E7(7) invariant Lagrangian of d=4 N=8 supergravity

We present an E7(7) invariant Lagrangian that leads to the equations of motion of d=4 N=8 supergravity without using Lagrange multipliers. The superinvariance of this new action and the closure of the supersymmetry algebra are proved explicitly for the terms that differ from the Cremmer--Julia formulation. Since the diffeomorphism symmetry is not realized in the standard way on the vector fields, we switch to the Hamiltonian formulation in order to prove the invariance of the E7(7) invariant action under general coordinate transformations. We also construct the conserved E7(7)-Noether current of maximal supergravity and we conclude with comments on the implications of this manifest off-shell E7(7)-symmetry for quantizing d=4 N=8 supergravity, in particular on the E7(7)-action on phase space.Comment: 45 pages, references adde

Higher Derivative Extension of 6D Chiral Gauged Supergravity

Six-dimensional (1,0) supersymmetric gauged Einstein-Maxwell supergravity is extended by the inclusion of a supersymmetric Riemann tensor squared invariant. Both the original model as well as the Riemann tensor squared invariant are formulated off-shell and consequently the total action is off-shell invariant without modification of the supersymmetry transformation rules. In this formulation, superconformal techniques, in which the dilaton Weyl multiplet plays a crucial role, are used. It is found that the gauging of the U(1) R-symmetry in the presence of the higher-order derivative terms does not modify the positive exponential in the dilaton potential. Moreover, the supersymmetric Minkowski(4) x S^2 compactification of the original model, without the higher-order derivatives, is remarkably left intact. It is shown that the model also admits non-supersymmetric vacuum solutions that are direct product spaces involving de Sitter spacetimes and negative curvature internal spaces.Comment: 32 pages; typos corrected, footnote in conclusions section adde

Exact solutions for supersymmetric stationary black hole composites

Four dimensional N=2 supergravity has regular, stationary, asymptotically flat BPS solutions with intrinsic angular momentum, describing bound states of separate extremal black holes with mutually nonlocal charges. Though the existence and some properties of these solutions were established some time ago, fully explicit analytic solutions were lacking thus far. In this note, we fill this gap. We show in general that explicit solutions can be constructed whenever an explicit formula is known in the theory at hand for the Bekenstein-Hawking entropy of a single black hole as a function of its charges, and illustrate this with some simple examples. We also give an example of moduli-dependent black hole entropy.Comment: 13 pages, 1 figur

BPS black holes in N=2 D=4 gauged supergravities

We construct and analyze BPS black hole solutions in gauged N=2, D=4 supergravity with charged hypermultiplets. A class of solutions can be found through spontaneous symmetry breaking in vacua that preserve maximal supersymmetry. The resulting black holes do not carry any hair for the scalars. We demonstrate this with explicit examples of both asymptotically flat and anti-de Sitter black holes. Next, we analyze the BPS conditions for asymptotically flat black holes with scalar hair and spherical or axial symmetry. We find solutions only in cases when the metric contains ripples and the vector multiplet scalars become ghost-like. We give explicit examples that can be analyzed numerically. Finally, we comment on a way to circumvent the ghost-problem by introducing also fermionic hair.Comment: 40 pages, 2 figures; v2 references added; v3 minor changes, published versio

Extremal Multicenter Black Holes: Nilpotent Orbits and Tits Satake Universality Classes

Four dimensional supergravity theories whose scalar manifold is a symmetric coset manifold U[D=4]/Hc are arranged into a finite list of Tits Satake universality classes. Stationary solutions of these theories, spherically symmetric or not, are identified with those of an euclidian three-dimensional sigma-model, whose target manifold is a Lorentzian coset U[D=3]/H* and the extremal ones are associated with H* nilpotent orbits in the K* representation emerging from the orthogonal decomposition of the algebra U[D=3] with respect to H*. It is shown that the classification of such orbits can always be reduced to the Tits-Satake projection and it is a class property of the Tits Satake universality classes. The construction procedure of Bossard et al of extremal multicenter solutions by means of a triangular hierarchy of integrable equations is completed and converted into a closed algorithm by means of a general formula that provides the transition from the symmetric to the solvable gauge. The question of the relation between H* orbits and charge orbits W of the corresponding black holes is addressed and also reduced to the corresponding question within the Tits Satake projection. It is conjectured that on the vanishing locus of the Taub-NUT current the relation between H*-orbit and W-orbit is rigid and one-to-one. All black holes emerging from multicenter solutions associated with a given H* orbit have the same W-type. For the S^3 model we provide a complete survey of its multicenter solutions associated with all of the previously classified nilpotent orbits of sl(2) x sl(2) within g[2,2]. We find a new intrinsic classification of the W-orbits of this model that might provide a paradigm for the analogous classification in all the other Tits Satake universality classes.Comment: 83 pages, LaTeX; v2: few misprints corrected and references adde

