The prepotential of N=2* supersymmetric theories with unitary gauge groups in an Omega-background satisfies a modular anomaly equation that can be recursively solved order by order in an expansion for small mass. By requiring that S-duality acts on the prepotential as a Fourier transform we generalise this result to N=2* theories with gauge algebras of the D and E type and show that their prepotentials can be written in terms of quasi-modular forms of SL(2,Z). The results are checked against microscopic multi-instanton calculus based on localization for the A and D series and reproduce the known 1-instanton prepotential of the pure N=2 theories for any gauge group of ADE type. Our results can also be used to obtain the multi-instanton terms in the exceptional theories for which the microscopic instanton calculus and the ADHM construction are not available.
We propose a modular anomaly equation for the prepotential of the N=2* super Yang-Mills theory on R^4 with gauge group U(N) in the presence of an Omega-background. We then study the behaviour of the prepotential in a large-N limit, in which N goes to infinity with the gauge coupling constant kept fixed. In this regime instantons are not suppressed. We focus on two representative choices of gauge theory vacua, where the vacuum expectation values of the scalar fields are distributed either homogeneously or according to the Wigner semi-circle law. In both cases we derive an all-instanton exact formula for the prepotential. As an application, we show that the gauge theory partition function on S^4 at large N localises around a Wigner distribution for the vacuum expectation values leading to a very simple expression in which the instanton contribution becomes independent of the coupling constant.
We investigate epsilon-deformed N=2 superconformal gauge theories in four dimensions, focusing on the N=2* and Nf=4 SU(2) cases. We show how the modular anomaly equation obeyed by the deformed prepotential can be efficiently used to derive its non-perturbative expression starting from the perturbative one. We also show that the modular anomaly equation implies that S-duality is implemented by means of an exact Fourier transform even for arbitrary values of the deformation parameters, and then we argue that it is possible, perturbatively in the deformation, to choose appropriate variables such that it reduces to a Legendre transform.
We investigate the properties of the twist line defect in the critical 3d Ising model using Monte Carlo simulations. In this model the twist line defect is the boundary of a surface of frustrated links or, in a dual description, the Wilson line of the Z2 gauge theory. We test the hypothesis that the twist line defect flows to a conformal line defect at criticality and evaluate numerically the low-lying spectrum of anomalous dimensions of the local operators which live on the defect as well as mixed correlation functions of local operators in the bulk and on the defect.
We derive the exact supergravity profile for the twisted scalar field emitted by a system of fractional D3 branes at a Z2 orbifold singularity supporting N=2 quiver gauge theories with unitary groups and bifundamental matter. At the perturbative level this twisted field is dual to the gauge coupling but it is corrected non-perturbatively by an infinite tower of fractional D-instantons. The explicit microscopic description allows to derive the gravity profile from disk amplitudes computing the emission rate of the twisted scalar field in terms of chiral correlators in the dual gauge theory. We compute these quantum correlators using multi-instanton localization techniques and/or Seiberg-Witten analysis. Finally, we discuss a non-perturbative relation between the twisted scalar and the effective coupling of the gauge theory for some simple choices of the brane set ups.
We propose a new approach to the study of the inter-quark potential in Lattice Gauge Theories. Instead of looking at the expectation value of Polyakov loop correlators we study the modifications induced in the chromoelectric flux by the presence of the Polyakov loops. In abelian LGTs, thanks to duality, this study can be performed in a very efficient way, allowing to reach high precision with a reasonable CPU cost. The major advantage of this numerical strategy is that it allows to eliminate the dominant effective string correction to the inter-quark potential (the Luscher term) thus giving an unique opportunity to test higher order corrections. Performing a set of simulations in the 3d gauge Ising model we were thus able to precisely identify and measure both the quartic and the sextic effective string corrections to the inter-quark potential. While the quartic term perfectly agrees with the Nambu-Goto one the sextic term is definitely different. Our result seems to disagree with the recent proof by Aharony and Karzbrun of the universality of the sextic correction. We discuss a few possible explanations of this disagreement. The numerical approach described above can also be applied to the study of Wilson loops. In this case, the numerical results are precise enough to test the two-loop prediction of the Nambu-Goto action. The two-loop NG result computed time ago by by Dietz and Filk is incompatible with the data; however, after correcting some mistakes in their expression, compatibility is restored. The viability of a first-order, operatorial description of the Wilson loop is also pointed out.
Motivated by possible implications on the problem of moduli stabilization and other phenomenological aspects, we study D-brane instanton effects in flux compactifications. We focus on a local model and compute non-perturbative interactions generated by gauge and stringy instantons in a N = 1 quiver theory with gauge group U(N_0) x U(N_1) and matter in the bifundamentals. This model is engineered with fractional D3-branes at a C^3/(Z_2 x Z_2) singularity, and its non-perturbative sectors are described by introducing fractional D-instantons. We find a rich variety of instanton-generated F- and D-term interactions, ranging from superpotentials and Beasley-Witten like multi-fermion terms to non-supersymmetric flux-induced instanton interactions.
We consider systems of magnetized D9 branes on orbifolds supporting N=1 gauge theories. In such realizations, the matter multiplets arise from twisted strings connecting different stacks of branes. The introduction of Euclidean 5-branes wrapped on the six-dimensional compact space leads to instanton effects. We examine the interplay between the annuli diagrams with an E5 boundary and the holomorphicity properties of the effective low-energy supergravity action which describes the system, including its instanton corrections. Mostly based on arXiv:0709.0245.
