Gauging Conformal Algebras with Relations between the Generators

We investigate the gauging of conformal algebras with relations between the generators. We treat the $W_{5/2}$--algebra as a specific example. We show that the gauge-algebra is in general reducible with an infinite number of stages. We show how to construct the BV-extended action, and hence the classical BRST charge. An important conclusion is that this can always be done in terms of the generators of the $W$--algebra only, that is, independent of the realisation. The present treatment is still purely classical, but already enables us to learn more about reducible gauge algebras and the BV-formalism.Comment: 10 pages, LaTex, This paper is based on proceedings for the Sixth Seminar on Quantum Gravity, Moscow, 12-17 June '95 and the Conference on Gauge theories, Applied Supersymmetry and Quantum Gravity, Leuven, 10-14 July '9

Lifshitz quasinormal modes and relaxation from holography

We obtain relaxation times for field theories with Lifshitz scaling and with holographic duals Einstein-Maxwell-Dilaton gravity theories. This is done by computing quasinormal modes of a bulk scalar field in the presence of Lifshitz black branes. We determine the relation between relaxation time and dynamical exponent z, for various values of boundary dimension d and operator scaling dimension. It is found that for d>z+1, at zero momenta, the modes are non-overdamped, whereas for d<=z+1 the system is always overdamped. For d=z+1 and zero momenta, we present analytical results.Comment: 16 pages and 5 figure

Static supersymmetric black holes in AdS_4 with spherical symmetry

We elaborate further on the static supersymmetric AdS_4 black holes found in arXiv:0911.4926, investigating thoroughly the BPS constraints for spherical symmetry in N = 2 gauged supergravity in the presence of Fayet-Iliopoulos terms. We find Killing spinors that preserve two of the original eight supercharges and investigate the conditions for genuine black holes free of naked singularities. The existence of a horizon is intimately related with the requirement that the scalars are not constant, but given in terms of harmonic functions in analogy to the attractor flow in ungauged supergravity. The black hole charges depend on the choice of the electromagnetic gauging, with only magnetic charges for purely electric gaugings. Finally we show how these black holes can be embedded in N = 8 supergravity and thus in M-theory.Comment: 28 pages; v2 minor change

Lifshitz entanglement entropy from holographic cMERA

We study entanglement entropy in free Lifshitz scalar field theories holographically by employing the metrics proposed by Nozaki, Ryu and Takayanagi in \cite{Nozaki:2012zj} obtained from a continuous multi-scale entanglement renormalisation ansatz (cMERA). In these geometries we compute the minimal surface areas governing the entanglement entropy as functions of the dynamical exponent $z$ and we exhibit a transition from an area law to a volume law analytically in the limit of large $z$. We move on to explore the effects of a massive deformation, obtaining results for any $z$ in arbitrary dimension. We then trigger a renormalisation group flow between a Lifshitz theory and a conformal theory and observe a monotonic decrease in entanglement entropy along this flow. We focus on strip regions but also consider a disc in the undeformed theory.Comment: 17 pages, v2: references added and improved discussions, v3: published versio

Phase transitions of magnetic AdS4 black holes with scalar hair

We determine the thermodynamic properties of a class of spherically symmetric and static black holes in AdS4 with magnetic charges and scalar hair. These black holes are solutions in 4d N=2 gauged supergravity that can arise from eleven-dimensional supergravity compactified on S^7. At zero temperature, they preserve supersymmetry and hence are stable. At non-zero temperatures, we explore in detail the canonical ensemble and stability of solutions and find a first order phase transition between small and large hairy black holes. The transition emerges as a liquid-gas phase transition in the dual three-dimensional field theory on R x S^2 with magnetic flux through S^2.Comment: 5 pages, v2: misprints corrected and references added, published versio

