Supergravity Equations Research Articles

The spinorial geometry of supersymmetric IIB backgrounds

We investigate the Killing spinor equations of IIB supergravity for one Killing spinor. We show that there are three types of orbits of Spin(9, 1) in the space of Weyl spinors which give rise to Killing spinors with stability subgroups and G2. We solve the Killing spinor equations for the and invariant spinors, give the fluxes in terms of the geometry and determine the conditions on the spacetime geometry imposed by supersymmetry. In both cases, the spacetime admits a null, self-parallel, Killing vector field. We also apply our formalism to examine a class of backgrounds which admit one and two pure spinors as Killing spinors and investigate the geometry of the spacetimes.

Brane Worlds in Collision

We obtain an exact solution of the supergravity equations of motion in which the four-dimensional observed Universe is one of a number of colliding D3 branes in a Calabi-Yau background. The collision results in the ten-dimensional spacetime splitting into disconnected regions, bounded by curvature singularities. However, near the D3 branes the metric remains static during and after the collision. We also obtain a general class of solutions representing p-brane collisions in arbitrary dimensions, including one in which the universe ends with the mutual annihilation of a positive-tension and a negative-tension 3 brane.

The spinorial geometry of supersymmetric backgrounds

We propose a new method to solve the Killing spinor equations of 11-dimensional supergravity based on a description of spinors in terms of forms and on the Spin(1, 10) gauge symmetry of the supercovariant derivative. We give the canonical form of Killing spinors for backgrounds preserving two supersymmetries, N = 2, provided that one of the spinors represents the orbit of Spin(1, 10) with stability subgroup SU(5). We directly solve the Killing spinor equations of N = 1 and some N = 2, N = 3 and N = 4 backgrounds. In the N = 2 case, we investigate backgrounds with SU(5) and SU(4) invariant Killing spinors and compute the associated spacetime forms. We find that N = 2 backgrounds with SU(5) invariant Killing spinors admit a timelike Killing vector and that the space transverse to the orbits of this vector field is a Hermitian manifold with an SU(5)-structure. Furthermore, N = 2 backgrounds with SU(4) invariant Killing spinors admit two Killing vectors, one timelike and one spacelike. The space transverse to the orbits of the former is an almost Hermitian manifold with an SU(4)-structure. The spacelike Killing vector field leaves the almost complex structure invariant. We explore the canonical form of Killing spinors for backgrounds preserving more than two supersymmetries, N > 2. We investigate a class of N = 3 and N = 4 backgrounds with SU(4) invariant spinors. We find that in both cases the space transverse to a timelike vector field is a Hermitian manifold equipped with an SU(4)-structure and admits two holomorphic Killing vector fields. We also present an application to M-theory Calabi–Yau compactifications with fluxes to one dimension.

On the fakeness of fake supergravity

We revisit and complete the study of curved BPS-domain walls in matter-coupled $5D$, $\mathcal{N}=2$ supergravity and carefully analyze the relation to gravitational theories known as ``fake supergravities.'' We first show that curved BPS-domain walls require the presence of nontrivial hypermultiplet scalars, whereas walls that are solely supported by vector multiplet scalars are necessarily flat, due to the constraints from very special geometry. We then recover fake supergravity as the effective description of true supergravity where one restricts the attention to the flowing scalar field of a given BPS-domain wall. In general, however, true supergravity can be simulated by fake supergravity at most locally, based upon two choices: (i) a suitable adapted coordinate system on the scalar manifold, such that only one scalar field plays a dynamical role, and (ii) a gauge fixing of the SU(2) connection on the quaternionic-K\"ahler manifold, as this connection does not fit the simple formalism of fake supergravity. Employing these gauge and coordinate choices, the BPS-equations for both vector and hypermultiplet scalars become identical to the fake supergravity equations, once the line of flow is determined by the full supergravity equations.

