Dilaton Supergravity Research Articles

Carroll dilaton supergravity in two dimensions

We construct and discuss generic N = 1 and N = 2 Carroll dilaton supergravity in two dimensions. We apply our general results to the supersymmetric Carroll-Jackiw-Teitelboim model, including a discussion of specific boundary conditions. For N = 2 Carroll dilaton supergravity, we find two versions, dubbed “democratic” and “despotic”.

Supergravity p -branes with scalar charge

Standard dilatonic supergravity $p$-branes have scalar charges that are not independent parameters, but are determined by the brane tension and Page charges. This feature can be traced to the no-hair theorem in the four-dimensional Einstein-scalar gravity, implying that more general solutions with independent scalar charges can have naked singularities. Since singular branes are also of interest as tentative classical counterparts of unstable tachyonic branes and/or brane-antibrane systems, it is worth investigating branes with independent scalar charges in more detail. Here we study singular branes associated with the Fisher-Janis-Newman-Winicour solution of four-dimensional gravity. In the case of codimension three, we also construct singular branes endowed with a Zipoy-Voorhees-type oblateness parameter. It is expected that such branes will not be supersymmetric in the string theory. We demonstrate this in the special case of NS5-branes of type II theory. We analyze geodesics and test scalar perturbations of new solutions focusing on possible quantum healing of classical singularities.

Twistor Actions for Integrable Systems

Many integrable systems can be reformulated as holomorphic vector bundles on twistor space. This is a powerful organizing principle in the theory of integrable systems. One shortcoming is that it is formulated at the level of the equations of motion. From this perspective, it is mysterious that integrable systems have Lagrangians. In this paper, we study a Chern-Simons action on twistor space and use it to derive the Lagrangians of some integrable sigma models. Our focus is on examples that come from dimensionally reduced gravity and supergravity. The dimensional reduction of general relativity to two spacetime dimensions is an integrable coset sigma model coupled to a dilaton and 2d gravity. The dimensional reduction of supergravity to two spacetime dimensions is an integrable coset sigma model coupled to matter fermions, a dilaton, and 2d supergravity. We derive Lax operators and Lagrangians for these 2d integrable systems using the Chern-Simons theory on twistor space. In the supergravity example, we use an extended setup in which twistor Chern-Simons theory is coupled to a pair of matter fermions.

Boundary theories for dilaton supergravity in 2D

The mathfrak{o}mathfrak{s}mathfrak{p}left(2, mathbb{N}right) -BF formulation of dilaton supergravity in two dimensions is considered. We introduce a consistent class of asymptotic conditions preserved by the extended superreparametrization group of the thermal circle at infinity. In the N = 1 and N = 2 cases the phase space foliation in terms of orbits of the super-Virasoro group allows to formulate suitable integrability conditions for the boundary terms that render the variational principle well-defined. Once regularity conditions are imposed, requiring trivial holonomy around the contractible cycle the asymptotic symmetries are broken to some subsets of exact isometries. Different coadjoint orbits of the asymptotic symmetry group yield different types of boundary dynamics; we find that the action principle can be reduced to either the extended super-Schwarzian theory, consistent with the dynamics of a non-vanishing Casimir function, or to superparticle models, compatible with bulk configurations whose Casimir is zero. These results are generalized to mathcal{N}ge 3 by making use of boundary conditions consistent with the loop group of OSp(2, ℕ). Appropriate integrability conditions permit to reduce the dynamics of dilaton supergravity to a particle moving on the OSp(2, ℕ) group manifold. Generalizations of the boundary dynamics for mathcal{N}>2 are obtained once bulk geometries are supplemented with super-AdS2 asymptotics.

The gravitational sector of 2d (0, 2) F-theory vacua

F-theory compactifications on Calabi-Yau fivefolds give rise to two-dimensional N = (0, 2) supersymmetric field theories coupled to gravity. We explore the dilaton supergravity defined by the moduli sector of such compactifications. The massless moduli spectrum is found by uplifting Type IIB compactifications on Calabi-Yau fourfolds. This spectrum matches expectations from duality with M-theory on the same elliptic fibration. The latter defines an N = 2 Supersymmetric Quantum Mechanics related to the 2d (0, 2) F-theory supergravity via circle reduction. Using our recent results on the gravitational anomalies of duality twisted D3-branes wrapping curves in Calabi-Yau fivefolds we show that the F-theory spectrum is anomaly free. We match the classical Chern-Simons terms of the M-theory Super Quantum Mechanics to one-loop contributions to the effective action by S1 reduction of the dual F-theory.

Two-dimensional N=(2,2) dilaton supergravity from graded Poisson-Sigma models II

The integrability of N=(2,2) dilaton supergravity in two dimensions is studied by the use of the graded Poisson-Sigma model approach. Though important differences compared to the purely bosonic models are found, the general analytic solutions are obtained. The latter include minimally gauged models as well as an ungauged version. BPS solutions are an especially interesting subclass.