Fivebrane Instanton Corrections to the Universal Hypermultiplet

We analyze the Neveu-Schwarz fivebrane instanton in type IIA string theory compactifications on rigid Calabi-Yau threefolds, in the low-energy supergravity approximation. It there appears as a finite action solution to the Euclidean equations of motion of a double-tensor multiplet (dual to the universal hypermultiplet) coupled to N=2, D=4 supergravity. We determine the bosonic and fermionic zero modes, and the single-centered instanton measure on the moduli space of collective coordinates. The results are then used to compute, in the semiclassical approximation, correlation functions that nonperturbatively correct the universal hypermultiplet moduli space geometry of the low-energy effective action. We find that only the Ramond-Ramond sector receives corrections, and we discuss the breaking of isometries due to instantons.Comment: 48 pages, v2: improved version with some correction

Hyperkahler Cones and Orthogonal Wolf Spaces

We construct the hyperkahler cones corresponding to the Quaternion-Kahler orthogonal Wolf spaces SO(n+4)/(SO(n)xSO(4)) and their non-compact versions, which appear in hypermultiplet couplings to N=2 supergravity. The geometry is completely encoded by a single function, the hyperkahler potential, which we compute from an SU(2) hyperkahler quotient of flat space. We derive the Killing vectors and moment maps for the SO(n+4) isometry group on the hyperkahler cone. For the non-compact case, the isometry group SO(n,4) contains n+2 abelian isometries which can be used to find a dual description in terms of n tensor multiplets and one double-tensor multiplet. Finally, using a representation of the hyperkahler quotient via quiver diagrams, we deduce the existence of a new eight dimensional ALE space.Comment: 19 pages, Latex, 2 figures (references added

A 5d/2d/4d correspondence

We propose a correspondence between two-dimensional (0,4) sigma models with target space the moduli spaces of r monopoles, and four-dimensional N=4, U(r) Yang-Mills theory on del Pezzo surfaces. In particular, the two- and four-dimensional BPS partition functions are argued to be equal. The correspondence relies on insights from five-dimensional supersymmetric gauge theory and its geometric engineering in M-theory, hence the name "5d/2d/4d correspondence". We provide various tests of our proposal. The most stringent ones are for r=1, for which we prove the equality of partition functions.Comment: 39 pages, final versio

Quaternion-Kahler spaces, hyperkahler cones, and the c-map

Under the action of the c-map, special Kahler manifolds are mapped into a class of quaternion-Kahler spaces. We explicitly construct the corresponding Swann bundle or hyperkahler cone, and determine the hyperkahler potential in terms of the prepotential of the special Kahler geometry.Comment: 12 pages, Submitted to the "Handbook of pseudo-Riemannian geometry and supersymmetry", IRMA Lectures in Mathematical Physics; references and typos corrected; published versio

Linear perturbations of quaternionic metrics

We extend the twistor methods developed in our earlier work on linear deformations of hyperkahler manifolds [arXiv:0806.4620] to the case of quaternionic-Kahler manifolds. Via Swann's construction, deformations of a 4d-dimensional quaternionic-Kahler manifold $M$ are in one-to-one correspondence with deformations of its $4d+4$-dimensional hyperkahler cone $S$. The latter can be encoded in variations of the complex symplectomorphisms which relate different locally flat patches of the twistor space $Z_S$, with a suitable homogeneity condition that ensures that the hyperkahler cone property is preserved. Equivalently, we show that the deformations of $M$ can be encoded in variations of the complex contact transformations which relate different locally flat patches of the twistor space $Z_M$ of $M$, by-passing the Swann bundle and its twistor space. We specialize these general results to the case of quaternionic-Kahler metrics with $d+1$ commuting isometries, obtainable by the Legendre transform method, and linear deformations thereof. We illustrate our methods for the hypermultiplet moduli space in string theory compactifications at tree- and one-loop level.Comment: 55 pages, 1 figure, uses JHEP3.cls; v2: one ref added, minor improvements; v3: title changed, sections 2.5 and 5.2 rewritten in part, ref [26] adde