The standard lore about the sum over topological sectors in quantum field theory is that locality and cluster decomposition uniquely determine the sum over such sectors, thus leading to the usual theta-vacua. We show that without changing the local degrees of freedom, a theory can be modified such that the sum over instantons should be restricted; e.g. one should include only instanton numbers which are divisible by some integer p. This conclusion about the configuration space of quantum field theory allows us to carefully reconsider the quantization of parameters in supergravity. In particular, we show that FI-terms and nontrivial Kahler forms are quantized. This analysis also leads to a new derivation of recent results about linearized supergravity.
Gravity mediated supersymmetry breakdown originated from a study of gaugino condensation in a hidden sector. We review this mechanism of supergravity breakdown from the original formulation in the early eighties to its natural implementation in superstring theory and M-theory. In the latter case hidden and observable sector become separated geometrically and supersymmetry is broken dynamically on a hidden wall.
The SU(3)--invariant sector of maximal supergravity in four dimensions with an SO(8) gauging is uplifted to $D=11$ supergravity. In order to do this, the SU(3)--neutral sector of the tensor and duality hierarchies of the $D=4$ ${\cal N}=8$ supergravity is first worked out. The consistent $D=11$ embedding of the full, dynamical SU(3) sector is then expressed at the level of the $D=11$ metric and three-form gauge field in terms of these $D=4$ tensors. The redundancies introduced by this approach are eliminated at the level of the $D=11$ four-form field strength by making use of the $D=4$ duality…
We study supersymmetry breaking by hidden-sector gaugino condensation in N=1 D=4 supergravity models with multiple dilaton-like moduli fields. Our work is motivated by Type I string theory, in which the low-energy effective Lagrangian can have different dilaton-like fields coupling to different sectors of the theory. We construct the effective Lagrangian for gaugino condensation and use it to compute the visible-sector gaugino masses. We find that the gaugino masses can be of order the gravitino mass, in stark contrast to heterotic string models with a single dilaton field.
We investigate the viability of Affleck-Dine baryogenesis in D=4, N=1 supergravity descending from string theory. The process relies on an initial condition where visible sector supersymmetric flat directions obtain tachyonic masses during inflation. We discuss this condition for a variety of cases where supersymmetry is broken during inflation by a geometric modulus or hidden sector scalar, and outline scenarios where the initial condition is satisfied.
Covariant actions for the bosonic fields of D=10 IIB supergravity are constructed with the help of a single auxiliary scalar field and in a formulation with an infinite series of auxiliary (anti)-self-dual 5-form fields.
It is generally believed that weak scale supersymmetry implies weak scale supergravity, in the sense that the masses of the gravitino and gravitationally coupled moduli have masses below 100 TeV. This paper presents a realistic framework for supersymmetry breaking in the hidden sector in which the masses of the gravitino and gravitational moduli can be much larger. This cleanly eliminates the cosmological problems of hidden sector models. Supersymmetry breaking is communicated to the visible sector by anomaly-mediated supersymmetry breaking. The framework is compatible with perturbative gauge …
In rigid supersymmetry, generic models of dynamical supersymmetry breaking contain a light Goldstone boson, called the R axion. We show that supergravity effects explicitly break the R symmetry and give mass to the R axion. For visible and renormalizable hidden sector models, the massive R axion is free from astrophysical and cosmological problems. For nonrenormalizable hidden sector models, the R axion suffers from cosmological difficulties similar to those of the moduli fields in string theory.
We study the hidden symmetries of the fermionic sector of D=11 supergravity, and the role of K(E10) as a generalised `R-symmetry'. We find a consistent model of a massless spinning particle on an E10/K(E10) coset manifold whose dynamics can be mapped onto the fermionic and bosonic dynamics of D=11 supergravity in the near space-like singularity limit. This E10-invariant superparticle dynamics might provide the basis of a new definition of M-theory, and might describe the `de-emergence' of space-time near a cosmological singularity.
