Graviton Multiplet Research Articles

Bimetric, conformal supergravity and its superstring embedding

We discuss the connection between Weyl2 supergravity and superstrings and further discuss holography between 4-dimensional, mathcal{N} = 4 superconformal Weyl2 supergravity and mathcal{N} = 8, higher spin-four theory on AdS5. The Weyl2 plus Einstein supergravity theory is a special kind of a bimetric gravity theory and consists of a massless graviton multiplet plus an additional massive spin-two supermultiplet. Here, we argue that the additional spin-two field and its superpartners originate from massive excitations in the open string sector; just like the mathcal{N} = 4 super Yang-Mills gauge fields, they are localized on the world volume of D3-branes. The ghost structure of the Weyl action should be considered as an artifact of the truncation of the infinitely many higher derivative terms underlying the massive spin 2 action. In field theory, mathcal{N} = 4 Weyl2 supergravity exhibits superconformal invariance in the limit of vanishing Planck mass. In string theory the additional spin-two fields become massless in the tensionless limit. Therefore low string scale scenarios with large extra dimensions provide (almost) superconformal field theories with almost massless open string spin-two fields. The full mathcal{N} = 4 scalar potential including the Yang-Mills matter multiplets is presented and the supersymmetric vacua of Einstein Supergravity are shown, as expected, to be vacua of massive Weyl supergravity. Other vacua are expected to exist which are not vacua of Einstein supergravity. Finally, we identify certain spin-four operators on the 4-dimensional boundary theory that could be the holographic duals of spin-four fields in the bulk.

Twisting and localization in supergravity: equivariant cohomology of BPS black holes

We develop the formalism of supersymmetric localization in supergravity using the deformed BRST algebra defined in the presence of a supersymmetric background as recently formulated in [1]. The gravitational functional integral localizes onto the cohomology of a global supercharge Qeq, obeying Qeq2 = H, where H is a global symmetry of the background. Our construction naturally produces a twisted version of supergravity whenever supersymmetry can be realized off-shell. We present the details of the twisted graviton multiplet and ghost fields for the superconformal formulation of four-dimensional mathcal{N} = 2 supergravity. As an application of our formalism, we systematize the computation of the exact quantum entropy of supersymmetric black holes. In particular, we compute the one-loop determinant of the Qeq mathcal{V} deformation operator for the off-shell fluctuations of the Weyl multiplet around the AdS2 × S2 saddle. This result, which is consistent with the corresponding large-charge on-shell analysis, is needed to complete the first-principles computation of the quantum entropy.

Quantum gravity, fakeons and microcausality

We investigate the properties of fakeons in quantum gravity at one loop. The theory is described by a graviton multiplet, which contains the fluctuation hμν of the metric, a massive scalar ϕ and the spin-2 fakeon χμν . The fields ϕ and χμν are introduced explicitly at the level of the Lagrangian by means of standard procedures. We consider two options, where ϕ is quantized as a physical particle or a fakeon, and compute the absorptive part of the self-energy of the graviton multiplet. The width of χμν , which is negative, shows that the theory predicts the violation of causality at energies larger than the fakeon mass. We address this issue and compare the results with those of the Stelle theory, where χμν is a ghost instead of a fakeon.

Aspects of Weyl supergravity

In this paper we study the spectrum of all conformal, mathcal{N} -extended supergravities ( mathcal{N} = 1, 2, 3, 4) in four space-time dimensions. When these theories are obtained as massless limit of Einstein plus Weyl2 supergravity, the appropriate counting of the enhanced gauge symmetries allow us to derive the massless spectrum which consist of a dipole ghost graviton multiplet, a mathcal{N} -fold tripole ghost gravitino, the third state belonging to a spin 3/2 multiplet and a residual vector multiplet present for non-maximal mathcal{N} < 4 theories. These theories are not expected to have a standard gravity holographic dual in five dimensions.

Loop corrections for Kaluza-Klein AdS amplitudes

Recently we conjectured the four-point amplitude of graviton multiplets in AdS5 × S5 at one loop by exploiting the operator product expansion of mathcal{N} = 4 super Yang-Mills theory. Here we give the first extension of those results to include Kaluza-Klein modes, obtaining the amplitude for two graviton multiplets and two states of the first KK mode. Our method again relies on resolving the large N degeneracy among a family of long double-trace operators, for which we obtain explicit formulas for the leading anomalous dimensions. Having constructed the one-loop amplitude we are able to obtain a formula for the one-loop corrections to the anomalous dimensions of all twist five double-trace operators.

