Physical resurgent extrapolation

Costin, Ovidiu; Dunne, Gerald V.

doi:10.1016/j.physletb.2020.135627

Cited by 71 publications

(79 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The technical goal is to extrapolate from small to large λ, starting from a finite number of terms in the weak coupling expansion. Optimal and near-optimal methods for such an extrapolation have been analyzed recently in [49][50][51]. The key information is some knowledge, either analytic or numerical, of the singularity structure of the function ∆F (λ).…”

Section: Padé-conformal Methodsmentioning

confidence: 99%

BPS Wilson loop in $$ \mathcal{N} $$ = 2 superconformal SU(N) “orientifold” gauge theory and weak-strong coupling interpolation

Beccaria

Dunne

Tseytlin

2021

J. High Energ. Phys.

View full text Add to dashboard Cite

We consider the expectation value $$ \left\langle \mathcal{W}\right\rangle $$ W of the circular BPS Wilson loop in $$ \mathcal{N} $$ N = 2 superconformal SU(N) gauge theory containing a vector multiplet coupled to two hypermultiplets in rank-2 symmetric and antisymmetric representations. This theory admits a regular large N expansion, is planar-equivalent to $$ \mathcal{N} $$ N = 4 SYM theory and is expected to be dual to a certain orbifold/orientifold projection of AdS5× S5 superstring theory. On the string theory side $$ \left\langle \mathcal{W}\right\rangle $$ W is represented by the path integral expanded near the same AdS2 minimal surface as in the maximally supersymmetric case. Following the string theory argument in [5], we suggest that as in the $$ \mathcal{N} $$ N = 4 SYM case and in the $$ \mathcal{N} $$ N = 2 SU(N) × SU(N) superconformal quiver theory discussed in [19], the coefficient of the leading non-planar 1/N2 correction in $$ \left\langle \mathcal{W}\right\rangle $$ W should have the universal λ3/2 scaling at large ’t Hooft coupling. We confirm this prediction by starting with the localization matrix model representation for $$ \left\langle \mathcal{W}\right\rangle $$ W . We complement the analytic derivation of the λ3/2 scaling by a numerical high-precision resummation and extrapolation of the weak-coupling expansion using conformal mapping improved Padé analysis.

show abstract

Section: Padé-conformal Methodsmentioning

confidence: 99%

BPS Wilson loop in $$ \mathcal{N} $$ = 2 superconformal SU(N) “orientifold” gauge theory and weak-strong coupling interpolation

Beccaria

Dunne

Tseytlin

2021

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…The Borel transform turns the asymptotic series into a convergent series. Often these transformations are supplemented with a conformal map, which further improves the accuracy [99][100][101][102]. In principle, one can apply the Padé approximant without the Borel transform, but then the results are less accurate.…”

Section: Example: the Anharmonic Oscillatormentioning

confidence: 99%

Lecture notes: Functional Renormalisation Group and Asymptotically Safe Quantum Gravity

Reichert¹

2020

Proceedings of XV Modave Summer School in Mathematical Physics — PoS(Modave2019)

View full text Add to dashboard Cite

These lecture notes give an introduction to the functional renormalisation group and asymptotically safe quantum gravity. We cover the basics of generating functionals in quantum field theories and derive the Wetterich equation. The anharmonic oscillator is presented as a simple example and compared to perturbation theory with resummation methods. A special focus is set on the implementation of symmetries in the functional renormalisation group. The second half of these notes is dedicated to quantum gravity, explaining the failure of perturbative gravity and how these issues are addressed in the non-perturbative approach. After detailing the implementation of the diffeomorphism symmetry, we present a simple computation in the Einstein-Hilbert truncation and give a short outlook on the state-of-the-art in the field. These notes are based on lectures given at the XV Modave Summer School in Mathematical Physics.

show abstract

“…Note that, without the conformal map, the Padé approximation to the Borel transform cannot see any physical singularities beyond the leading ones, because Padé tries to represent the leading branch cut with an array of poles and zeros, which have no physical content beyond a crude representation of the cut, and these unphysical poles therefore obscure further physical singularities. On the other hand, the Padé approximation to the conformally mapped expansion, as described in Appendix C, does not place unphysical singularities on the cut [33,36], so higher physical singularities can be seen. These results suggest a relation between the leading-order renormalon factorial growth and the singularities in the divergent part of the nested diagrams.…”

Section: Finite Parts and Renormalonsmentioning

confidence: 99%

“…The Padé-conformal analytic continuation procedure for a truncated series in the presence of a branch cut is (i) first, make a conformal transformation from the cut complex plane to the unit disk; (ii) second, reexpand to the same order inside the conformal disk; (iii) third, make a Padé approximation to the resulting series inside the disk; (iv) finally, map back to the original cut plane with the inverse conformal transformation. This procedure is algorithmically straightforward and is provably exponentially more precise than just Padé if there is a cut [33,36].…”

Section: Appendix C: Padé Versus Padé-conformalmentioning

confidence: 99%

See 1 more Smart Citation

Towards the QED beta function and renormalons at 1/Nf2 and 1/Nf3

et al. 2020

Self Cite

View full text Add to dashboard Cite

We determine the 1=N 2 f and 1=N 3 f contributions to the QED beta function stemming from the closed set of nested diagrams. At the order of 1=N 2 f , we discover a new logarithmic branch cut closer to the origin when compared to the 1=N f results. The same singularity location appears at 1=N 3 f , and these correspond to a UV renormalon singularity in the finite part of the photon two-point function.

show abstract

Physical resurgent extrapolation

Cited by 71 publications

References 36 publications

BPS Wilson loop in $$ \mathcal{N} $$ = 2 superconformal SU(N) “orientifold” gauge theory and weak-strong coupling interpolation

BPS Wilson loop in $$ \mathcal{N} $$ = 2 superconformal SU(N) “orientifold” gauge theory and weak-strong coupling interpolation

Lecture notes: Functional Renormalisation Group and Asymptotically Safe Quantum Gravity

Towards the QED beta function and renormalons at 1/Nf2 and 1/Nf3

Contact Info

Product

Resources

About