We find a new non BPS solution in $N=2$ $D=4$ gauged supergravity coupled to $U(1)$ gauge fields and matter. It consists in a closed universe with two extremal black holes of equal size, surrounding two singularities. They have opposite magnetic charges (and no electric charges), but stay in static equilibrium thanks to the positive pressure of a cosmological constant. The geometry is perfectly symmetric under the exchange of the black holes and the flip of the sign of the charges. However the scalar field is non constant and non symmetric, with different values at the horizons, which depend on a real modulus. At one of the horizon the solution becomes $\frac 12$-BPS supersymmetric, while at the other one there is no supersymmetry, but the entropy remains independent from the scalar modulus.
We study de Sitter configurations in ten-dimensional string models where supersymmetry is either absent or broken at the string scale. To this end, we derive expressions for the cosmological constant in general warped flux compactifications with localized sources, which yield no-go theorems that extend previous works on supersymmetric cases. We frame our results within a dimensional reduction and connect them to a number of Swampland conjectures, corroborating them further in the absence of supersymmetry. Furthermore, we construct a top-down string embedding of de Sitter brane-world cosmologie…
Stable non-supersymmetric Anti-de Sitter (AdS) vacua of string theory are widely believed not to exist. In this letter, we analytically compute the full bosonic Kaluza-Klein spectrum around the ${\rm G_2}$-invariant non-supersymmetric $\textrm{AdS}_4$ solution of massive IIA supergravity, and show that it is perturbatively stable. We also provide evidence that six other non-supersymmetric $\textrm{AdS}_4$ solutions of massive IIA supergravity are perturbatively stable. Since previous studies have indicated that these AdS vacua may also be non-perturbatively stable, our findings pose a challeng…
We test the robustness of the conditions required for the existence of (supersymmetric) warped flux anti-de Sitter, de Sitter, and Minkowski backgrounds in supergravity theories using as examples suitable foliations of anti-de Sitter spaces. We find that there are supersymmetric de Sitter solutions in supergravity theories including maximally supersymmetric ones in 10- and 11-dimensional supergravities. Moreover, warped flux Minkowski backgrounds can admit Killing spinors which are not Killing on the Minkowski subspace and therefore cannot be put in a factorized form.
We show that there exists a supersymmetric de Sitter background for the D=6, N=2, F(4) supergravity preserving the compact R-symmetry and gauging with respect to the conventional Anti de Sitter version of the theory. We construct the gauged matter coupled F(4) de Sitter supergravity explicitly and show that it contains ghosts in the vector sector.
We determine the most general near-horizon geometry of a supersymmetric, asymptotically anti-de Sitter, black hole solution of five-dimensional minimal gauged supergravity that admits two rotational symmetries. The near-horizon geometry is that of the supersymmetric, topologically spherical, black hole solution of Chong et al. This proves that regular supersymmetric anti-de Sitter black rings with two rotational symmetries do not exist in minimal supergravity. However, we do find a solution corresponding to the near-horizon geometry of a supersymmetric black ring held in equilibrium by a conic…
We construct a four dimensional Yang-Mills theory with ${\cal N}=4$ twisted supersymmetry whose classical vacua correspond to four dimensional anti-de Sitter space. The theory utilizes a complex gauge field whose real part is a spin connection which is used to enforce local Lorentz invariance. The imaginary part of the connection can then be interpreted as a vierbein. The topological construction ensures that the partition function and classical vacua are independent of the background geometry. Additionally a supersymmetric and gauge invariant lattice construction is possible yielding a non-pe…
We use the one loop vacuum polarization induced by scalar quantum electrodynamics to compute the electric and magnetic fields of point charges and magnetic dipoles on a locally de Sitter background. Our results are consistent with the physical picture of an inflating universe filling with a vast sea of charged particles as more and more virtual infrared scalar are ripped out of the vacuum. One consequence is that vacuum polarization quickly becomes nonperturbatively strong. Our computation employs the Schwinger-Keldysh effective field equations and is done in flat, conformal coordinates. Resul…
We describe new non-supersymmetric conformal field theories in three and four dimensions, using the CFT/AdS correspondence. In order to believe in their existence at large N_c and strong 't Hooft coupling, we explicitly check the stability of the corresponding non-supersymmetric anti-de Sitter backgrounds. Cases of particular interest are the relevant deformations of the N=4 SCFT in SU(3) and SO(5) invariant directions. It turns out that the former is a stable, and the latter an unstable non-supersymmetric type IIB background.