Quantum gravity from conformal field theory

We bootstrap loop corrections to AdS5 supergravity amplitudes by enforcing the consistency of the known classical results with the operator product expansion of mathcal{N} = 4 super Yang-Mills theory. In particular this yields much new information on the spectrum of double-trace operators which can then be used, in combination with superconformal symmetry and crossing symmetry, to obtain a prediction for the one-loop amplitude for four graviton multiplets in AdS. This in turn yields further new results on subleading O(1/N4) corrections to certain double-trace anomalous dimensions.

Two-loop supersymmetric QCD and half-maximal supergravity amplitudes

Using the duality between color and kinematics, we construct two-loop four-point scattering amplitudes in mathcal{N}=2 super-Yang-Mills (SYM) theory coupled to Nf fundamental hypermultiplets. Our results are valid in D ≤ 6 dimensions, where the upper bound corresponds to six-dimensional chiral mathcal{N}=left(1,0right) SYM theory. By exploiting a close connection with mathcal{N}=4 SYM theory — and, equivalently, six-dimensional mathcal{N}=left(1,1right) SYM theory — we find compact integrands with four-dimensional external vectors in both the maximally-helicity-violating (MHV) and all-chiral-vector sectors. Via the double-copy construction corresponding D-dimensional half-maximal supergravity amplitudes with external graviton multiplets are obtained in the MHV and all-chiral sectors. Appropriately tuning Nf enables us to consider both pure and matter-coupled supergravity, with arbitrary numbers of vector multiplets in D = 4. As a bonus, we obtain the integrands of the genuinely six-dimensional supergravities with mathcal{N}=left(1,1right) and mathcal{N}=left(2,0right) supersymmetry. Finally, we extract the potential ultraviolet divergence of half-maximal supergravity in D = 5 − 2ϵ and show that it non-trivially cancels out as expected.

Tree-level S-matrix elements from S-duality

It has been speculated that the S-matrix elements of type IIB superstring theory satisfy the Ward identity associated with the S-duality. This indicates that a group of S-matrix elements at each loop level are invariant under the linear $SL(2,R)$ transformations. If one evaluates one element of such S-dual multiplet, then all other components can be found by the simple use of the linear $SL(2,R)$ transformations. In this paper, we calculate the disk-level S-matrix element of one graviton(dilaton), one B-field and one gauge boson on the word volume of D$_3$-brane. The S-dual multiplet corresponding to the graviton(dilaton) amplitude has three(six) components. In particular, the graviton multiplet has the S-matrix element of one graviton, one R-R two-form and one gauge boson, and the dilaton multiplet has the S-matrix element of one R-R scalar, one B-field and one gauge boson vertex operators. We calculate explicitly these particular components and show that they are precisely the ones predicted by the S-duality. We have also found the low energy contact terms of the dilaton multiplet at order $\alpha'^2$.

Supergravity at the boundary of AdS supergravity

We give a general analysis of AdS boundary conditions for spin-$3/2$ Rarita-Schwinger fields and investigate boundary conditions preserving supersymmetry for a graviton multiplet in ${\mathrm{AdS}}_{4}$. Linear Rarita-Schwinger fields in ${\mathrm{AdS}}_{d}$ are shown to admit mixed Dirichlet-Neumann boundary conditions when their mass is in the range $0\ensuremath{\le}|m|&lt;1/2{l}_{\mathrm{AdS}}$. We also demonstrate that mixed boundary conditions are allowed for larger masses when the inner product is ``renormalized'' accordingly with the action. We then use the results obtained for $|m|=1/{l}_{\mathrm{AdS}}$ to explore supersymmetric boundary conditions for $\mathcal{N}=1$ ${\mathrm{AdS}}_{4}$ supergravity in which the metric and Rarita-Schwinger fields are fluctuating at the boundary. We classify boundary conditions that preserve boundary supersymmetry or superconformal symmetry. Under the AdS/CFT dictionary, Neumann boundary conditions in $d=4$ supergravity correspond to gauging the superconformal group of the three-dimensional CFT describing M2-branes, while $\mathcal{N}=1$ supersymmetric mixed boundary conditions couple the CFT to $\mathcal{N}=1$ superconformal topologically massive gravity.