Two-dimensional N=(2,2) dilaton supergravity from graded Poisson-Sigma models I

The formalism of graded Poisson-Sigma models allows the construction of $N=\left(2,2\right)$ dilaton supergravity in terms of a minimal number of fields. For the gauged chiral U(1) symmetry the full action, involving all fermionic contributions, is derived. The twisted chiral case follows by simple redefinition of fields. The equivalence of our approach to the standard second order one in terms of superfields is presented, although for the latter so far only the bosonic part of the action seems to have been available in the literature. It is shown how ungauged models can be obtained in a systematic way and some relations to relevant literature in superstring theory are discussed.

Quantization of 2D dilaton supergravity with matter

General N = (1,1) dilaton supergravity in two dimensions allows a background independent exact quantization of the geometric part, if these theories are formulated as specific graded Poisson-sigma models. The strategy developed for the bosonic case can be carried over, although considerable computational complications arise when the hamiltonian constraints are evaluated in the presence of matter. Nevertheless, the constraint structure is the same as in the bosonic theory. In the matterless case gauge independent nonlocal correlators are calculated non-perturbatively. They respect local quantum triviality and allow a topological interpretation. In the presence of matter the ensuing nonlocal effective theory is expanded in matter loops. The lowest order tree vertices are derived and discussed, entailing the phenomenon of virtual black holes which essentially determine the corresponding S-matrix. Not all vertices are conformally invariant, but the S-matrix is invariant, as expected. Finally, the proper measure for the 1-loop corrections is addressed. It is argued how to exploit the results from fixed background quantization for our purposes.

Supersymmetric black holes in 2D dilaton supergravity: baldness and extremality

We present a systematic discussion of supersymmetric solutions of 2D dilaton supergravity. In particular those solutions which retain at least half of the supersymmetries are ground states with respect to the bosonic Casimir function (essentially the ADM mass). Nevertheless, by tuning the prepotential appropriately, black hole solutions may emerge with an arbitrary number of Killing horizons. The absence of dilatino and gravitino hair is proven. Moreover, the impossibility of supersymmetric dS ground states and of nonextremal black holes is confirmed, even in the presence of a dilaton. In these derivations the knowledge of the general analytic solution of 2D dilaton supergravity plays an important role. The latter result is addressed in the more general context of gPSMs which have no supergravity interpretation. Finally it is demonstrated that the inclusion of non-minimally coupled matter, a step which is already nontrivial by itself, does not change these features in an essential way.

Complete solution of 2D superfield supergravity from graded Poisson-sigma models, and the super point particle

Recently an alternative description of 2D supergravities in terms of graded Poisson-sigma models (GPSM) has been given. As pointed out previously by the present authors a certain subset of GPSMs can be interpreted as ``genuine'' supergravity, satisfying the well-known limits of supergravity, albeit deformed by the dilaton field. In our present paper we show that precisely that class of GPSMs corresponds one-to-one to the known dilaton supergravity superfield theories presented a long time ago by Park and Strominger. Therefore, the unique advantages of the GPSM approach can be exploited for the latter: We are able to provide the first complete classical solution for any such theory. On the other hand, the straightforward superfield formulation of the point particle in a supergravity background can be translated back into the GPSM frame, where ``supergeodesics'' can be discussed in terms of a minimal set of supergravity field degrees of freedom. Further possible applications such as the (almost) trivial quantization are mentioned.

Superstrings in 2D backgrounds with R–R flux and new extremal black holes

The hybrid formalism is used to quantize the superstring compactified to two-dimensional target-space in a manifestly spacetime supersymmetric manner. A quantizable sigma model action is then constructed for the type II superstring in curved two-dimensional supergravity backgrounds which can include Ramond–Ramond flux. Such curved backgrounds include Calabi–Yau four-fold compactifications with Ramond–Ramond flux, and new extremal black hole solutions in two-dimensional dilaton supergravity theory. These black hole solutions are a natural generalization of the CGHS model and might be possible to describe using a supergroup version of the SL(2, R)/ U(1) WZW model. We also study some dynamical aspects of the new black holes, such as formation and evaporation.

Super Liouville black holes

We describe in superspace a classical theory of of two dimensional $(1,1)$ dilaton supergravity coupled to a super-Liouville field, and find exact super black hole solutions to the field equations that have non-constant curvature. We consider the possibility that a gravitini condensate forms and look at the implications for the resultant spacetime structure. We find that all such condensate solutions have a condensate and/or naked curvature singularity.

Conformal anomaly for 2D and 4D dilaton coupled spinors

We study quantum dilaton coupled spinors in two and four dimensions. Making a classical transformation of the metric, the dilaton coupled spinor theory is transformed into the minimal spinor theory with another metric and in the 4D case a spinor also in the background of the nontrivial vector field. This makes it possible to calculate 2D and 4D dilaton-dependent conformal (or Weyl) anomalies easily. The anomaly-induced effective action for such spinors is derived. In the 2D case, the effective action reproduces, without any extra terms, the term added by hand in the quantum correction for the Russo-Susskind-Thorlacius model, which is exactly solvable. For the 4D spinor the chiral anomaly which depends explicitly on the dilaton is also found. As some applications we discuss supersymmetric black holes (BH's) in dilatonic supergravity with Wess-Zumino-type matter and Hawking radiation in the same theory. As another application we investigate spherically reduced Einstein gravity with a 2D dilaton coupled fermion anomaly-induced effective action and show the existence of quantum-corrected Schwarzchild--de Sitter (Nariai) BH's with multiple horizons.