It has recently been conjectured that string theory does not admit de Sitter critical points. This note points out that in several cases, including KKLT or racetrack models, this statement is equivalent to the absence of supersymmetric Minkowski or AdS solutions. This equivalence arises from establishing the positivity of the potential in a large-radius limit, requiring a turnover of the potential before reaching an AdS vacuum. For example, this conjecture is incompatible with the simplest 1-modulus KKLT AdS supersymmetric solution.
We classify all pseudo-supersymmetric extremal near-horizon geometries in minimal five-dimensional de-Sitter supergravity. It is shown that the only such near-horizon geometry is the near-horizon geometry of the de-Sitter BMPV solution, and hence there are no regular extremal pseudo-supersymmetric asymptotically de-Sitter black rings.
We propose a new mechanism for obtaining de Sitter vacua in type IIB string theory compactified on (orientifolded) Calabi-Yau manifolds similar to those recently studied by Kachru, Kallosh, Linde and Trivedi (KKLT). dS vacuum appears in KKLT model after uplifting an AdS vacuum by adding an anti-D3-brane, which explicitly breaks supersymmetry. We accomplish the same goal by adding fluxes of gauge fields within the D7-branes, which induce a D-term potential in the effective 4D action. In this way we obtain dS space as a spontaneously broken vacuum from a purely supersymmetric 4D action. We argue…
We study two fermionic systems that have an underlying supersymmetric structure, namely a color superconductor and Dirac fermion in a Reissner-Nordström-anti-de Sitter gravitational background. In the chiral limit of the color superconductor, the localized fermionic zero modes around the vortex form an N=2 with zero central charge $d=1$ quantum algebra, with all the operators being Fredholm. We compute the Witten index of this algebra and we find an unbroken supersymmetry. The fermionic gravitational system in the chiral limit too, has two underlying unbroken N=2, $d=1$ supersymmetric algebras…
We study a noninteracting supersymmetric model in de Sitter spacetime. Supersymmetry breaking induces a nonzero vacuum energy density. A short distance cut-off of the order of Planck length provides a matching between the vacuum energy density and the cosmological constant related to the de Sitter expansion parameter.
Rotating dilaton black hole solution for asymptotically anti-de Sitter spacetime are obtained in the small angular momentum limit with an appropriate combination of three Liouville-type dilaton potentials. The angular momentum, magnetic dipole moment and the gyromagnetic ratio of such a black hole are determined for arbitrary values of the dilaton-electromagnetic coupling parameter.
We construct a general class of non-extremal charged Kerr-de Sitter black holes in five dimensions, in which the two rotation parameters are set equal. There are three non-trivial parameters, namely the mass, charge and angular momentum. All previously-known cases, supersymmetric and non-supersymmetric, that have equal angular momenta are encompassed as special cases.
We examine supersymmetry of four-dimensional asymptotically anti-de Sitter (AdS) dyonic black holes in the context of gauged N=2 supergravity. Our calculations concentrate on black holes with unusual topology and their rotating generalizations, but we also reconsider the spherical rotating dyonic Kerr-Newman-AdS black hole, whose supersymmetry properties have previously been investigated by Kostelecký and Perry within another approach. We find that in the case of spherical, toroidal or cylindrical event horizon topology, the black holes must rotate in order to preserve some supersymmetry; the …
We propose higher spin supercurrent multiplets for ${\cal N}=1$ supersymmetric field theories in four-dimensional anti-de Sitter space (AdS). Their explicit realisations are derived for various supersymmetric theories, including a model of $N$ massive chiral scalar superfields with an arbitrary mass matrix. We also present new off-shell gauge formulations for the massless ${\cal N}=1$ supersymmetric multiplet of integer superspin $s$ in AdS, where $s =2,3,\dots$, as well as for the massless gravitino multiplet (superspin $s=1$) which requires special consideration.