IIB supergravity and [formula omitted

We analyze the geodesic E10/K(E10)σ-model in a level decomposition w.r.t. the A8×A1 subalgebra of E10, adapted to the bosonic sector of type IIB supergravity, whose SL(2,R) symmetry is identified with the A1 factor. The bosonic supergravity equations of motion, when restricted to zeroth and first order spatial gradients, are shown to match with the σ-model equations of motion up to level ℓ=4. Remarkably, the self-duality of the five-form field strength is implied by E10 and the matching.

M5-brane Effective Action as an On-shell Action in Supergravity

We show that the covariant effective action for M5-brane is a solution to the Hamilton-Jacobi (H-J) equations of 11-dimensional supergravity. The solution to the H-J equations reproduces the supergravity solution that represents the M2-M5 bound states.

Non-critical supergravity (d> 1) and holography

In this paper we investigate the supergravity equations of motion associated with non-critical ($d>1$) type II string theories that incorporate RR forms. Using a superpotential formalism we determine several classes of solutions. In particular we find analytic backgrounds with a structure of $AdS_{p+2}\times S^{d-p-2}$ and numerical solutions that asymptote a linear dilaton with a topology of $R^{1,d-3}\times R \times S^1$. The SUGRA solutions we have found can serve as anti holographic descriptions of gauge theories in a large $N$ limit which is different than the one of the critical gauge/gravity duality. It is characterized by $N\rt \infty$ and $g_{YM}^2 N \sim 1$. We have made the first steps in analyzing the corresponding gauge theory properties like Wilson loops and the glue-ball spectra.

Wrapped D-branes as BPS monopoles: The moduli space perspective

We study the four dimensional effective action of a system of D6-branes wrapped on the $K3$ manifold times a torus, allowing the volume of the internal manifolds to remain dynamical. An unwrapped brane is at best a Dirac monopole of the dual RR sector field to which it couples. After wrapping, a brane is expected to behave as a BPS monopole, where the Higgs vacuum expectation value is set by the size of the $K3.$ We determine the moduli space of an arbitrary number of these wrapped branes by introducing a time dependent perturbation of the static solution and expanding the supergravity equations of motion to determine the dynamics of this perturbation, in the low velocity limit. The result is the hyper-K\"ahler generalization of the Euclidean Taub-NUT metric presented by Gibbons and Manton. We note that our results also pertain to the behavior of bound states of Kaluza-Klein monopoles and wrapped NS5-branes in the ${T}^{4}$ compactified heterotic string.

D=4supergravity dynamically coupled to superstring in a superfield Lagrangian approach

We elaborate a full superfield description of the interacting system of dynamical $D=4,$ $N=1$ supergravity and a dynamical superstring. As far as a minimal formulation of simple supergravity is used, such a system should contain as well the tensor (real linear) multiplet which describes the dilaton and the two-superform gauge field whose pullback provides the Wess-Zumino term for the superstring. The superfield action is given by the sum of the Wess-Zumino action for $D=4,$ $N=1$ superfield supergravity, the superfield action for the tensor multiplet in curved superspace, and the Green-Schwarz superstring action. The latter includes the coupling to the tensor multiplet both in the Nambu-Goto and in the Wess-Zumino terms. We derive superfield equations of motion including, besides the superfield supergravity equations with the source, the source-full superfield equations for the linear multiplet. The superstring equations keep the same form as for the superstring in supergravity and 2-superform background. The analysis of gauge symmetries shows that the superfield description of the interacting system is gauge equivalent to the dynamical system described by the sum of the spacetime, component action for supergravity interacting with the tensor multiplet, and of the purely bosonic string action.

