Krzysztof Pilch

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.

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.

New vacua of gauged N=8 supergravity in five dimensions

We analyze a particular SU(2) invariant sector of the scalar manifold of gauged N=8 supergravity in five dimensions, and find all the critical points of the potential within this sector. The critical points give rise to Anti-de Sitter vacua, and preserve at least an SU(2) gauge symmetry. Consistent truncation implies that these solutions correspond to Anti-de Sitter compactifications of IIB supergravity, and hence to possible near-horizon geometries of 3-branes. Thus we find new conformal phases of softly broken N=4 Yang--Mills theory. One of the critical points preserves N=2 supersymmetry in the bulk and is therefore completely stable, and corresponds to an N=1 superconformal fixed point of the Yang--Mills theory. The corresponding renormalization group flow from the N=4 point has c_{IR}/c_{UV} = 27/32. We also discuss the ten-dimensional geometries corresponding to these critical points.

Quantum group structure in the Fock space resolutions of\(\widehat{sl}(n)\) representations

AbstractWe describe a complex of Wakimoto-type Fock space modules for the affine Kac-Moody algebra

New Vacua of Gauged N=8 Supergravity

\widehat{sl}(n)

A new supersymmetric compactification of chiral IIB supergravity

. The intertwining operators that build the complex are obtained from contour integrals of so-called screening operators. We show that a quantum group structure underlies the algebra of screening operators. This observation greatly facilitates the explicit determination of the intertwiners. We conjecture that the complex provides a resolution of an irreducible highest weight module in terms of Fock spaces.

Supersymmetric IIB Solutions with Schrodinger Symmetry

Abstract We find M-theory solutions that are holographic duals of flows of the maximally supersymmetric ( N =8 ) scalar-fermion theory in 2+1 dimensions. In particular, we construct the M-theory solution dual to a flow in which a single chiral multiplet is given a mass, and the theory goes to a new infra-red fixed point. We also examine this new solution using M2-brane probes. The (2+1)-dimensional field theory fixed-point is closely related to that of Leigh and Strassler, while the M-theory solution is closely related to the corresponding IIB flow solution. We recast the IIB flow solution in a more geometric manner and use this to obtain an ansatz for the M-theory flow. We are able to generalize our solution further to obtain flows with del Pezzo submanifolds, and we give an explicit solution with a conifold singularity.

Free field realizations of WZNW models. The BRST complex and its quantum group structure

We analyze a particular SU(2) invariant sector of the scalar manifold of gauged N=8 supergravity in five dimensions, and find all the critical points of the potential within this sector. The critical points give rise to Anti-de Sitter vacua, and preserve at least an SU(2) gauge symmetry. Consistent truncation implies that these solutions correspond to Anti-de Sitter compactifications of IIB supergravity, and hence to possible near-horizon geometries of 3-branes. Thus we find new conformal phases of softly broken N=4 Yang--Mills theory. One of the critical points preserves N=2 supersymmetry in the bulk and is therefore completely stable, and corresponds to an N=1 superconformal fixed point of the Yang--Mills theory. The corresponding renormalization group flow from the N=4 point has c_{IR}/c_{UV} = 27/32. We also discuss the ten-dimensional geometries corresponding to these critical points.