Picard-Lefschetz decomposition and Cheshire Cat resurgence in 3D $$ \mathcal{N} $$ = 2 field theories

We develop a new approach to extracting the physical consequences of S-duality of four-dimensional $$ \mathcal{N} $$ N = 4 super Yang-Mills (SYM) and its string theory dual, based on SL(2, ℤ) spectral theory.We observe that CFT observables 𝒪, invariant under SL(2, ℤ) transformations of a complexified gauge coupling τ, admit a unique spectral decomposition into a basis of square-integrable functions. This formulation has direct implications for the analytic structure of $$ \mathcal{N} $$ N = 4 SYM data, both perturbatively and non-perturbatively in all parameters. These are especially constraining for the structure of instantons: k-instanton sectors are uniquely determined by the zero- and one-instanton sectors, and Borel summable series around k-instantons have convergence radii with simple k-dependence. In large N limits, we derive the existence and scaling of non-perturbative effects, in both N and the ‘t Hooft coupling, which we exhibit for certain $$ \mathcal{N} $$ N = 4 SYM observables. An elegant benchmark for these techniques is the integrated stress tensor multiplet four-point function, conjecturally determined by [1] for all τ for SU(N) gauge group; we elucidate its form, and explain how the SU(2) case is the simplest possible observable consistent with SL(2, ℤ)-invariant perturbation theory.These results have ramifications for holography. We explain how $$ \left\langle \mathcal{O}\right\rangle $$ O , the ensemble average of 𝒪 over the $$ \mathcal{N} $$ N = 4 supersymmetric conformal manifold with respect to the Zamolodchikov measure, is cleanly isolated by the spectral decomposition. We prove that the large N limit of $$ \left\langle \mathcal{O}\right\rangle $$ O equals the large N, large ‘t Hooft coupling limit of 𝒪. Holographically speaking, $$ \left\langle \mathcal{O}\right\rangle $$ O = 𝒪sugra, its value in type IIB supergravity on AdS5× S5. This result, which extends to all orders in 1/N, embeds ensemble averaging into the traditional AdS/CFT paradigm. The statistics of the SL(2, ℤ) ensemble exhibit both perturbative and non-perturbative 1/N effects. We discuss further implications and generalizations to other AdS compactifications of string/M-theory.

mentioning

confidence: 81%

Section: Jhep08(2022)195mentioning

confidence: 99%

Section: Jhep08(2022)195mentioning

confidence: 99%

See 1 more Smart Citation

Harnessing S-duality in $$ \mathcal{N} $$ = 4 SYM & supergravity as SL(2, ℤ)-averaged strings

Collier

Perlmutter

2022

“…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%

“…Figure3: Asymptotical investigation of the a n series in (44). We subtracted the16 eπ asymptotical value and show the first 100 terms for the original series, the 1 st , 10 th and 100 th Richardson transforms. The inset demonstrates the deviation in the asymptotics of the 80 th , 90 th and 100 th Richardson transform between 201 and 600.…”

mentioning

confidence: 99%

Resurgence in the O(4) sigma model

Abbott

Bajnok

Balog

et al. 2021

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.

Asymptotics in an asymptotic CFT

Schepers

Thompson

2023

In this work we illustrate the resurgent structure of the λ-deformation; a two-dimensional integrable quantum field theory that has an RG flow with an SU(N)k Wess-Zumino-Witten conformal fixed point in the UV. To do so we use modern matched asymptotic techniques applied to the thermodynamic Bethe ansatz formulation to compute the free energy to 38 perturbative orders in an expansion of large applied chemical potential. We find numerical evidence for factorial asymptotic behaviour with both alternating and non-alternating character which we match to an analytic expression. A curiosity of the system is that the leading non-alternating factorial growth vanishing when k divides N. The ambiguities associated to Borel resummation of this series are suggestive of non-perturbative contributions. This is verified with an analytic study of the TBA system demonstrating a cancellation between perturbative and non-perturbative ambiguities.