Strong coupling expansion of free energy and BPS Wilson loop in $\mathcal{N}=2$ superconformal models with fundamental hypermultiplets

Abstract

As a continuation of the study (in arXiv:2102.07696 and arXiv:2104.12625) of strong-coupling expansion of non-planar corrections in $\mathcal{N}=2$ 4d superconformal models we consider two special theories with gauge groups $SU(N)$ and $Sp(2N)$. They contain $N$-independent numbers of hypermultiplets in rank 2 antisymmetric and fundamental representations and are planar-equivalent to the corresponding $\mathcal{N}=4$ SYM theories. These $\mathcal{N}=2$ theories can be realised on a system of $N$ D3-branes with a finite number of D7-branes and O7-plane; the dual string theories should be particular orientifolds of $Ad{S}_5\times S^5$ superstring. Starting with the localization matrix model representation for the $\mathcal{N}=2$ partition function on $S^4$ we find exact differential relations between the $1/N$ terms in the corresponding free energy $F$ and the $\frac{1}{2}$-BPS Wilson loop expectation value $⟨\mathcal{W}⟩$ and also compute their large 't Hooft coupling ($\lambda \gg 1$) expansions. The structure of these expansions is different from the previously studied models without fundamental hypermultiplets. In the more tractable $Sp(2N)$ case we find an exact resummed expression for the leading strong coupling terms at each order in the $1/N$ expansion. We also determine the exponentially suppressed at large $\lambda$ contributions to the non-planar corrections to $F$ and $⟨\mathcal{W}⟩$ and comment on their resurgence properties. We discuss dual string theory interpretation of these strong coupling expansions.

arXiv comment38 pages. v3: minor corrections and note added on recent exact results in arXiv:2207.11475

References in corpus (36)

• Large N Field Theories, String Theory and Gravity
• The Holographic Weyl anomaly
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Baryons And Branes In Anti de Sitter Space
• Wilson Loops in N=4 Supersymmetric Yang--Mills Theory
• An Exact Prediction of N=4 SUSYM Theory for String Theory
• Localization techniques in quantum field theories
• D=4 Super Yang Mills, D=5 gauged supergravity and D=4 conformal supergravity
• Comments on operators with large spin
• Green-Schwarz String in AdS_5 x S^5: Semiclassical Partition Function
• A Primer on Resurgent Transseries and Their Asymptotics
• The Large N Limit of $\mathcal{N}=2,1$ Field Theories from Threebranes in F-theory
• Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
• Large N Superconformal Gauge Theories and Supergravity Orientifolds
• On Subleading Contributions to the AdS/CFT Trace Anomaly
• New Methods in QFT and QCD: From Large-N Orbifold Equivalence to Bions and Resurgence
• 1/4 BPS circular loops, unstable world-sheet instantons and the matrix model
• Large N Limit of N=2 SU(N) Gauge Theories from Localization
• Two-point Correlators in N=2 Gauge Theories
• A Note on Anomalies in the AdS/CFT Correspondence
• N=2 Conformal SYM theories at large N
• BPS Wilson loops in generic conformal N=2 SU(N) SYM theories
• A Note on Superconformal N=2 theories and Orientifolds
• Localization and AdS/CFT Correspondence
• Elliptic Models, Type IIB Orientifolds and the Ads/CFT Correspondence
• Resurgence of the Cusp Anomalous Dimension
• Probing N=2 superconformal field theories with localization
• The Resurgence of the Cusp Anomalous Dimension
• $1/N$ expansion of circular Wilson loop in $\mathcal{N}=2$ superconformal $SU(N)\times SU(N)$ quiver
• Nonperturbative scales in AdS/CFT
• Strong coupling expansion of circular Wilson loops and string theories in AdS${}_5\times {\mathrm{S}}^5$ and AdS${}_4\times {\mathrm{CP}}^3$
• Exact probes of orientifolds
• The planar limit of $\mathcal{N}=2$ superconformal field theories
• An orientifold of adS_5xT^11 with D7-branes, the associated alpha'^2- corrections and their role in the dual N=1 Sp(2N+2M)xSp(2N) gauge theory
• Group-theoretic relations for amplitudes in gauge theories with orthogonal and symplectic groups
• Group-theoretic relations for partial amplitudes in gauge theories with orthogonal group