The M theory lift of two O6 planes and four D6 branes

We solve for the effective actions on the Coulomb branches of a class of N=2 supersymmetric theories by finding the complex structure of an M5 brane in an appropriate background hyperkahler geometry corresponding to the lift of two O6^- orientifolds and four D6 branes to M theory. The resulting Seiberg-Witten curves are of finite genus, unlike other solutions proposed in the literature. The simplest theories in this class are the scale invariant Sp(k) theory with one antisymmetric and four fundamental hypermultiplets and the SU(k) theory with two antisymmetric and four fundamental hypermultiplets. Infinite classes of related theories are obtained by adding extra SU(k) factors with bifundamental matter and by turning on masses to flow down to various asymptotically free theories. The N=4 supersymmetric SU(k) theory can be embedded in these asymptotically free theories, allowing a derivation of a subgroup of its S duality group as an exact equivalence of quantum field theories.Comment: 45 pages, 3 figures. Reference adde

Degeneracy of Decadent Dyons

A quarter-BPS dyon in $\mathcal{N}=4$ super Yang-Mills theory is generically `decadent' in that it is stable only in some regions of the moduli space and decays on submanifolds in the moduli space. Using this fact, and from the degeneracy of the system close to the decay, a new derivation for the degeneracy of such dyons is given. The degeneracy obtained from these very simple physical considerations is in precise agreement with the results obtained from index computations in all known cases. Similar considerations apply to dyons in $\mathcal{N}=2$ gauge theories. The relation between the $\mathcal{N} =4$ field theory dyons and those counted by the Igusa cusp form in toroidally compactified heterotic string is elucidated.Comment: Some typos corrected and references adde

Universality of Sypersymmetric Attractors

The macroscopic entropy-area formula for supersymmetric black holes in N=2,4,8 theories is found to be universal: in d=4 it is always given by the square of the largest of the central charges extremized in the moduli space. The proof of universality is based on the fact that the doubling of unbroken supersymmetry near the black hole horizon requires that all central charges other than Z=M vanish at the attractor point for N=4,8. The ADM mass at the extremum can be computed in terms of duality symmetric quartic invariants which are moduli independent. The extension of these results for d=5, N=1,2,4 is also reported. A duality symmetric expression for the energy of the ground state with spontaneous breaking of supersymmetry is provided by the power 1/2 (2/3) of the black hole area of the horizon in d=4 (d=5). It is suggested that the universal duality symmetric formula for the energy of the ground state in supersymmetric gravity is given by the modulus of the maximal central charge at the attractor point in any supersymmetric theory in any dimension.Comment: few misprints removed, version to appear in Phys. Rev. 20 pages, 1 figur

Superconformal Invariants and Extended Supersymmetry

The superconformal invariants in analytic superspace are found. Superconformal invariance is shown to imply that the Green's functions of analytic operators are invariant holomorphic sections of a line bundle on a product of certain harmonic superspaces. It is argued that the correlation functions for a class of sufficiently low dimension gauge invariant operators in N=2 and N=4 supersymmetric Yang-Mills theory can be evaluated up to constants.Comment: 10p, late

Simplifications of four-point functions in N=4 supersymmetric Yang-Mills theory at two loops

The superconformal Ward identities combined with N=2 harmonic analyticity are used to evaluate two-loop four-point correlation functions of gauge-invariant operators in D=4, N=4 supersymmetric Yang-Mills theory in terms of the well-known one-loop box integral. The result is confirmed by a direct numerical computation

E_{11} origin of Brane charges and U-duality multiplets

We derive general equations which determine the decomposition of the G^{+++} multiplet of brane charges into the sub-algebras that arise when the non-linearly realised G^{+++} theory is dimensionally reduced on a torus. We apply this to calculate the low level E_8 multiplets of brane charges that arise when the E_{8}^{+++}, or E_{11}, non-linearly realised theory is dimensionally reduced to three dimensions on an eight dimensional torus. We find precise agreement with the U-duality multiplet of brane charges previously calculated, thus providing a natural eleven dimensional origin for the "mysterious" brane charges found that do not occur as central charges in the supersymmetry algebra. We also discuss the brane charges in nine dimensions and how they arise from the IIA and IIB theories.Comment: 30 pages, plain te

Superconformal Ward Identities and N=2 Yang-Mills Theory

A reformulation of the superconformal Ward identities that combines all the superconformal currents and the associated parameters in one multiplet is given for theories with rigid N=1 or N=2 supersymmetry. This form of the Ward Identities is applied to spontaneously broken N=2 Yang-Mills theory and used to derive a condition on the low energy effective action. This condition is satisfied by the solution proposed by Seiberg and Witten.Comment: 25 pages, plain Te

S-duality, 't Hooft operators and the operator product expansion

We study S-duality in N=4 super Yang-Mills with an arbitrary gauge group by determining the operator product expansion of the circular BPS Wilson and 't Hooft loop operators. The coefficients in the expansion of an 't Hooft loop operator for chiral primary operators and the stress-energy tensor are calculated in perturbation theory using the quantum path-integral definition of the 't Hooft operator recently proposed. The corresponding operator product coefficients for the dual Wilson loop operator are determined in the strong coupling expansion. The results for the 't Hooft operator in the weak coupling expansion exactly reproduce those for the dual Wilson loop operator in the strong coupling expansion, thereby demonstrating the quantitative prediction of S-duality for these observables.Comment: 33 pages; v2: references adde

Schwarzschild Solution on the Brane

In this communication we have shown that Schwarzschild solution is possible in brane world for some specific choices of brane matter and the non local effects from the bulk. A conformally flat bulk space time with fine-tuned vacuum energy (brane tension) shows that, Schwarzschild solution may also be the vacuum solution for brane world scenario.Comment: 3 page