In these notes we consider relation between conformal blocks and the Nekrasov partition function of certain \( \mathcal{N} = 2 \) SYM theories proposed recently by Alday, Gaiotto and Tachikawa. We concentrate on \( \mathcal{N} = {2^*} \) theory, which is the simplest example of AGT relation.

We write the thermodynamic Bethe ansatz for the massive OSp(2|2) Gross Neveu and sigma models. We find evidence that the GN S matrix proposed by Bassi and Leclair [12] is the correct one. We determine features of the sigma model S matrix, which seem highly unconventional; we conjecture in particular a relation between this sigma model and the complex sine-Gordon model at a...

We improve on a recently constructed graphical representation of the supergravity 7-brane solution and apply this refined representation to re-study the open string description of the A-D-E-singularities in F-theory on K3. A noteworthy feature of the graphical representation is that it provides the complete global branch cut structure of the 7-brane solution which plays an...

In theories of phyiscs beyond the Standard Model (SM), visible sector fields often carry quantum numbers under additional gauge symmetries. One could then imagine a scenario in which these extra gauge symmetries play a role in transmitting supersymmetry breaking from a hidden sector to the Supersymmetric Standard Model (SSM). In this paper we present a general formalism for...

We consider loop observables in gauged Wess-Zumino-Witten models, and study the action of renormalization group flows on them. In the WZW model based on a compact Lie group G, we analyze at the classical level how the space of renormalizable defects is reduced upon the imposition of global and affine symmetries. We identify families of loop observables which are invariant with...

A combination is presented of the inclusive deep inelastic cross sections measured by the H1 and ZEUS Collaborations in neutral and charged current unpolarised e ± p scattering at HERA during the period 1994-2000. The data span six orders of magnitude in negative four-momentum-transfer squared, Q 2, and in Bjorken x. The combination method used takes the correlations of...

We study aspects of the large-N volume independence on \( {\mathbb{R}^3} \times {L^\Gamma } \), where L Γ is a Γ-site lattice for Yang-Mills theory with adjoint Wilson-fermions. We find the critical number of lattice sites above which the center-symmetry analysis on L Γ agrees with the one on the continuum S 1. For Wilson parameter set to one and Γ≥2, the two analyses agree. One...

Dimensional reduction along time offers a powerful way to study stationary solutions of 4D symmetric supergravity models via group-theoretical methods. We apply this approach systematically to extremal, BPS and non-BPS, spherically symmetric black holes, and obtain their “fake superpotential” W. The latter provides first order equations for the radial problem, governs the mass...

We study the constraints of supersymmetry on flavour in recently proposed models of F-theory GUTs. We relate the topologically twisted theory to the canonical presentation of eight-dimensional super Yang-Mills and provide a dictionary between the two. We describe the constraints on Yukawa couplings implied by holomorphy of the superpotential in the effective 4-dimensional...

In this paper, the issues of the quark mass hierarchies and the Cabbibo Kobayashi Maskawa mixing are analyzed in a class of intersecting D-brane configurations with Standard Model gauge symmetry. The relevant mass matrices are constructed taking into account the constraints imposed by extra abelian symmetries and anomaly cancelation conditions. Possible mass generating mechanisms...

We study the fine-tuning problem in the context of general gauge mediation. Numerical analyses toward for relaxing fine-tuning are presented. We analyse the problem in typical three cases of the messenger scale, that is, GUT (2 × 1016 GeV), intermediate (1010 GeV), and relatively low energy (106 GeV) scales. In each messenger scale, the parameter space reducing the degree of...

We find new non-supersymmetric solutions of five-dimensional ungauged supergravity coupled to two vector multiplets. The solutions are regular, horizonless and have the same asymptotic charges as non-extremal charged black holes. An essential ingredient in our construction is a four-dimensional Euclidean base which is a solution to Einstein-Maxwell equations. We construct...

This paper studies F-theory SU(5) GUT models where the three generations of the standard model come from three different curves. All the matter is taken to come from curves intersecting at a point of enhanced E 8 gauge symmetry. Giving a vev to some of the GUT singlets naturally implements a Froggatt-Nielsen approach to flavour structure. A scan is performed over all possible...