Cosmological backgrounds of superstring theory and solvable algebras: oxidation and branes

We develop a systematic algorithm to construct, classify and study exact solutions of type IIA/B supergravity which are time-dependent and homogeneous and, hence, represent candidate cosmological backgrounds. Using the formalism of solvable Lie algebras to represent the geometry of non-compact coset manifolds U/H we are able to reduce the supergravity field equations to the geodesic equations in U/H and rephrase these latter in a completely algebraic setup by means of the so-called Nomizu operator representation of covariant derivatives in solvable group manifolds. In this way a systematic method of integration of supergravity equations is provided. We show how the possible D=3 solutions are classified by non-compact subalgebras G⊂E 8(8) and their ten-dimensional physical interpretation (oxidation) depends on the classification of the different embeddings G↪E 8(8). We give some preliminary examples of explicit solutions based on the simplest choice G=A 2. We also show how, upon oxidation, these solutions provide a smooth and exact realization of the bouncing phenomenon on Weyl chamber walls envisaged by the cosmological billiards of Damour et al. We also show how this physical phenomenon is triggered by the presence of Euclidean D-branes possibly interpretable at the microscopic level as S-branes. We outline how our analysis could be extended to a wider setup where, by further reducing to D=2,1, more general backgrounds could be constructed applying our method to the infinite algebras E 9,10.

New D=6, [formula omitted] gauged supergravity with supersymmetric (Minkowski)4×S2 vacuum

We obtain a new gauged D=6, N=(1,1) pure supergravity by a generalised consistent Kaluza–Klein reduction of M-theory on K3×R. The reduction requires a conspiratory gauging of both the Cremmer–Julia type global (rigid) symmetry and the homogeneous rescaling symmetry of the supergravity equations of motion. The gauged supergravity is different from the Romans D=6 gauged supergravity in that the four vector fields in our new theory are all abelian. We show that it admits a supersymmetric (Minkowski)4×S2 vacuum, which can be lifted to D=11 where it becomes the near-horizon geometry of two intersecting M5-branes wrapping on a supersymmetric two-cycle of K3.

On higher-order corrections in M theory

A theoretical analysis of higher-order corrections to D=11 supergravity is given in a superspace framework. It is shown that any deformation of D=11 supergravity for which the lowest-dimensional component of the four-form $G_4$ vanishes is trivial. This implies that the equations of motion of D=11 supergravity are specified by an element of a certain spinorial cohomology group and generalises previous results obtained using spinorial or pure spinor cohomology to the fully non-linear theory. The first deformation of the theory is given by an element of a different spinorial cohomology group with coefficients which are local tensorial functions of the massless supergravity fields. The four-form Bianchi Identities are solved, to first order and at dimension $-{1/2}$, in the case that the lowest-dimensional component of $G_4$ is non-zero. Moreover, it is shown how one can calculate the first-order correction to the dimension-zero torsion and thus to the supergravity equations of motion given an explicit expression for this object in terms of the supergravity fields. The version of the theory with both a four-form and a seven-form is discussed in the presence of the five-brane anomaly-cancelling term. It is shown that the supersymmetric completion of this term exists and it is argued that it is the unique anomaly-cancelling invariant at this dimension which is at least quartic in the fields. This implies that the first deformation of the theory is completely determined by the anomaly term from which one can, in principle, read off the corrections to all of the superspace field strength tensors.

On the Equivalence of Bound State Solutions

In this paper we show the equivalence of various (nonthreshold) bound state solutions of branes, or equivalently branes in background potentials, in ten- and eleven-dimensional supergravity. We compare solutions obtained in two very different ways. One method uses a zero mode analysis to make an ansatz which makes it possible to solve the full nonlinear supergravity equations. The other method utilizes T duality techniques to turn on the fields on the brane. To be specific, in eleven dimensions we show the equivalence for the (M2,M5) bound state, or equivalently an M5-brane in a C(3) field, where we also consider the (MW,M2,M2′,M5) solution, which can be obtained from the (M2,M5) bound state by a boost. In ten dimensions we show the equivalence for the ((F,D1),D3) bound states as well as the bound states of (p,q) five-branes with lower dimensional branes in type IIB, corresponding to D3-branes in B(2) and C(2) fields and (p,q) five-branes in B(2), C(2) and C(4) fields. We also comment on the recently proposed V duality related to infinitesimally boosted solutions.

