Resurgence of the dressing phase for AdS5 × S5

Arutyunov, Gleb; Dorigoni, Daniele; Savin, Sergei

doi:10.1007/jhep01(2017)055

Cited by 29 publications

(24 citation statements)

References 57 publications

(81 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…which is manifestly real for x > 0, as expected from (5.26). Following a discussion very similar to that in [33] we can show that this median resummation is identical to (5.21). In other words, we deduce that the leading N 2 term (5.21), when expanded at strong coupling λ → ∞, does include an infinite sum over non-perturbative corrections of the form e −2n √ λ .…”

Section: Jhep05(2021)089supporting

confidence: 72%

“…In other words, we deduce that the leading N 2 term (5.21), when expanded at strong coupling λ → ∞, does include an infinite sum over non-perturbative corrections of the form e −2n √ λ . Since the proof is extremely close to the analysis of [33] we have relegated the details to appendix D.1.…”

Section: Jhep05(2021)089mentioning

confidence: 96%

“…n we see that, unlike the weak coupling expansion, the strong coupling expansion is factorially divergent and so we will analyse it using Borel summation (more details are given in appendix D). As in [33] we need to consider the modified Borel transformation, B :…”

Section: Jhep05(2021)089mentioning

confidence: 99%

See 2 more Smart Citations

Exact properties of an integrated correlator in $$ \mathcal{N} $$ = 4 SU(N) SYM

Dorigoni

Green

Wen

2021

J. High Energ. Phys.

Self Cite

235

View full text Add to dashboard Cite

We present a novel expression for an integrated correlation function of four superconformal primaries in SU(N) $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills ($$ \mathcal{N} $$ N = 4 SYM) theory. This integrated correlator, which is based on supersymmetric localisation, has been the subject of several recent developments. In this paper the correlator is re-expressed as a sum over a two dimensional lattice that is valid for all N and all values of the complex Yang-Mills coupling $$ \tau =\theta /2\pi +4\pi i/{g}_{\mathrm{YM}}^2 $$ τ = θ / 2 π + 4 πi / g YM 2 . In this form it is manifestly invariant under SL(2, ℤ) Montonen-Olive duality. Furthermore, it satisfies a remarkable Laplace-difference equation that relates the SU(N) correlator to the SU(N + 1) and SU(N − 1) correlators. For any fixed value of N the correlator can be expressed as an infinite series of non-holomorphic Eisenstein series, $$ E\left(s;\tau, \overline{\tau}\right) $$ E s τ τ ¯ with s ∈ ℤ, and rational coefficients that depend on the values of N and s. The perturbative expansion of the integrated correlator is an asymptotic but Borel summable series, in which the n-loop coefficient of order (gYM/π)2n is a rational multiple of ζ(2n + 1). The n = 1 and n = 2 terms agree precisely with results determined directly by integrating the expressions in one-loop and two-loop perturbative $$ \mathcal{N} $$ N = 4 SYM field theory. Likewise, the charge-k instanton contributions (|k| = 1, 2, . . .) have an asymptotic, but Borel summable, series of perturbative corrections. The large-N expansion of the correlator with fixed τ is a series in powers of $$ {N}^{\frac{1}{2}-\mathrm{\ell}} $$ N 1 2 − ℓ (ℓ ∈ ℤ) with coefficients that are rational sums of $$ E\left(s;\tau, \overline{\tau}\right) $$ E s τ τ ¯ with s ∈ ℤ + 1/2. This gives an all orders derivation of the form of the recently conjectured expansion. We further consider the ’t Hooft topological expansion of large-N Yang-Mills theory in which $$ \lambda ={g}_{\mathrm{YM}}^2N $$ λ = g YM 2 N is fixed. The coefficient of each order in the 1/N expansion can be expanded as a series of powers of λ that converges for |λ| < π2. For large λ this becomes an asymptotic series when expanded in powers of $$ 1/\sqrt{\lambda } $$ 1 / λ with coefficients that are again rational multiples of odd zeta values, in agreement with earlier results and providing new ones. We demonstrate that the large-λ series is not Borel summable, and determine its resurgent non-perturbative completion, which is $$ O\left(\exp \left(-2\sqrt{\lambda}\right)\right) $$ O exp − 2 λ .