Using the flux compactification scenario in a generic supergravity model we construct a set of conditions which are necessary to generate de-Sitter or anti de-Sitter vacua for appropriate choices of the parameters in superpotential. It is shown that a mass spectrum consistent with softly broken TeV scale supersymmetry in a minimal supersymmetric standard model at the observable sector can be obtained along with a tiny cosmological constant when the Kahler and superpotential of the hidden sector satisfy a set of general constraints. Constructing a specific model with Kahler and superpotentials …
We investigate split supersymmetry (SUSY) within a supergravity framework, where local SUSY is broken by the F-term of a hidden sector chiral superfield X. With reasonably general assumptions, we show that the fermionic component of X will always have mass within a Tev. Though its coupling to the observable sector superfields is highly suppressed in Tev scale SUSY, we show that it can be enhanced by many orders in split SUSY, leading to its likely participation in accelerator phenomenology.We conclude with a specific example of such a scenario in a string based supergravity model.
Recently a new maximally supersymmetric, dyonically gauged supergravity in four-dimenions has been constructed. This theory admits several supersymmetric AdS solutions, and a Chern- Simons-matter dual theory has been proposed for a solution with an unbroken SU(3) symmetry. The gravity side and the field theory side of the free energy computation show nice agreements at superconformal point. With a view to a study of non-conformal deformations, in this paper we study a consistent truncation of the full theory where SU(3) is broken to U(1)$^2$. We elucidate the geometry of the scalar sector, and…
We consider the type IIB supergravity in ten dimensions compactified on S^1 \times T^4, with intersecting one and five D-branes in the compact dimensions. By imposing the spherical symmetry in the resulting five dimensional theory, we further reduce the s-wave sector of the theory to a two dimensional dilaton gravity. Via this construction, the techniques developed for the general two dimensional dilaton gravities are applicable in this context. Specifically, we obtain the bosonic sector general static solutions. In addition to the well-known asymptotically flat black hole solutions, they incl…
We calculate gaugino masses in string-derived models with hidden-sector gaugino condensation. The linear multiplet formulation for the dilaton superfield is used to implement perturbative modular invariance. The contribution arising from quantum effects in the observable sector includes the term recently found in generic supergravity models. A much larger contribution is present if matter fields with Standard Model gauge couplings also couple to the Green-Schwarz counter term. We comment on the relation of our Kähler U(1) superspace formalism to other calculations.
We introduce a $N=1$ supergravity model with a very simple hidden sector coupled to the electroweak gauge and Higgs sectors of the MSSM. At the classical level, supersymmetry and $SU(2)\times U(1)$ are both spontaneously broken, with vanishing vacuum energy. Two real flat directions control the two symmetry-breaking scales $m_{3/2}$ and $m_Z$. The two massless scalars are a gauge singlet and the standard Higgs boson. All other unobserved particles have masses of order $m_{3/2}$. This may be a new starting point for studying the compatibility of naturalness with the observed mass hierarchies.
Some of the soft SUSY breaking parameters in hidden sector supergravity model depend on the expectation value of the hidden sector scalar potential, $<V_h>$, whose tree level value is equal to the tree level cosmological constant. The current practice of calculating soft parameters assumes that $<V_h>=0$. Quantum correction to the cosmological constant can differ from the correction to $<V_h>$ by an amount of order $m^2_{3/2}M_{Pl}^2/8π$. This implies that, for the vanishing cosmological constant, the $<V_h>$--dependent parts of soft terms can be sizable, and hence the supergravity phenomenolo…
Half-maximal, $\,\mathcal{N}=4\,$, sectors of $\,D=4\,$ $\,\mathcal{N}=8\,$ supergravity with a dyonic ISO(7) gauging are investigated. We focus on a half-maximal sector including three vector multiplets, that arises as a certain $\,\textrm{SO}(3)_{\textrm{R}}$-invariant sector of the full theory. We discuss the embedding of this sector into the largest half-maximal sector of the $\,\mathcal{N}=8\,$ supergravity retaining six vector multiplets. We also provide its canonical $\,\mathcal{N}=4\,$ formulation and show that, from this perspective, our model leads in its own right to a new explicit …
We review the origin of soft supersymmetry-breaking terms in N=1 supergravity models of particle physics. We first consider general formulae for those terms in general models with a hidden sector breaking supersymmetry at an intermediate energy scale. The results for some simple models are given. We then consider the results obtained in some simple superstring models in which particular assumptions about the origin of supersymmetry breaking are made. These are models in which the seed of supersymmetry breaking is assumed to be originated in the dilaton/moduli sector of the theory.
Starting from the bosonic sector of the M-theory super-five-brane we obtain the action for duality-symmetric three-brane and construct the consistent coupling of the proposed action with the bosonic sector of type IIB supergravity.
