetry in the action. This kind of idea will be useful, in particular, in supersymmetric field theories as in [41][42][43][44][45].…”

Section: Introductionmentioning

confidence: 99%

Resurgence of one-point functions in a matrix model for 2D type IIA superstrings

Kuroki

Sugino

2019

J. High Energ. Phys.

View full text Add to dashboard Cite

In the previous papers, the authors pointed out correspondence between a supersymmetric double-well matrix model and two-dimensional type IIA superstring theory on a Ramond-Ramond background. This was confirmed by agreement between planar correlation functions in the matrix model and tree-level amplitudes in the superstring theory. Furthermore, in the matrix model we computed one-point functions of single-trace operators to all orders of genus expansion in its double scaling limit, and found that the large-order behavior of this expansion is stringy and not Borel summable. In this paper, we discuss resurgence structure of these one-point functions and see cancellations of ambiguities in their trans-series. More precisely, we compute both series of ambiguities arising in a zero-instanton sector and in a one-instanton sector, and confirm how they cancel each other. In case that the original integration contour is a finite interval not passing through a saddle point, we have to choose an appropriate integration path in order for resurgence to work.1 Resurgence structure has been studied in various models and theories based on several motivations: see e.g. in quantum mechanics [9][10][11][12][13][14][15][16][17][18][19][20][21], string theories [22][23][24] as well as quantum field theories .

show abstract

“…The weak coupling expansion of QFT in the context of resurgence theory has been studied in 2D quantum field theories [37][38][39][40][41][42][43][44][45][46], 3D pure Chern-Simons theory [47,48], 4D non-SUSY QFT [49][50][51] and supersymmetric (SUSY) gauge theories in various dimensions [52][53][54][55][56][57][58]. In all the known examples with sufficient data, observables have resurgent structures with respect to the coupling parameter and unambiguous transseries expressions, which agree with exact results.…”

mentioning

confidence: 99%

“…The prepotentials of 4d N = 2 theories receive an infinite number of instanton corrections but its perturbative series in each sector is truncated [62]. One of more non-trivial examples is a class of SUSY observables in 4d N = 2 theories which also receive instanton corrections and have an asymptotic perturbative series in every sector, but all the perturbative series are Borel summable and hence unambiguous [52][53][54]58].…”

mentioning

confidence: 99%

Resurgence and Lefschetz thimble in three-dimensional $\mathcal{N}=2$ supersymmetric Chern–Simons matter theories

Fujimori

Honda

Kamata

et al. 2018

Progress of Theoretical and Experimental Physics

Self Cite

View full text Add to dashboard Cite

We study a certain class of supersymmetric (SUSY) observables in 3d N = 2 SUSY Chern-Simons (CS) matter theories and investigate how their exact results are related to the perturbative series with respect to coupling constants given by inverse CS levels. We show that the observables have nontrivial resurgent structures by expressing the exact results as a full transseries consisting of perturbative and non-perturbative parts. As real mass parameters are varied, we encounter Stokes phenomena at an infinite number of points, where the perturbative series becomes non-Borel-summable due to singularities on the positive real axis of the Borel plane. We also investigate the Stokes phenomena when the phase of the coupling constant is varied. For these cases, we find that the Borel ambiguities in the perturbative sector are canceled by those in nonperturbative sectors and end up with an unambiguous result which agrees with the exact result even on the Stokes lines. We also decompose the Coulomb branch localization formula, which is an integral representation for the exact results, into Lefschetz thimble contributions and study how they are related to the resurgent transseries. We interpret the non-perturbative effects appearing in the transseries as contributions of complexified SUSY solutions which formally satisfy the SUSY conditions but are not on the original path integral contour. * Electronic address: toshiaki.fujimori018(at)

show abstract

Resumming perturbative series in the presence of monopole bubbling effects

Cited by 13 publications

References 73 publications

A primer on resurgent transseries and their asymptotics

A primer on resurgent transseries and their asymptotics

Resurgence of one-point functions in a matrix model for 2D type IIA superstrings

Resurgence and Lefschetz thimble in three-dimensional $\mathcal{N}=2$ supersymmetric Chern–Simons matter theories

Contact Info

Product

Resources

About