show abstract

Section: Jhep05(2021)089supporting

confidence: 72%

Section: Jhep05(2021)089mentioning

confidence: 96%

See 1 more Smart Citation

Exact properties of an integrated correlator in $$ \mathcal{N} $$ = 4 SU(N) SYM

Dorigoni

Green

Wen

2021

J. High Energ. Phys.

Self Cite

235

View full text Add to dashboard Cite

show abstract

“…The resurgence program has been pushed forward for several quantum field theories including supersymmetric theories [11][12][13][14][15][16], various quantities in the maximally supersymmetric 4D gauge theory in the large N limit [17][18][19], the simple φ 4 theory in 2D, [20,21]. Factorial growth can be seen in lattice simulations [22].…”

Section: Jhep05(2021)253mentioning

confidence: 99%

Resurgence in the O(4) sigma model

Abbott

Bajnok

Balog

et al. 2021

J. High Energ. Phys.

View full text Add to dashboard Cite

We analyze the free energy of the integrable two dimensional O(4) sigma model in a magnetic field. We use Volin’s method to extract high number (2000) of perturbative coefficients with very high precision. The factorial growth of these coefficients are regulated by switching to the Borel transform, where we perform several asymptotic analysis. High precision data allowed to identify Stokes constants and alien derivatives with exact expressions. These reveal a nice resurgence structure which enables to formulate the first few terms of the ambiguity free trans-series. We check these results against the direct numerical solution of the exact integral equation and find complete agreement.

show abstract

“…However not everything is lost from the resurgence point of view since it now happens that the strong coupling expansions of these two observables give rise to asymptotic series, see [22] and [24] respectively. The full resurgence machinery can be then applied to the strong coupling side of planar = 4 SYM to obtain the complete transseries for the cusp anomaly [25,26] and the dressing phase [27] leading to important implications for weak/strong coupling interpolation with the stringy AdS 5 ×S 5 side, although the semi-classical origin of the non-perturbative effects predicted in [27] is still somewhat mysterious. The strong coupling side of planar = 4 SU(N ) SYM can also be studied within the context of the AdS/CFT correspondence.…”

Section: Introductionmentioning

confidence: 99%

The grin of Cheshire cat resurgence from supersymmetric localization

Dorigoni

Glass

2018

SciPost Phys.

Self Cite

View full text Add to dashboard Cite

First we compute the S 2 partition function of the supersymmetric N −1 model via localization and as a check we show that the chiral ring structure can be correctly reproduced. For the 1 case we provide a concrete realisation of this ring in terms of Bessel functions. We consider a weak coupling expansion in each topological sector and write it as a finite number of perturbative corrections plus an infinite series of instantonanti-instanton contributions. To be able to apply resurgent analysis we then consider a non-supersymmetric deformation of the localized model by introducing a small unbalance between the number of bosons and fermions. The perturbative expansion of the deformed model becomes asymptotic and we analyse it within the framework of resurgence theory. Although the perturbative series truncates when we send the deformation parameter to zero we can still reconstruct non-perturbative physics out of the perturbative data in a nice example of Cheshire cat resurgence in quantum field theory. We also show that the same type of resurgence takes place when we consider an analytic continuation in the number of chiral fields from N to r ∈ . Although for generic real r supersymmetry is still formally preserved, we find that the perturbative expansion of the supersymmetric partition function becomes asymptotic so that we can use resurgent analysis and only at the end take the limit of integer r to recover the undeformed model.

show abstract

Resurgence of the dressing phase for AdS5 × S5

Cited by 29 publications

References 57 publications

Exact properties of an integrated correlator in $$ \mathcal{N} $$ = 4 SU(N) SYM

Exact properties of an integrated correlator in $$ \mathcal{N} $$ = 4 SU(N) SYM

Resurgence in the O(4) sigma model

The grin of Cheshire cat resurgence from supersymmetric localization

Contact Info

Product

Resources

About