Apply the T-duality and smeared twist to the D3-brane solution one can construct the supergravity backgrounds which may dual to supersymmetric or non-supersymmetric non-commutative dipole field theory. We introduce D7-brane probe into the dual supergravity background to study the chiral dynamics and meson spectrum therein. We first find that the non-commutative dipole field does not induce the chiral symmetry breaking even if the supersymmetry was completely broken, contrast to the conventional believing that the chiral symmetry will be broken in the non-supersymmetric theory. Next, we find th…
We present two types of obstacles for constructing de Sitter space in supersymmetric theories that appear as effective theories of quantum gravity. The first obstacle concerns de Sitter critical points in extended supergravity with charged massless gravitini. We show that all such critical points have a Hubble scale of the same order or above the UV cutoff dictated by the magnetic Weak Gravity Conjecture. The second obstacle concerns the dynamics of the goldstino in models with non-linearly realized supersymmetry, such as string models involving anti-branes. We show, using an exact renormaliza…
There are five maximally supersymmetric backgrounds in four-dimensional off-shell N=1 supergravity, two of which are well known: Minkowski superspace M^{4|4} and anti-de Sitter superspace AdS^{4|4}. The three remaining supermanifolds support spacetimes of different topology, which are: R x S^3, AdS_3 x R, and a supersymmetric plane wave isometric to the Nappi-Witten group. As is well known, the Minkowski and anti-de Sitter superspaces are solutions of the Poincaré and anti-de Sitter supergravity theories, respectively. Here we demonstrate that the other three superspaces are solutions of no-sc…
We put forward a unimodular $N=1, d=4$ anti-de Sitter supergravity theory off shell. This theory, where the Cosmological Constant does not couple to gravity, has a unique maximally supersymmetric classical vacuum which is Anti-de Sitter spacetime with radius given by the equation of motion of the auxiliary scalar field, ie, $S=\frac{3}{κL}$. However, we see that the non-supersymmetric classical vacua of the unimodular theory are Minkowski and de Sitter spacetimes as well as anti-de Sitter spacetime with radius $l\neq L$.
We construct a seven-parameter family of supergravity solutions that describe non-supersymmetric black rings and black tubes with three charges, three dipoles and two angular momenta. The black rings have regular horizons and non-zero temperature. They are naturally interpreted as the supergravity descriptions of thermally excited configurations of supertubes, specifically of supertubes with two charges and one dipole, and of supertubes with three charges and two dipoles. In order to fully describe thermal excitations near supersymmetry of the black supertubes with three charges and three dipo…
We study the glueball spectrum in the supersymmetric and non-supersymmetric 4D non-commutative dipole gauge theory from the holographic description. We adopt the semiclassical WKB approximation to solve the dilaton and antisymmetric tensor field equations on the dual supergravity backgrounds to find the analytic formula of the spectrum of $0^{++}$ and $1^{--}$ glueballs, respectively. In the supersymmetric theory we see that the dipole length plays the intrinsic scale which reflects the discrete spectrum therein. In the non-supersymmetric theory, the temperature (or the radius of compactificat…
As a test for the non-supersymmetric attractor mechanism, we consider extremal Reissner-Nordström-(anti-)de Sitter black holes. Based on the simple observation that the near-horizon geometry of a generic extremal black hole contains two-dimensional anti-de Sitter factor even in the presence of the positive cosmological constant, we apply Ashoke Sen's entropy function method to compute the entropy of these black holes. We find the results which exactly agree with the Bekenstein-Hawking entropy. We also obtain the constant higher-order correction to the entropy due to the Gauss-Bonnet term.
In this paper, we study slowly rotating black hole solutions in Lovelock gravity (n=3). These exact slowly rotating black hole solutions are obtained in uncharged and charged cases, respectively. Up to the linear order of the rotating parameter a, the mass, Hawking temperature and entropy of the uncharged black holes get no corrections from rotation. In charged case, we compute magnetic dipole moment and gyromagnetic ratio of the black holes. It is shown that the gyromagnetic ratio keeps invariant after introducing the Gauss-Bonnet and third order Lovelock interactions.
We extend a recent scenario of Kachru, Kallosh, Linde and Trivedi to fix the string moduli fields by using a combination of fluxes and non-perturbative superpotentials, leading to de Sitter vacua. In our scenario the non-perturbative superpotential is taken to be the N=1^* superpotential for an SU(N) theory, originally computed by Dorey and recently rederived using the techniques of Dijkgraaf-Vafa. The fact that this superpotential includes the full instanton contribution gives rise to the existence of a large number of minima, increasing with N. In the absence of supersymmetry breaking these …
We study massive spinor fields in the geometry of a straight cosmic string in a de Sitter background. We find a hidden N=2 supersymmetry in the fermionic solutions of the equations of motion. We connect the zero mode solutions to the heat-kernel regularized Witten index of the supersymmetric algebra.
It is shown that the five-dimensional anti-de Sitter black hole is a supersymmetric solution of the low-energy field equations of type IIB string theory compactified on an Einstein space. A statistical interpretation of the mass dependence of the entropy can be obtained from considerations of the three-dimensional BTZ black hole.
