Branes at Generalized Conifolds and Toric Geometry

We use toric geometry to investigate the recently proposed relation between a set of D3 branes at a generalized conifold singularity and type IIA configurations of D4 branes stretched between a number of relatively rotated NS5 branes. In particular we investigate how various resolutions of the singularity corresponds to moving the NS branes and how Seiberg's duality is realized when two relatively rotated NS-branes are interchanged.Comment: 19 pages, 8 figures; v2: references added, clarifying footnote on Seiberg's duality adde

Naturalness and Chaotic Inflation in Supergravity from Massive Vector Multiplets

We study the embedding of the quadratic model of chaotic inflation into the 4D, N=1 minimal theories of supergravity by the use of massive vector multiplets and investigate its robustness against higher order corrections. In particular, we investigate the criterion of technical naturalness for the inflaton potential. In the framework of the new-minimal formulation the massive vector multiplet is built in terms of a real linear multiplet coupled to a vector multiplet via the 4D analog of the Green-Schwarz term. This theory gives rise to a single-field quadratic model of chaotic inflation, which is protected by an shift symmetry which naturally suppresses the higher order corrections. The embedding in the old-minimal formulation is again achieved in terms of a massive vector multiplet and also gives rise to single-field inflation. Nevertheless in this case there is no obvious symmetry to protect the model from higher order corrections.Comment: 15 pages, version accepted in JHE

Constraints on Higher Derivative Operators in Maximally Supersymmetric Gauge Theory

Following the work of Dine and Seiberg for SU(2), we study the leading irrelevant operators on the moduli space of N=4 supersymmetric SU(N) gauge theory. These operators are argued to be one-loop exact, and are explicitly computed.Comment: 6 pages, harvmac. Note added. (Only a subset of the leading irrelevant operators have been shown to be one-loop exact.

Hyperkahler quotients and algebraic curves

We develop a graphical representation of polynomial invariants of unitary gauge groups, and use it to find the algebraic curve corresponding to a hyperkahler quotient of a linear space. We apply this method to four dimensional ALE spaces, and for the A_k, D_k, and E_6 cases, derive the explicit relation between the deformations of the curves away from the orbifold limit and the Fayet-Iliopoulos parameters in the corresponding quotient construction. We work out the orbifold limit of E_7, E_8, and some higher dimensional examples.Comment: Two typos corrected--Journal version; 23 pages, 13 figures, harvma

A potential for Generalized Kahler Geometry

We show that, locally, all geometric objects of Generalized Kahler Geometry can be derived from a function K, the "generalized Kahler potential''. The metric g and two-form B are determined as nonlinear functions of second derivatives of K. These nonlinearities are shown to arise via a quotient construction from an auxiliary local product (ALP) space.Comment: 12 pages, contribution to "Handbook of pseudo-Riemannian Geometry and Supersymmetry

E8 Quiver Gauge Theory and Mirror Symmetry

We show that the Higgs branch of a four-dimensional Yang-Mills theory, with gauge and matter content summarised by an E_8 quiver diagram, is identical to the generalised Coulomb branch of a four-dimensional superconformal strongly coupled gauge theory with E_8 global symmetry. This is the final step in showing that there is a Higgs-Coulomb identity of this kind for each of the cases {0}, A_1, A_2, D_4, E_6, E_7 and E_8. This series of equivalences suggests the existence of a mirror symmetry between the quiver theories and the strongly coupled theories. We also discuss how to interpret the parameters of the quiver gauge theory in terms of the Hanany-Witten picture.Comment: 19 pages, 3 figures, references adde