Geometric precipices in string cosmology

We consider the effects of graviton multiplet fields on transitions between string gas phases. Focusing on the dilaton field, we show that it may obstruct transitions between different thermodynamic phases of the string gas, because the sign of its dimensionally reduced, $T$-duality invariant, part is conserved when the energy density of the Universe is positive. Thus, many interesting solutions for which this sign is positive end up in a future curvature singularity. Because of this, some of the thermodynamic phases of the usual gravitating string gases behave like superselection sectors. For example, a past-regular Hagedorn phase and an expanding Friedmann-Robertson-Walker (FRW) phase dominated by string momentum modes cannot be smoothly connected in the framework of string cosmology with positive sources. The singularity separates them like a geometric precipice in the moduli space, preventing the dynamics of the theory from bridging across. Sources which simultaneously violate the positivity of energy and null energy condition (NEC) could modify these conclusions. We provide a quantitative measure of positivity of energy and NEC violations that would be necessary for such transitions. These effects must dominate the Universe at the moment of transition, altering the standard gas pictures. At present, it is not known how to construct such sources from first principles in string theory.

Massive 4D, N = 1 Superspin 1 and 3/2 Multiplets and Dualities

Lagrangians for several new off-shell 4D, N = 1 supersymmetric descriptions of massive superspin-1 and superspin-3/2 multiplets are described. Taken together with the models previously constructed, there are now four off-shell formulations for the massive gravitino multiplet (superspin-1) and six off-shell formulations for the massive graviton multiplet (superspin-3/2). Duality transformations are derived which relate some of these dynamical systems.

Heterotic string dark matter from the graviton multiplet

Abstract In the string theory framework for physics beyond the standard model the hidden sector of E 8 × E 8 heterotic string theory and the graviton multiplet provide compelling sources for the dark matter in the universe. In the present investigation I consider the graviton multiplet as one particular dark matter source in heterotic string theory. In particular, it is pointed out that an appreciable fraction of dark matter from the graviton multiplet requires a mass generating phase transition around T c ≃10 8 GeV, where the symmetry partners of the graviton would evolve from an ultrahard fluid to pressureless dark matter. This indicates m ≃10 MeV for the massive components of the graviton multiplet, and it is reassuring that the corresponding dilaton lifetime τ ≃10 17 s is compatible with a dark matter interpretation.

Anatomy of two holographic renormalization group flows

We derive and solve a subset of the fluctuation equations about two domain wall solutions of D=5, N=8 gauged supergravity. One solution is dual to D=4, N=4 SYM theory perturbed by an N=1, SO(3)-invariant mass term and the other to a Coulomb branch deformation. In the first case we study all SO(3)-singlet fields. These are assembled into bulk multiplets dual to the stress tensor multiplet and to the N=1 chiral multiplets Tr Phi^2 and Tr W^2, the former playing the role of anomaly multiplet. Each of these three multiplets has a distinct spectrum of "glueball" states. This behavior is contrasted with the Coulomb branch flow in which all fluctuations studied have a continuous spectrum above a common mass gap, and spontaneous breaking of conformal symmetry is driven by a bulk vector multiplet. R-symmetry is preserved in the field theory, and correspondingly the bulk vector is dual to a linear anomaly multiplet. Generic features of the fluctuation equations and solutions are emphasized. For example, the transverse traceless modes of all fields in the graviton multiplet can be expressed in terms of an auxiliary massless scalar, and gauge fields associated with R-symmetry have a universal effective mass.