We discuss inflaton decay in supergravity, taking account of the gravitational effects. It is shown that, if the inflaton has a nonzero vacuum expectation value, it generically couples to any matter fields that appear in the superpotential at the tree level, and to any gauge sectors through anomalies in the supergravity. Through these processes, the inflaton generically decays into the supersymmetry breaking sector, producing many gravitinos. The inflaton also directly decays into a pair of the gravitinos. We derive constraints on both inflation models and supersymmetry breaking scenarios for …
We analyze the constraints which follow both on the geometry and on the gauge sector for a consistent supergravity reduction of a general matter-coupled N=2 supergravity theory in four dimensions. These constraints can be derived in an elegant way by looking at the fermionic sector of the theory.
We investigate the SU(3)-invariant sector of the one-parameter family of SO(8) gauged maximal supergravity that has been recently proposed. To this end, we construct the N=2 truncation of this theory and analyse its full vacuum structure. The number of critical point is doubled and includes new N=0 and N=1 branches. We numerically exhibit the parameter dependence of the location and cosmological constant of all extrema. Moreover, we provide their analytic expressions for cases of special interest. Connections with three-dimensional RG-flows are pointed out. Finally, while the mass spectra are …
By studying various, known extrema of 1) SU(3) sectors, 2) SO(5) sectors and 3) SO(3)xSO(3) sectors of gauged N =8 supergravity in four-dimensions, one finds that the deformation of seven sphere §^7 gives rise to non-trivial renormalization group(RG) flow in three-dimensional boundary conformal field theory from UV fixed point to IR fixed point. For SU(3) sectors, this leads to four-parameter subspace of the supergravity scalar-gravity action and we identify one of the eigenvalues of A_1 tensor of the theory with a superpotential of scalar potential that governs RG flows on this subspace. We a…
We show that (massive) D=10 type IIA supergravity possesses a hidden rigid SO(9,9) symmetry and a hidden local SO(9) x SO(9) symmetry upon dimensional reduction to one (time-like) dimension. We explicitly construct the associated locally supersymmetric Lagrangian in one dimension, and show that its bosonic sector, including the mass term, can be equivalently described by a truncation of an E10/K(E10) non-linear sigma-model to the level \ell<=2 sector in a decomposition of E10 under its so(9,9) subalgebra. This decomposition is presented up to level 10, and the even and odd level sectors are id…
We apply the heat kernel method (using Avramidi's non-recursive technique) to the study of the effective action of chiral matter in a complex representation of an arbitrary gauge sector coupled to background U(1) supergravity. This generalizes previous methods, which restricted to 1) real representations of the gauge sector in traditional Poincaré supergravity or 2) vanishing supergravity background. In this new scheme, we identify a classical ambiguity in these theories which mixes the supergravity U(1) with the gauge U(1). At the quantum level, this ambiguity is maintained since the effectiv…
Use of supergravity equations in astronomy and late-universe cosmology is often criticized on three grounds: (i) phenomenological success usually depends on the supergravity form for the scalar potential applying at the relevant energies; (ii) the low-energy scalar potential is extremely sensitive to quantum effects involving very massive particles and so is rarely well-approximated by classical calculations of its form; and (iii) almost all Standard Model particles count as massive for these purposes and none of these are supersymmetric. Why should Standard Model loops preserve the low-energy…
The structure of gauged R supergravity Lagrangians is reviewed, and we consider models with a hidden sector plus light fields of the MSSM. A simple potential for the hidden sector is presented which has a global minimum with zero cosmological constant and spontaneously broken SUSY and R-symmetry. The $\rm U(1)_R$ vector multiplet acquires a Planck scale mass through the Higgs mechanism, and it decouples at low energy. Due to very interesting cancellations, the $\rm U(1)_R$ D-terms also drop out at low energy. Thus no direct effects of the gauging of R-symmetry remain in the low energy effectiv…
Wess-Zumino gauge for analytic prepotentials of off-shell $\mathcal{N}=2$ supergravity: bosonic sector
Bogoliubov Laboratory of Theoretical Physics, JINR（约飞联合核子研究所博戈留博夫理论物理实验室）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Institute of Theoretical and Mathematical Physics, Lomonosov Moscow State University（莫斯科国立大学理论与数学物理研究所）
General forms of the Kähler and superpotenials that lead to consistent low energy broken Supersymmetry originating from $N=1$ Supergravity have been classified and used for model building since more than three decades. We point out the incompleteness of this classification when hidden sector vacuum expectation values are of the order of the Planck mass. Focusing in this paper mainly on the case of minimal Kähler potential, we adopt a rigorous approach that retrieves on the one hand the known forms, and demonstrate on the other hand the existence of a whole set of new forms for the superpotenti…
We study the stability of the gauge hierarchy in hidden-sector supergravity theories. We show that a destabilizing tadpole can appear if a theory has a gauge- and global-symmetry singlet with renormalizable couplings to the visible fields. We also find a quadratically divergent two-loop contribution to the supersymmetric effective potential. This term illustrates the difficulty of using the "LHC mechanism" to control quadratic divergences in theories with Planck-scale vevs.
