Nicholas P. Warner

Chiral rings in N = 2 superconformal theories

We investigate the properties of chiral operators in N = 2 superconformal theories. In particular, we study the spectral flow of such models under a one-parameter family of twists generated by the U(1) current, and use this to deduce various properties of the ring of chiral primary fields. We furthermore investigate under what conditions a given superconformal theory can be represented as the fixed point of an N = 2 Landau-Ginzburg theory and show how to determine the superpotential. We also investigate the coset models of Kazama and Suzuki and find a simple cohomological characterization for the elements of the chiral primary ring. Moreover we show how some of them can be represented as LG models.

Self-dual strings and N = 2 supersymmetric field theory

We show how the Riemann surfaceof N = 2 Yang-Mills field theory arises in type II string compactifications on Calabi-Yau threefolds. The relevant local geometry is given by fibrations of ALE spaces. The 3-branes that give rise to BPS multiplets in the string descend to self-dual strings on the Riemann surface, with tension determined by a canonically fixed Seiberg-Witten differential λ. This gives, effectively, a dual formulation of Yang-Mills theory in which gauge bosons and monopoles are treated on equal footing, and represents the rigid analog of type II-heterotic string duality. The existence of BPS states is essentially reduced to a geodesic problem on the Riemann surface with metric |λ| 2 . This allows us, in particular, to easily determine the spectrum of stable BPS states in field theory. Moreover, we identify the six-dimensional space IR 4 × � as the world-volume of a five-brane and show that BPS states correspond to two-branes ending on this five-brane.

Catastrophes and the classification of conformal theories

Abstract Using ideas from renormalization group theory we show that the study of catastrophes (singularities) is a powerful tool in the classification of conformal theories. The results are most powerful when applied to N =2 superconformal models. The ideas are illustrated by considering some examples including the minimal superconformal models.

Integrable systems and supersymmetric gauge theory

Abstract After the work of Seiberg and Witten, it has been seen that the dynamics of N = 2 Yang-Mills theory is governed by a Riemann surface ϵ In particular, the integral of a special differential ωSW over (a subset of) the periods of ϵ gives the mass formula for BPS-saturated states. We show that, for each simple group G, the Riemann surface is a spectral curve of the periodic Toda lattice for the dual group, GV whose affine Dynkin diagram is the dual of that of G. This curve is not unique, rather it depends on the choice of a representation ϱ of GV; however, different choices of ϱ lead to equivalent constructions. The Seiberg-Witten differential ωSW is naturally expressed in Toda variables, and the N = 2Yang-Mills pre-potential is the free energy of a topological field theory defined by the data eg, π and ωSW.

Black Holes, Black Rings, and their Microstates

In this review article, we describe some of the recent progress towards the construction and analysis of three-charge configurations in string theory and supergravity. We begin by describing the Born-Infeld construction of three-charge supertubes with two dipole charges and then discuss the general method of constructing three-charge solutions in five dimensions. We explain in detail the use of these methods to construct black rings, black holes, as well as smooth microstate geometries with black hole and black ring charges, but with no horizon. We present arguments that many of these microstate geometries are dual to boundary states that belong to the same sector of the D1-D5-P CFT as the typical states. We end with an extended discussion of the implications of this work for the physics of black holes in string theory.

Continuous distributions of D3-branes and gauged supergravity

States on the Coulomb branch ofN = 4 super-Yang-Mills theory are studied from the point of view of gauged supergravity in ve dimensions. These supersymmetric solutions provide examples of consistent truncation from type-IIB supergravity in ten dimensions. A mass gap for states created by local operators and perfect screening for external quarks arise in the supergravity approximation. Weoeraninterpretationofthesesurprising featuresintermsofensembles ofbrane distributions.

Compact and non-compact gauged supergravity theories in five dimensions☆

Abstract We give a detailed construction of gauged N = 8 supergravity theories in five dimensions with Yang-Mills gauge groups SO( p , 6− p )( p =0, 1, 2, 3), physical global symmetry SU(1, 1), and local composite symmetry USp(8). The scalar potentials are studied and several critical points are found for the SO(6) and SO(3,3) theories. Those of the SO(6) theory are related to compactifications of the chiral N = 2 theory in ten dimensions. We discuss truncations of the SO(6) theory and give an independent discussion of the relevant N = 2,4,6 and 8 anti-de Sitter supermultiplets.

Calabi-Yau manifolds and renormalization group flows

Using ideas of renormalization group flows we show how to represent a large class of Calabi-Yau manifolds in terms of renormalization group fixed points of Landau-Ginzburg models. In particular we show why Gepners construction yields Calabi-Yau compactifications. More precisely, we show that all of his models correspond to strings propagating on algebraic varieties in weighted projective spaces.

N=2 Supersymmetric RG Flows and the IIB Dilaton

We show that there is a non-trivial relationship between the dilaton of IIB supergravity, and the coset of scalar fields in five-dimensional, gauged N=8 supergravity. This has important consequences for the running of the gauge coupling in massive perturbations of the AdS/CFT correspondence. We conjecture an exact analytic expression for the ten-dimensional dilaton in terms of five-dimensional quantities, and we test this conjecture. Specifically, we construct a family of solutions to IIB supergravity that preserve half of the supersymmetries, and are lifts of supersymmetric flows in five-dimensional, gauged N=8 supergravity. Via the AdS/CFT correspondence these flows correspond to softly broken N=4, large N Yang–Mills theory on part of the Coulomb branch of N=2 supersymmetric Yang–Mills. Our solutions involve non-trivial backgrounds for all the tensor gauge fields as well as for the dilaton and axion.

Some new extrema of the scalar potential of gauged N = 8 supergravity

Five new critical points are found for the scalar potential of gauged N = 8 supergravity. These comprise a complete list of all the extrema which induce a symmetry breaking of SO(8) to some smaller group containing SU(3). Possible relationships between solutions based on these extrema and dimensional reduction schemes are suggested. One of the new extrema may have phenomonological significance since it breaks SO(8) to SU(3) × U(1) and has gauged N = 2 supersymmetry.