We discuss various physical aspects of nonextremal, extremal and supersymmetric black holes in asymptotically anti-de Sitter (ADS) spacetimes. Specifically, we discuss how the isolated horizon (IH) framework leads to an ambiguity-free description of rotating black holes in these spacetimes. We then apply this framework to investigate the properties of supersymmetric isolated horizons (SIHs) in four-dimensional N = 2 gauged supergravity. Among other results we find that they are necessarily extremal, that rotating SIHs must have non-trivial electromagnetic fields, and that non-rotating SIHs nec…
We compute the radiative corrections to the mass of a test boson field in an inflating space-time. The calculations are carried out in case of a boson part of a supersymmetric chiral multiplet. We show that its mass is preserved up to logarithmic divergences both in ultraviolet and infrared domains. Consequences of these results for inflationary models are discussed.
We give a pedagogical introduction to certain aspects of supersymmetric field theories in anti-de Sitter space. Among them are the presence of masslike terms in massless wave equations, irreducible unitary representations and the phenomenon of multiplet shortening.
We construct a model of an electrically charged magnetic dipole with arbitrary N-extended world-line supersymmetry, which exhibits a supersymmetric Zeeman effect. By including supersymmetric constraint terms, the ambient space of the dipole may be tailored into an algebraic variety, and the supersymmetry broken for almost all parameter values. The so exhibited obstruction to supersymmetry breaking refines the standard one, based on the Witten index alone.
In this paper, we give a systematic procedure for building locally stable dS vacua in $\mathcal{N}=1$ supergravity models motivated by string theory. We assume that one of the superfields has a Kahler potential of no-scale type and impose a hierarchy of supersymmetry breaking conditions. In the no-scale modulus direction the supersymmetry breaking is not small, in all other directions it is of order $ε$. We establish the existence of an abundance of vacua for large regions in the parameter space spanned by $ε$ and the cosmological constant. These regions exist regardless of the details of the …
We consider theories with gravity, gauge fields and scalars in four-dimensional asymptotically flat space-time. By studying the equations of motion directly we show that the attractor mechanism can work for non-supersymmetric extremal black holes. Two conditions are sufficient for this, they are conveniently stated in terms of an effective potential involving the scalars and the charges carried by the black hole. Our analysis applies to black holes in theories with ${\cal N} \le 1$ supersymmetry, as well as non-supersymmetric black holes in theories with ${\cal N} = 2$ supersymmetry. Similar r…
We present supergravity solutions for 1/8-supersymmetric black supertubes with three charges and three dipoles. Their reduction to five dimensions yields supersymmetric black rings with regular horizons and two independent angular momenta. The general solution contains seven independent parameters and provides the first example of non-uniqueness of supersymmetric black holes. In ten dimensions, the solutions can be realized as D1-D5-P black supertubes. We also present a worldvolume construction of a supertube that exhibits three dipoles explicitly. This description allows an arbitrary cross-se…
We rederive and extend the amplitude for charged spherical shells tunneling through the outer horizon of charged black holes. In particular, we explicitly confirm that an effective action approach with natural initial conditions for a spherical shell, including backreaction, reduces to the tunneling integral. Consequently, we establish a universal expression for the probability of emission in terms of the change in the horizon entropy. Notably, the result for the charged black hole also captures the superradiant regime of charged particle decay at low energies. We then explore an appropriately…
We provide a classification of near-horizon geometries of supersymmetric, asymptotically anti-de Sitter, black holes of five-dimensional U(1)^3-gauged supergravity which admit two rotational symmetries. We find three possibilities: a topologically spherical horizon, an S^1 \times S^2 horizon and a toroidal horizon. The near-horizon geometry of the topologically spherical case turns out to be that of the most general known supersymmetric, asymptotically anti-de Sitter, black hole of U(1)^3-gauged supergravity. The other two cases have constant scalars and only exist in particular regions of thi…
We study supergravity theories with supersymmetry intrinsically non-linearly realized supported only by four-form flux. We demonstrate that supersymmetry can be restored by the evaporation of the goldstino multiplet. Such procedure requires the existence of a super-extremal 2-brane, in accordance with the WGC, and suggests an imminent decay in de Sitter supergravity, leaving the system to relax in supersymmetric AdS after the transition. In particular, the same decay mechanism also implies that the KKLT de Sitter vacua are short-lived. Our findings thus provide an effective realization of KPV-…
A new supersymmetric, asymptotically anti-de Sitter, black hole solution of five-dimensional U(1)^3 gauged supergravity is presented. All known examples of such black holes arise as special cases of this solution, which is characterized by three charges and two angular momenta, with one constraint relating these five quantities. Analagous solutions of U(1)^n gauged supergravity are also presented.