Motivated by the recent use of certain consistent truncations of M-theory to study condensed matter physics using holographic techniques, we study the SU(3)-invariant sector of four-dimensional, N=8 gauged supergravity and compute the complete scalar spectrum at each of the five non-trivial critical points. We demonstrate that the smaller SU(4)^- sector is equivalent to a consistent truncation studied recently by various authors and find that the critical point in this sector, which has been proposed as the ground state of a holographic superconductor, is unstable due to a family of scalars th…
We construct gauged supergravity actions which describe the dynamics of M-theory on a Calabi-Yau threefold in the vicinity of a conifold transition. The actions explicitly include N charged hypermultiplets descending from wrapped M2-branes which become massless at the conifold point. While the vector multiplet sector can be treated exactly, we approximate the hypermultiplet sector by the non-compact Wolf spaces X(1+N). The effective action is then uniquely determined by the charges of the wrapped M2-branes.
We dimensionally reduce the bosonic sector of 10D Euclidean type IIA supergravity over a Calabi-Yau three-fold. The resulting theory describes the bosonic sector of 4D, N = 2 Euclidean supergravity coupled to vector- and hyper-multiplets. We show that the scalar target manifold of the vector-multiplets is projective special para-Kahler, and is therefore of split signature, whereas the target manifold of the hyper-multiplets is (positive-definite) quaternionic Kahler.
Conventional approaches to cosmology in supergravity assume the existence of multiple sectors that only communicate gravitationally. In principle these sectors decouple in the limit Planck mass to infinity. In practice such a limit is delicate: for generic supergravities, where sectors are combined by adding their Kahler functions, the separate superpotentials must contain non-vanishing vacuum expectation values supplementing the naive global superpotential. We show that this requires non-canonical scaling in the naive supergravity superpotential couplings to recover independent sectors of glo…
We consider a class of models with gauged U(1)_R symmetry in 4D N=1 supergravity that have, at the classical level, a metastable ground state, an infinitesimally small (tunable) positive cosmological constant and a TeV gravitino mass. We analyse if these properties are maintained under the addition of visible sector (MSSM-like) and hidden sector state(s), where the latter may be needed for quantum consistency. We then discuss the anomaly cancellation conditions in supergravity as derived by Freedman, Elvang and Körs and apply their results to the special case of a U(1)_R symmetry, in the prese…
We study reheating processes and its cosmological consequences in the Starobinsky model embedded in the old-minimal supergravity. First, we consider minimal coupling between the gravity and matter sectors in the higher curvature theory, and transform it to the equivalent standard supergravity coupled to additional matter superfields. We then discuss characteristic decay modes of the inflaton and the reheating temperature $T_{\rm R}$. Considering a simple model of supersymmetry breaking sector, we estimate gravitino abundance from inflaton decay, and obtain limits on the masses of gravitino and…
We study small perturbations around the supersymmetric CVMN monopole solution of the gauged supergravity in D=4. We find that the perturbation spectrum contains an infinite tower of Coulomb-type bound states both in the bosonic and fermionic parts of the supergravity multiplet. Due to supersymmetry, the eigenvalues are the same for the two bosonic parity sectors, as well as for the fermionic sector. We also find that the fermion scattering on the monopole is accompanied by isospin flip. This is analogous to the Rubakov-Callan effect of monopole catalysis of proton decay and suggests that there…
We consistently incorporate Yang Mills matter fields into string corrected (deformed), D=10, N=1 Supergravity. We solve the Bianchi identities within the framework of the modified beta function favored constraints to second order in the string slope parameter $\g$ also including the Yang Mills fields. In the torsion, curvature and H sectors we find that a consistent solution is readily obtained with a Yang Mills modified supercurrent $A_{abc}$. We find a solution in the F sector following our previously developed method.