Target-superspace in 2d dilatonic supergravity

The N=1 supersymmetric version of generalized 2d dilaton gravity can be cast into the form of a Poisson σ-model, where the target space and its Poisson bracket are graded. The target space consists of a 1+1 superspace and the dilaton, which is the generator of Lorentz boosts therein. The Poisson bracket on the target space induces the invariance of the worldsheet theory against both diffeomorphisms and local supersymmetry transformations (superdiffeomorphisms). The machinery of Poisson σ-models is then used to find the general local solution to the field equations. As a byproduct, classical equivalence between the bosonic theory and its supersymmetric extension is found.

Cosmological supergravity from a massive superparticle and super-cosmological black holes

We describe in superspace a classical theory of two-dimensional (1, 1) dilaton supergravity with a cosmological constant, both with and without coupling to a massive superparticle. We give general exact non-trivial superspace solutions for the compensator superfield that describes the supergravity in both cases. We then use these compensator solutions to construct models of two-dimensional supersymmetric cosmological black holes.

Quantum cosmology in the models of 2D and 4D dilatonic supergravity with WZ matter

We consider N=1 two-dimensional (2d) dilatonic supergravity (SG), 2d dilatonic SG obtained by dimensional reduction from N=1 four-dimensional (4d) SG, N=2 2d dilatonic SG and string-inspired 4d dilatonic SG. For all the theories, the corresponding action on a bosonic background is constructed and the interaction with $N$ (dilatonic) Wess-Zumino (WZ) multiplets is presented. Working in the large-N approximation, it is enough to consider the trace anomaly induced effective action due to dilaton-coupled conformal matter as a quantum correction (for 2d models s-waves approximation is additionally used). The equations of motion for all such models with quantum corrections are written in a form convenient for numerical analysis. Their solutions are numerically investigated for 2d and 4d Friedmann-Robertson-Walker (FRW) or 4d Kantowski-Sacks Universes with a time-dependent dilaton via exponential dilaton coupling. The evolution of the corresponding quantum cosmological models is given for different choices of initial conditions and theory parameters. In most cases we find quantum singular Universes. Nevertheless, there are examples of Universe non-singular at early times. Hence, it looks unlikely that quantum matter back reaction on dilatonic background (at least in large $N$ approximation) may really help to solve the singularity problem.

Super black hole from cosmological supergravity with a massive superparticle

We describe in superspace a classical theory of two dimensional (1,1) cosmological dilaton supergravity coupled to a massive superparticle. We give an exact non-trivial superspace solution for the compensator superfield that describes the supergravity, and then use this solution to construct a model of a two-dimensional supersymmetric black hole.

Trace anomaly induced effective action and 2D black holes for dilaton coupled supersymmetric theories

The action for two-dimensional (2D) dilatonic supergravity with dilaton coupled matter and dilaton multiplets is constructed. A trace anomaly and anomaly induced effective action (in components as well as in supersymmetric form) for a matter supermultiplet on a bosonic background are found. The one-loop effective action and large-$N$ effective action for quantum dilatonic supergravity are also calculated. Using an induced effective action one can estimate the back reaction of dilaton coupled matter to the classical black hole solutions of dilatonic supergravity. That is done on the example of a supersymmetric CGHS model with dilaton coupled quantum matter where Hawking radiation which turns out to be zero is calculated. A similar 2D analysis may be used to study spherically symmetric collapse for other models of 4D supergravity.

Supergravity from a massive superparticle and the simplest super black hole

We describe in superspace a theory of a massive superparticle coupled to a version of two-dimensional (1,1) dilaton supergravity. The (1 + 1)-dimensional supergravity is generated by the stress-energy of the superparticle, and the evolution of the superparticle is reciprocally influenced by the supergravity. We obtain exact superspace solutions for both the superparticle worldline and the supergravity fields. We use the resultant non-trivial compensator superfield solution to construct a model of a two-dimensional supersymmetric black hole.

Trace anomaly induced effective action and Hawking radiation for 2d dilatonic supergravity

We construct the theory of 2d dilatonic supergravity(SG) with matter and dilaton supermultiplets coupled to dilaton functions. Trace anomaly and induced effective action for matter supermultiplet are calculated (what gives also large-N effective action for dilatonic SG). Study of black holes and Hawking radiation which turns out to be zero in supersymmetric CGHS model with dilaton coupled matter is presented. In the same way one can study spherically symmetric collapse for other 4d SG using simplified 2d approach.