Recently, a duality between Liouville theory and four dimensional \( \mathcal{N} = 2 \) gauge theory has been uncovered by some of the authors. We consider the role of extended objects in gauge theory, surface operators and line operators, under this correspondence. We map such objects to specific operators in Liouville theory. We employ this connection to compute the expectation...

Recently Kazakov, Vieira and the author conjectured the Y-system set of equations describing the planar spectrum of AdS/CFT. In this paper we solve the Y-system equations in the strong coupling scaling limit. We show that the quasi-classical spectrum of string moving inside AdS 3 × S 1 matches precisely with the prediction of the Y-system. Thus the Y-system, unlike the asymptotic...

We study the prospects for detecting a light boson X with mass m X ≾ 100 MeV at a low energy electron-proton collider. We focus on the case where X dominantly decays to e + e − as motivated by recent “dark force” models. In order to evade direct and indirect constraints, X must have small couplings to the standard model (α X ≾ 10−8) and a sufficiently large mass (m X ≳ 10 MeV...

We construct the Lax connection of the Green-Schwarz superstring in AdS 5 × S 5 within the Hamiltonian formalism and obtain precisely that used in 0810.4136. It differs in a crucial way from the Bena-Polchinski-Roiban connection by terms proportional to the Hamiltonian constraints. These extra terms ensure firstly that the integrals of motion are all first class and secondly that...

We have performed a direct calculation of Witten index I in \( \mathcal{N} = 1,2,3 \) supersymmetric Yang-Mills Chern-Simons (SYMCS) 3d theories. We do it in the framework of Born-Oppenheimer (BO) approach by putting the system into a small spatial box and studying the effective Hamiltonian depending on the zero field harmonics. At the tree level, our results coincide with the...

We propose an electric-magnetic symmetry group in non-abelian gauge theory, which we call the skeleton group. We work in the context of non-abelian unbroken gauge symmetry, and provide evidence for our proposal by relating the representation theory of the skeleton group to the labelling and fusion rules of charge sectors. We show that the labels of electric, magnetic and dyonic...

We obtain a family of heterotic supergravity backgrounds describing warped non-Kähler conifolds with three-form flux and an Abelian gauge bundle, preserving \( \mathcal{N} \) = 1 supersymmetry in four dimensions. At large distance from the singularity the usual Ricci- at conifold is recovered. By performing a ℤ2 orbifold of the T 1,1 base, the conifold singularity can be blown-up...

We perform a detailed numerical analysis of inflationary solutions in Kahler moduli of type IIB flux compactifications. We show that there are inflationary solutions even when all the fields play an important role in the overall shape of the scalar potential. Moreover, there exists a direction of attraction for the inflationary trajectories that correspond to the constant volume...

Within the context of local type IIB models arising from branes at toric Calabi-Yau singularities, we present a systematic way of joining any number of desired sectors into a consistent theory. The different sectors interact via massive messengers with masses controlled by tunable parameters. We apply this method to a toy model of the minimal supersymmetric standard model (MSSM...

We study the finite-size scaling of heavy-light mesons in the static limit. We compute two-point functions of chiral current densities as well as pseudoscalar densities in the ϵ-regime of heavy meson Chiral Perturbation Theory (HMChPT). As expected, finite volume dependence turns out to be significant in this regime and can be predicted in the effective theory in terms of the...

Twistor ideas have led to a number of recent advances in our understanding of scattering amplitudes. Much of this work has been indirect, determining the twistor space support of scattering amplitudes by examining the amplitudes in momentum space. In this paper, we construct the actual twistor scattering amplitudes themselves. We show that the recursion relations of Britto...

We investigate D-branes on the product G×G of two group manifolds described as Wess-Zumino-Novikov-Witten models. When the levels of the two groups coincide, it is well known that there exist permutation D-branes which are twisted by the automorphism exchanging the two factors. When the levels are different, the D-brane charge group demands that there should be generalisations of...