We investigate the stability of the hidden sector gaugino condensate in a SL(2,Z)-invariant supergravity model inspired by the E8*E8 heterotic string, using the chiral superfield formalism. We calculate the Planck-suppressed corrections to the ``truncated approximation'' for the condensate value and the scalar potential. A transition to a phase with zero condensate occurs near special points in moduli space and at large compactification radius. We discuss the implications for the T-modulus dependence of supersymmetry-breaking.
We have extended previous analysis of the bulk/brane supersymmetrizations involving non-zero brane mass terms of bulk fermions (gravitini) and twisting of boundary conditions. We have constructed new brane/bulk models that may be relevant for realistic model building. In particular, we have built a model with the Randall-Sundrum bosonic sector, orthogonal projection operators on the branes in the fermionic sector, and an unbroken N=1 supersymmetry. We have also constructed 5d super-bigravity with static vacuum and unbroken N=1 supersymmetry, which may be viewed as a deconstruction of 5d superg…
We note that the non-perturbative quantisation of supergravity as recently investigated using loop quantum gravity techniques provides an opportunity to probe an interesting sector of the AdS/CFT correspondence, which is usually not considered in conventional treatments. In particular, assuming a certain amount of convergence between the quantum supergravity sector of string theory and quantum supergravity constructed via loop quantum gravity techniques, we argue that the large quantum number expansion in loop quantum supergravity corresponds to the $1/N^2_c$ expansion in the corresponding gau…
A description of the bosonic sector of massive IIA supergravity as a non-linear realisation is given. An essential feature of this construction is that the momentum generators have non-trivial commutation relations with the generators associated with the gauge fields.
Drawing an analogy between gravity dynamical equation of motion and that of Maxwell electrodynamics with an electric source we outline a way of appearance of a dual to graviton field. We propose a dimensional reduction ansatz for the field strength of this field which reproduces the correct duality relations between fields arising in the dimensional reduction of D-dimensional gravity action to D-1 dimensions. Modifying the PST approach we construct a new term entering the action of D=11 duality-symmetric gravity and by use of the proposed ansatz we confirm the relevance of such a term to repro…
A new heterotic N=2 string with manifest target space supersymmetry is constructed by combining a conventional N=2 string in the right-moving sector and a Green-Schwarz-Berkovits type string in the left-moving sector. The corresponding sigma model is then obtained by turning on background fields for the massless excitations. We compute the beta functions and we partially check the OPE's of the superconformal algebra perturbatively in $α'$, all in superspace. The resulting field equations describe N=1 self-dual supergravity.
A new supergravity D-term, not associated to gauged R-symmetry, was recently discovered and used to construct new supergravity models. In this paper we use a generalization of the new D-term that we used in previous works, to construct a supergravity model of slow-roll inflation with the observable sector of the minimal supersymmetric standard model. Supersymmetry is broken at a high scale in the hidden sector and communicated to the observable sector by gravity mediation. The new D-term contains free parameters that can give large masses to scalar superpartners of quarks and leptons and to th…
We use a new mechanism for generating a Fayet-Iliopoulos term in supergravity, which is not associated to an R symmetry, to construct a semi-realistic theory of slow-roll inflation for a theory with the same Kähler potential and superpotential as the KKLT string background (without anti-D3 branes). In our model, supersymmetry must be broken at a high scale in a hidden sector to ensure that the cutoff of the effective field theory is above the Hubble scale of inflation. The gravitino has a super-EeV mass and supersymmetry breaking is communicated to the observable sector through gravity mediati…
Some dynamical aspects of five-dimensional supergravity as a Chern-Simons theory for the SU(2,2|N) group, are analyzed. The gravitational sector is described by the Einstein-Hilbert action with negative cosmological constant and a Gauss-Bonnet term with a fixed coupling. The interaction between matter and gravity is characterized by intricate couplings which give rise to dynamical features not present in standard theories. Depending on the location in phase space, the dynamics can possess different number of propagating degrees of freedom, including purely topological sectors. This inhomogenei…
We establish a direct correspondence between certain higher-rank p-form Chern-Simons topological type theories in the bulk of a manifold with boundary and particular sectors of supergravity models on the boundary, provided that certain boundary conditions are satisfied. The cases we investigate include eleven-dimensional supergravity and both of the type II theories in ten dimensions.