Shadow multiplets in AdS/CFT and the super-Higgs mechanism

We discuss a general pairing that occurs in compactifications of M-theory on AdS_4 x X^7 backgrounds between massless ultra short multiplets and their massive shadows, namely certain universal long multiplets with fixed protected dimensions. In particular we consider the shadow of the short graviton multiplet in N=3 compactifications. It turns out to be a massive spin 3/2 multiplet with scale dimension E_0=3 and with the quantum numbers of a super-Higgs multiplet. Hence each N=3 AdS_4 x X^7 vacuum is actually to be interpreted as a spontaneously broken phase of an N=4 theory. Comparison with standard gauged N=4 supergravity in 4 dimensions reveals the unexpected bound E_0<3 on the dimension of the broken gravitino multiplet. This hints to the existence of new versions of extended supergravities, in particular N=4 where such upper bounds are evaded and where all possible vacua have a reduced supersymmetry N_0<N. We name them shadow supergravities. In particular, using arguments based on the solvable Lie algebra parametrization of the scalar manifold, we discuss the possible structure of shadow N=4 supergravity. Using our previous results on the SCFT dual of the AdS_4 x N^{0,1,0} vacuum we discuss the SCFT realization of the universal N=3 shadow multiplet. RG flows from an N=4 to an N=3 phase are ruled out by the fact that the N=4 vacuum is at infinite distance in moduli space, denoting the presence of a topology change.

Four-point functions of lowest weight chiral primary operators inN=4four-dimensional supersymmetric Yang-Mills theory in the supergravity approximation

We show that the recently found quartic action for the scalars from the massless graviton multiplet of type IIB supergravity compactified on AdS_5\times S^5 background coincides with the relevant part of the action of the gauged N=8 5d supergravity on AdS_5. We then use this action to compute the 4-point function of the lowest weight chiral primary operators $\tr(\phi^{(i}\phi^{j)})$ in N=4 SYM_4 at large $N$ and at strong `t Hooft coupling.

The complete [formula omitted] Kaluza–Klein spectrum of [formula omitted] supergravity on [formula omitted

We derive the invariant operators of the zero-form, the one-form, the two-form and the spinor from which the mass spectrum of Kaluza–Klein of eleven-dimensional supergravity on AdS 4×N 010 can be derived by means of harmonic analysis. We calculate their eigenvalues for all representations of SU(3)×SO(3) . We show that the information contained in these operators is sufficient to reconstruct the complete N=3 supersymmetry content of the compactified theory. We find the N=3 massless graviton multiplet, the Betti multiplet and the SU(3) Killing vector multiplet.

K–K excitations on AdS 5× S5 as N=4 “primary” superfields

We show that the K–K spectrum of IIB string on AdS 5× S 5 is described by “twisted chiral” N=4 superfields, naturally described in “harmonic superspace”, obtained by taking suitable gauge singlets polynomials of the D3-brane boundary SU( n) superconformal field theory. To each p-order polynomial is associated a massive K–K short representation with 256× 1 12 p 2(p 2−1) states. The p=2 quadratic polynomial corresponds to the “supercurrent multiplet” describing the “massless” bulk graviton multiplet.

Interaction of moving D-branes on orbifolds

We use the boundary state formalism to study the interaction of two moving identical D-branes in the Type II superstring theory compactified on orbifolds. By computing the velocity dependence of the amplitude in the limit of large separation we can identify the nature of the different forces between the branes. In particular, in the Z_3 orbifold case we find a boundary state which is coupled only to the N=2 graviton multiplet containing just a graviton and a vector like in the extremal Reissner-Nordstr\"{o}m configuration. We also discuss other cases including $T_4/Z_2$.

Symmetries in a unified gauge theory with torsion

We consider aGL4×Un generalization of the Bonnor-Moffat-Boal formulation of Einstein unified field theory. Choosing a suitable form of the curvature tensor and introducing a phenomenological electric-current density, we show that charge conjugation corresponds to complex conjugation of the nonsymmetric unified fields. Making use of the complex tetrads underlying the fundamental Hermitian tensor field, we show that the gauge-covariant Dirac equation is obtained by minimal replacement of the Christoffel affinity of GR, with the generalized torsion containing connection. Finally, we consider spontaneous breaking of theUn gauge symmetry. The formalism splits into a vector sector and a tensor sector, the rotation angles\(\theta _W \) and\(\theta _G \) diagonalizing the vector and tensor mass matrices being related by\(\theta _G = \theta _W + \frac{1}{2}\pi \). TheUn components of the torsion vector describe the vector bosons mediating the electromagnetic and weak interactions, while theUn components of the symmetric part of the fundamental tensor describe the graviton and aSUn multiplet of tensor mesons.