3D N=6 Gauged Supergravity: Admissible Gauge Groups, Vacua and RG Flows

We study N=6 gauged supergravity in three dimensions with scalar manifolds $\frac{SU(4,k)}{S(U(4)\times U(k))}$ for $k=1,2,3,4$ in great details. We classify some admissible non-compact gauge groups which can be consistently gauged and preserve all supersymmetries. We give the explicit form of the embedding tensors for these gauge groups as well as study their scalar potentials on the full scalar manifold for each value of $k=1,2,3,4$ along with the corresponding vacua. Furthermore, the potentials for the compact gauge groups, $SO(p)\times SO(6-p)\times SU(k)\times U(1)$ for $p=3,4,5,6$, identified previously in the literature are partially studied on a submanifold of the full scalar manifold. This submanifold is invariant under a certain subgroup of the corresponding gauge group. We find a number of supersymmetric AdS vacua in the case of compact gauge groups. We then consider holographic RG flow solutions in the compact gauge groups $SO(6)\times SU(4)\times U(1)$ and $SO(4)\times SO(2)\times SU(4)\times U(1)$ for the k=4 case. The solutions involving one active scalar can be found analytically and describe operator flows driven by a relevant operator of dimension 3/2. For non-compact gauge groups, we find all types of vacua namely AdS, Minkowski and dS, but there is no possibility of RG flows in the AdS/CFT sense for all gauge groups considered here.Comment: 43 pages, no figures references added, typoes corrected and more information adde

Nernst branes in gauged supergravity

We study static black brane solutions in the context of N = 2 U(1) gauged supergravity in four dimensions. Using the formalism of first-order flow equations, we construct novel extremal black brane solutions including examples of Nernst branes, i.e. extremal black brane solutions with vanishing entropy density. We also discuss a class of non-extremal generalizations which is captured by the first-order formalism.Comment: 44 pages, 3 figures, v2: added appendix B and references, minor typographic changes, v3: added some clarifying remarks, version published in JHE

Semiclassical Analysis of M2-brane in AdS_4 x S^7 / Z_k

We start from the classical action describing a single M2-brane on AdS_4 x S^7/ Z_k and consider semiclassical fluctuaitions around a static, 1/2 BPS configuration whose shape is AdS_2 x S^1. The internal manifold S^7/ Z_k is described as a U(1) fibration over CP^3 and the static configuration is wrapped on the U(1) fiber. Then the configuration is reduced to an AdS_2 world-sheet of type IIA string on AdS_4 x CP^3 through the Kaluza-Klein reduction on the S^1. It is shown that the fluctuations form an infinite set of N=1 supermultiplets on AdS_2, for k=1,2. The set is invariant under SO(8) which may be consistent with N=8 supersymmetry on AdS_2. We discuss the behavior of the fluctuations around the boundary of AdS_2 and its relation to deformations of Wilson loop operator.Comment: 27 pages, v2: references added, v3: major revision including the clarification of k=2 case, references added, version to appear in JHE

Nernst branes from special geometry

We construct new black brane solutions in $U(1)$ gauged ${\cal N}=2$ supergravity with a general cubic prepotential, which have entropy density $s\sim T^{1/3}$ as $T \rightarrow 0$ and thus satisfy the Nernst Law. By using the real formulation of special geometry, we are able to obtain analytical solutions in closed form as functions of two parameters, the temperature $T$ and the chemical potential $\mu$. Our solutions interpolate between hyperscaling violating Lifshitz geometries with $(z,\theta)=(0,2)$ at the horizon and $(z,\theta)=(1,-1)$ at infinity. In the zero temperature limit, where the entropy density goes to zero, we recover the extremal Nernst branes of Barisch et al, and the parameters of the near horizon geometry change to $(z,\theta)=(3,1)$.Comment: 37 pages. v2: numerical pre-factors of scalar fields q_A corrected in Section 3. No changes to conclusions. References adde

S-duality in Twistor Space

In type IIB string compactifications on a Calabi-Yau threefold, the hypermultiplet moduli space $M_H$ must carry an isometric action of the modular group SL(2,Z), inherited from the S-duality symmetry of type IIB string theory in ten dimensions. We investigate how this modular symmetry is realized at the level of the twistor space of $M_H$, and construct a general class of SL(2,Z)-invariant quaternion-Kahler metrics with two commuting isometries, parametrized by a suitably covariant family of holomorphic transition functions. This family should include $M_H$ corrected by D3-D1-D(-1)-instantons (with fivebrane corrections ignored) and, after taking a suitable rigid limit, the Coulomb branch of five-dimensional N=2 gauge theories compactified on a torus, including monopole string instantons. These results allow us to considerably simplify the derivation of the mirror map between type IIA and IIB fields in the sector where only D1-D(-1)-instantons are retained.Comment: 29 pages, 1 figur