Maximal Stability Regions for Superconducting Ground States of Generalized Hubbard Models

For a class of generalized Hubbard models, we determine the maximal stability region for the superconducting eta-pairing ground state. We exploit the Optimized Ground State (OGS) approach and the Lanczos diagonalization procedure to derive a sequence of improved bounds. We show that some pieces of the stability boundary are asymptotic, namely independent on the OGS cluster size. In this way, necessary and sufficient conditions are obtained to realize superconductivity in terms of an eta-pairing ground state. The phenomenon is explained by studying the properties of certain exact eigenstates of the OGS hamiltonians.Comment: 9 pages, 5 PostScript figures, submitted to Phys. Rev. Let

Double scaling limit of N=2 chiral correlators with Maldacena-Wilson loop

We consider $\mathcal N=2$ conformal QCD in four dimensions and the one-point correlator of a class of chiral primaries with the circular $\frac{1}{2}$-BPS Maldacena-Wilson loop. We analyze a recently introduced double scaling limit where the gauge coupling is weak while the R-charge of the chiral primary $\Phi$ is large. In particular, we consider the case $\Phi=(\text{tr}\varphi^{2})^{n}$ , where $\varphi$ is the complex scalar in the vector multiplet. The correlator defines a non-trivial scaling function at fixed $\kappa = n\,g_{\rm YM}^{2}$ and large $n$ that may be studied by localization. For any gauge group $SU(N)$ we provide the analytic expression of the first correction $\sim \zeta(3)\,\kappa^{2}$ and prove its universality. In the $SU(2)$ and $SU(3)$ theories we compute the scaling functions at order $\mathcal O(\kappa^{6})$. Remarkably, in the $SU(2)$ case the scaling function is equal to an analogous quantity describing the chiral 2-point functions $\langle\Phi\overline\Phi\rangle$ in the same large R-charge limit. We conjecture that this $SU(2)$ scaling function is computed at all-orders by a $\mathcal N=4$ SYM expectation value of a matrix model object characterizing the one-loop contribution to the 4-sphere partition function. The conjecture provides an explicit series expansion for the scaling function and is checked at order $\mathcal O(\kappa^{10})$ by showing agreement with the available data in the sector of chiral 2-point functions.Comment: 21 page

Sudakov Expansions and Top Quark Physics at LHC

We review some peculiar features of Sudakov expansions in the calculation of electroweak radiative corrections in the MSSM at high energy. We give specific examples and consider in particular the process b g -> t W of single top quark production relevant for the top quark physics programme at LHC.Comment: 4 pages, PostScript fil

Monte Carlo study of exact S-matrix duality in non simply laced affine Toda theories

The $(g_2^{(1)}, d_4^{(3)})$\ pair of non simply laced affine Toda theories is studied from the point of view of non perturbative duality. The classical spectrum of each member is composed of two massive scalar particles. The exact S-matrix prediction for the dual behaviour of the coupling dependent mass ratio is found to be in strong agreement with Monte Carlo data.Comment: 15 pages, 2 Postscript figures. Packed by uufiles. Two references adde

On the large R-charge N=2\mathcal N=2 chiral correlators and the Toda equation

We consider $\mathcal N=2$ $SU(N)$ SQCD in four dimensions and a weak-coupling regime with large R-charge recently discussed in arXiv:1803.00580. If $\varphi$ denotes the adjoint scalar in the $\mathcal N=2$ vector multiplet, it has been shown that the 2-point functions in the sector of chiral primaries $(\text{Tr} \varphi^2)^n$ admit a finite limit when $g_\text{YM}\to 0$ with large R-charge growing like $\sim 1/g^2_\text{YM}$. The correction with respect to $\mathcal N=4$ correlators is a non-trivial function $F(\lambda; N)$ of the fixed coupling $\lambda=n\,g^2_\text{YM}$ and the gauge algebra rank $N$. We show how to exploit the Toda equation following from the $tt^*$ equations in order to control the R-charge dependence. This allows to determine $F(\lambda; N)$ at order $O(\lambda^{10})$ for generic $N$, greatly extending previous results and placing on a firmer ground a conjecture proposed for the $SU(2)$ case. We show that a similar Toda equation, discussed in the past, may indeed be used for the additional sector $(\text{Tr}\varphi^2)^n\,\text{Tr}\varphi^3$ due to the special mixing properties of these composite operators on the 4-sphere. We discuss the large R-limit in this second case and compute the associated scaling function $F$ at order $O(\lambda^7)$ and generic $N$. Large $N$ factorization is also illustrated as a check of the computation.Comment: 27 pages. v2: minor clarifications adde