Sound of M theory

We consider sound propagation on M5- and M2-branes in the hydrodynamic limit. In particular, we look at the low energy description of a stack of N M-branes at finite temperature. At low energy, the M-branes are well described, via the AdS/CFT correspondence, in terms of classical solutions to the eleven dimensional supergravity equations of motion. From this gravitational description, we calculate Lorentzian signature two-point functions of the stress-energy tensor on these M-branes in the long-distance, low-frequency limit, i.e. the hydrodynamic limit. The poles in these Green's functions show evidence for sound propagation in the field theory living on the M-branes.

Superstrings in graviphoton background and Script N = 1/2+3/2 supersymmetry

Motivated by Ooguri and Vafa, we study superstrings in flat R^4 in a constant self-dual graviphoton background. The supergravity equations of motion are satisfied in this background which deforms the N=2 d=4 flat space super-Poincare algebra to another algebra with eight supercharges. A D-brane in this space preserves a quarter of the supercharges; i.e. N=1/2 supersymmetry is realized linearly, and the remaining N=3/2 supersymmetry is realized nonlinearly. The theory on the brane can be described as a theory in noncommutative superspace in which the chiral fermionic coordinates $\theta^\alpha$ of N=1 d=4 superspace are not Grassman variables but satisfy a Clifford algebra.

String theoretic bounds on Lorentz-violating warped compactification

We consider warped compactifications that solve the 10 dimensional supergravity equations of motion at a point, stabilize the position of a D3-brane world, and admit a warp factor that violates Lorentz invariance along the brane. This gives a string embedding of ``asymmetrically warped'' models which we use to calculate stringy (\alpha') corrections to standard model dispersion relations, paying attention to the maximum speeds for different particles. We find, from the dispersion relations, limits on gravitational Lorentz violation in these models, improving on current limits on the speed of graviton propagation, including those derived from field theoretic loops. We comment on the viability of models that use asymmetric warping for self-tuning of the brane cosmological constant.

Null-brane solutions in supergravities

We find a new class of time-dependent brane solutions in supergravities in arbitrary dimensions D. These are general intersecting light-like branes (null-branes), and their superposition and intersection rules are obtained. This is achieved by directly solving bosonic field equations for supergravity coupled to a dilaton and antisymmetric tensor fields. We discuss their possible significance.

Intersection rules for S-branes

We give a model-independent derivation of general intersecting rules for spacelike branes (S-branes) in arbitrary dimensions d. This is achieved by directly solving bosonic field equations for supergravity coupled to a dilaton and antisymmetric tensor fields with minimal ansätze. We compare the results with those in eleven-dimensional supergravity and other solutions.

The Hydrodynamics of M-Theory

We consider the low energy limit of a stack of N M-branes at finite temperature. In this limit, the M-branes are well described, via the AdS/CFT correspondence, in terms of classical solutions to the eleven dimensional supergravity equations of motion. We calculate Minkowski space two-point functions on these M-branes in the long-distance, low-frequency limit, i.e. the hydrodynamic limit, using the prescription of Son and Starinets [hep-th/0205051]. From these Green's functions for the R-currents and for components of the stress-energy tensor, we extract two kinds of diffusion constant and a viscosity. The N dependence of these physical quantities may help lead to a better understanding of M-branes.

An orientifold ofAdS5×T11with D7-branes, the associated α′2-corrections and their role in the dual Script N = 1 Sp(2N+2M) × Sp(2N) gauge theory

We study the N=1 Sp(2N+2M)xSp(2N) gauge theory on a stack of N physical and M fractional D3-branes in the background of an orientifolded conifold. The gravity dual is a type IIB orientifold of adS_5xT^11 (with certain background fluxes turned on) containing an O7-plane and 8 D7-branes. In the conformal case (M=0), we argue that the alpha'^2-corrections localized on the 8 D7-branes and the O7-plane should give vanishing contributions to the supergravity equations of motion for the bulk fields. In the cascading case (M not equal to 0), we argue that the alpha'^2-terms give rise to corrections which in the dual Sp(2N+2M)xSp(2N) gauge theory can be interpreted as corrections to the anomalous dimensions of the matter fields.