We continue our study of codimension two solutions of warped space-time varying compactifications of string theory. In this letter we discuss a non-supersymmetric solution of the classical type IIB string theory with de Sitter gravity on a codimension two uncompactified part of spacetime. A non-zero positive value of the cosmological constant is induced by the presence of non-trivial stringy moduli, such as the axion-dilaton system for the type IIB string theory. Furthermore, the naked singularity of the codimension two solution is resolved by the presence of a small but non-zero cosmological …
We formulate a unimodular N=1, d=4 supergravity theory off shell. We see that the infinitesimal Grassmann parameters defining the unimodular supergravity transformations are constrained and show that the conmutator of two infinitesinal unimodular supergravity transformations closes on transverse diffeomorphisms, Lorentz transformations and unimodular supergravity transformations. Along the way, we also show that the linearized theory is a supersymmetric theory of gravitons and gravitinos. We see that de Sitter and anti-de Sitter spacetimes are non-supersymmetric vacua of our unimodular supergr…
We propose to sharpen the weak gravity conjecture by the statement that, except for BPS states in a supersymmetric theory, the gravitational force is strictly weaker than any electric force and provide a number of evidences for this statement. Our conjecture implies that any non-supersymmetric anti-de Sitter vacuum supported by fluxes must be unstable, as is the case for all known attempts at such holographic constructions.
Pseudo-supersymmetric solutions of minimal $N=2$, $D=4$ de Sitter supergravity are classified using spinorial geometry techniques. We find three classes of solutions. The first class of solution consists of geometries which are fibrations over a 3-dimensional manifold equipped with a Gauduchon-Tod structure. The second class of solution is the cosmological Majumdar-Papapetrou solution of Kastor and Traschen, and the third corresponds to gravitational waves propagating in the Nariai cosmology.
The electric dipole moment of magnetic monopoles with spin is studied in the N=2 supersymmetric gauge theory. The dipole moments of the electric charge distributions, as well as the dipole moments due to the magnetic currents, are calculated. The contribution of charge distribution of the fermion to the gyroelectric ratio is expressed by using zeta(3).
Aharonov-Casher effect from a supersymmetric N=1 D=4 model with Kalb-Ramond Lorentz-violating background: a SUSY-preserving mechanism via the Fayet-Iliopoulos term
Universidade Federal Rural do Semi-Árido（塞米阿拉多联邦农村大学）；Universidade Federal do Ceará (UFC)（塞阿拉联邦大学）
We present a simple class of warped-product vacuum (Ricci-flat) solutions to ten and eleven-dimensional supergravity, where the internal space is flat and the warp factor supports de Sitter (dS) and anti-de Sitter (AdS) vacua in addition to trivial Minkowski vacua. We outline the construction of consistent Kaluza-Klein (KK) reductions and show that, although our vacuum solutions are non-supersymmetric, these are closely related to the bosonic part of well-known maximally supersymmetric reductions on spheres. We comment on the stability of our solutions, noting that (A)dS$_3$ vacua pass routine…
We find the exact quantum gravity partition function on the static patch of 3d de Sitter spacetime. We have worked in the Chern Simons Formulation of 3d Gravity. To obtain a non-perturbative result, we supersymmetrized the Chern Simons action and used the technique of supersymmetric localization. We have obtained an exact non-perturbative result for the spin-2 gravity case. We comment on the divergences present in the theory. We also comment on higher spin gravity theories and analyse the nature of divergences present in such theories.
AdS/CFT is a conjectured equivalence between a field theory without gravity (conformal field theory) and a string theory in a special curved background (anti de-Sitter space), where theories on both sides of the equivalence is supersymmetric. Since the nature as we observe at low energy is non-supersymmetric, it will be very useful if we can have this conjecture in the non-supersymmetric case. Here we will give some evidence that AdS/CFT type duality must work for non-supersymmetric system. We will indicate some calculation which leads us to such conclusion.
We study moduli stabilization for type IIB orientifold compactifications on Calabi-Yau three-folds with (non-)geometric fluxes. For this setting it is possible to stabilize all closed-string moduli classically without the need for non-perturbative contributions, and examples of stable de-Sitter constructions can be found in the literature which violate a prominent swampland conjecture. In this paper we derive general properties of non-geometric flux-compactifications, we argue that the contribution of fluxes to the tadpole cancellation conditions should be similar to D-branes (and not anti-D-b…
In this paper we present a method for computing the total probability corresponding to the processes of fermion pair production in dipole magnetic field and external Coulomb field in a de Sitter geometry. For that we rewrite the functions that define the amplitudes in terms of oscillatory functions and we use the Taylor expansion of these functions for arriving at the final form of the momenta integrals. The total probability is analysed in terms of the ratio between the mass of the fermion and expansion parameter and we recover the Minkowski limit when the expansion parameter is vanishing. Fi…