Optimization of Trial Wave Functions for Hamiltonian Lattice Models

We propose a new Monte Carlo algorithm for the numerical study of general lattice models in Hamiltonian form. The algorithm is based on an initial Ansatz for the ground state wave function depending on a set of free parameters which are dynamically optimized. The method is discussed in details and results are reported from explicit simulations of U(1) lattice gauge theory in 1+1 dimensions.Comment: 4 pages, 2 PostScript figure

Y-system for Z_S Orbifolds of N=4 SYM

We propose a twisted Y-system for the calculation of leading wrapping corrections to physical states of general Z_S orbifold projections of N=4 super Yang-Mills theory. Agreement with available thermodynamical Bethe Ansatz results is achieved in the non supersymmetric case. Various examples of new computations, including other supersymmetric orbifolds are illustrated.Comment: 21 pages, 1 eps figur

Resummation of scalar correlator in higher spin black hole background

We consider the proposal that predicts holographic duality between certain 2D minimal models at large central charge and Vasiliev 3D higher spin gravity with a single complex field. We compute the scalar correlator in the background of a higher spin black hole at order $\mathcal O(\alpha^{5})$ in the chemical potential $\alpha$ associated with the spin-3 charge. The calculation is performed at generic values of the symmetry algebra \mbox{hs}[\lambda] parameter $\lambda$ and for the scalar in three different representations. We then study the perturbative data in the large $\lambda$ limit and discover remarkable regularities. This leads to formulate a closed formula for the resummation of the leading and subleading terms that scale like $\mathcal O(\alpha^{n}\lambda^{2n})$ and $\mathcal O(\alpha^{n}\,\lambda^{2n-1})$ respectively.Comment: 18 page

Large NN expansion of Wilson loops in the Gross-Witten-Wadia matrix model

We study the large $N$ expansion of winding Wilson loops in the off-critical regime of the Gross-Witten-Wadia (GWW) unitary matrix model. These have been recently considered in arXiv:1705.06542 and computed by numerical methods. We present various analytical algorithms for the precise computation of both the perturbative and instanton corrections to the Wilson loops. In the gapped phase of the GWW model we present the genus five expansion of the one-cut resolvent that captures all winding loops. Then, as a complementary tool, we apply the Periwal-Shevitz orthogonal polynomial recursion to the GWW model coupled to suitable sources and show how it generates all higher genus corrections to any specific loop with given winding. The method is extended to the treatment of instanton effects including higher order $1/N$ corrections. Several explicit examples are fully worked out and a general formula for the next-to-leading correction at general winding is provided. For the simplest cases, our calculation checks exact results from the Schwinger-Dyson equations, but the presented tools have a wider range of applicability.Comment: 28 pages, 3 pdf figures. v2: minor additions, extended reference

Analysis of higher spin black holes with spin-4 chemical potential

We consider the $AdS_{3}/CFT_{2}$ duality between certain coset WZW theories at large central charge and Vasiliev 3D higher spin gravity with a single complex field. On the gravity side, we discuss a higher spin black hole solution with chemical potential coupled to the spin-4 charge. We compute the perturbative expansion of the higher spin charges and of the partition function at high order in the chemical potential. The result is obtained with its exact dependence on the parameter $\lambda$ characterising the symmetry algebra \mbox{hs}[\lambda]. The cases of $\lambda=0,1$ are successfully compared with a CFT calculation. The special point $\lambda=\infty$, the Bergshoeff-Blencowe-Stelle limit, is also solved in terms of the exact generating function for the partition function. The thermodynamics of both the spin-4 and the usual spin-3 black holes is studied in order to discuss the $\lambda$ dependence of the BTZ critical temperature $T_{\rm BTZ}(\lambda)$. In the spin-3 case, it is shown that $T_{\rm BTZ}(\lambda)$ converges for large $\lambda$ to the critical point of the $\lambda=\infty$ known partition function previously found by the authors. In the spin-4 black hole, the picture is qualitatively similar and $T_{\rm BTZ}(\infty)$ is accurately determined by various numerical methods.Comment: 27 pages, 6 figures, one more referenc