The first-order formulation of the Salam-Sezgin D=8 supergravity coupled to N vector multiplets is discussed. The non-linear realization of the bosonic sector of the D=8 matter coupled Salam-Sezgin supergravity is introduced by the dualisation of the fields and by constructing the Lie superalgebra of the symmetry group of the doubled field strength.
We formulate the bosonic sector of IIB supergravity as a non-linear realisation. We show that this non-linear realisation contains the Borel subalgebras of SL(11) and $E_7$ and argue that it can be enlarged so as to be based on the rank eleven Kac-Moody algebra $E_{11}$
A covariant closed superstring field theory, equivalent to classical ten-dimensional Type II supergravity, is presented. The defining conformal field theory is the ambitwistor string worldsheet theory of Mason and Skinner. This theory is known to reproduce the scattering amplitudes of Cachazo, He and Yuan in which the scattering equations play an important role and the string field theory naturally incorporates these results. We investigate the operator formalism description of the ambitwsitor string and propose an action for the string field theory of the bosonic and supersymmetric theories. …
It has recently been demonstrated that the Classical Yang-Baxter Equation (CYBE) emerges from supergravity via the open-closed string map. Thus, given any solution with an isometry group, there exists a deformed solution based on an $r$-matrix solution to the homogeneous CYBE. In this work, we argue that the CYBE emerges exclusively from the NS sector, while the RR sector acts largely as a spectator that supports the spacetimes. Moreover, shifting the dilaton by a constant, one can incorporate $r$-matrix solutions to the modified CYBE, but only for original geometries that are a direct-product…
In our companion paper, we focussed on the quantisation of the Rarita-Schwinger sector of Supergravity theories in various dimensions by using an extension of Loop Quantum Gravity to all spacetime dimensions. In this paper, we extend this analysis by considering the quantisation of additional bosonic fields necessary to obtain a complete SUSY multiplet next to graviton and gravitino in various dimensions. As a generic example, we study concretely the quantisation of the 3-index photon of 11d SUGRA, but our methods easily extend to more general p-form fields. Due to the presence of a Chern-Simo…
We study the supersymmetric quantum dynamics of the cosmological models obtained by reducing $D=5$ supergravity to one timelike dimension. This consistent truncation has fourteen bosonic degrees of freedom, while the quantization of the homogeneous gravitino field leads to a $2^{16}$--dimensional fermionic Hilbert space. We construct a consistent quantization of the model in which the wave function of the Universe is a $2^{16}$--component spinor %\textcolor{red}{of Spin(24,8)} depending on fourteen continuous coordinates, which satisfies eight Dirac-like wave equations (supersymmetry constrain…
Bosonic sector of d5 gauged supergravity with specific parametrization of full scalar coset is considered (multi-dilaton gravity). Using holographic RG in the form suggested by de Boer-Verlinde-Verlinde the holographic d4 conformal anomaly (in the sector of curvature invariants) is found when bulk potential is not constant. Its comparison with the earlier calculation done in the scheme where expansion of metric and dilaton over radial coordinate of AdS space is used demonstrates scheme dependence of holographic conformal anomaly. In AdS/CFT correspondence where dilatons play role of coupling c…
The bosonic sector of various supergravity theories reduces to a homogeneous space G/H in three dimensions. The corresponding algebras g are simple for (half-)maximal supergravity, but can be semi-simple for other theories. We extend the existing literature on the Kac-Moody extensions of simple Lie algebras to the semi-simple case. Furthermore, we argue that for N=2 supergravity the simple algebras have to be augmented with an su(2) factor.
We analyze a particular SU(2) invariant sector of the scalar manifold of gauged N=8 supergravity in five dimensions, and find all the critical points of the potential within this sector. The critical points give rise to Anti-de Sitter vacua, and preserve at least an SU(2) gauge symmetry. Consistent truncation implies that these solutions correspond to Anti-de Sitter compactifications of IIB supergravity, and hence to possible near-horizon geometries of 3-branes. Thus we find new conformal phases of softly broken N=4 Yang--Mills theory. One of the critical points preserves N=2 supersymmetry in …
