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

As a continuation of the study (in arXiv:2102.07696 and arXiv:2104.12625) of strong-coupling expansion of non-planar corrections in $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N = 4 SYM theories. These $$ \mathcal{N} $$ 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 AdS5 × S5 superstring. Starting with the localization matrix model representation for the $$ \mathcal{N} $$ N = 2 partition function on S4 we find exact differential relations between the 1/N terms in the corresponding free energy F and the $$ \frac{1}{2} $$ 1 2 -BPS Wilson loop expectation value $$ \left\langle \mathcal{W}\right\rangle $$ W and also compute their large ’t Hooft coupling (λ » 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 λ contributions to the non-planar corrections to F and $$ \left\langle \mathcal{W}\right\rangle $$ W and comment on their resurgence properties. We discuss dual string theory interpretation of these strong coupling expansions.

Strong coupling methods in QCD thermodynamics

For a long time, strong coupling expansions have not been applied systematically in lattice QCD thermodynamics, in view of the success of numerical Monte Carlo studies. The persistent sign problem at finite baryo-chemical potential, however, has motivated investigations using these methods, either by themselves or combined with numerical evaluations, as a route to finite density physics. This article reviews the strategies, by which a number of qualitative insights have been attained, notably the emergence of the hadron resonance gas or the identification of the onset transition to baryon matter in specific regions of the QCD parameter space. For the simpler case of Yang–Mills theory, the deconfinement transition can be determined quantitatively even in the scaling region, showing possible prospects for continuum physics.

Spectra of elliptic potentials and supersymmetric gauge theories

We study a relation between asymptotic spectra of the quantum mechanics problem with a four components elliptic function potential, the Darboux-Treibich-Verdier (DTV) potential, and the Omega background deformed N=2 supersymmetric SU(2) QCD models with four massive flavors in the Nekrasov-Shatashvili limit. The weak coupling spectral solution of the DTV potential is related to the instanton partition function of supersymmetric QCD with surface operator. There are two strong coupling spectral solutions of the DTV potential, they are related to the strong coupling expansions of gauge theory prepotential at the magnetic and dyonic points in the moduli space. A set of duality transformations relate the two strong coupling expansions for spectral solution, and for gauge theory prepotential.