AdS2 supergravity and superconformal quantum mechanics

We investigate the asymptotic dynamics of topological anti-de Sitter supergravity in two dimensions. Starting from the formulation as a BF theory, it is shown that the AdS₂ boundary conditions imply that the asymptotic symmetries form a super-Virasoro algebra. Using the central charge of this algebra in Cardy’s formula, we exactly reproduce the thermodynamical entropy of AdS₂ black holes. Furthermore, we show that the dynamics of the dilaton and its superpartner reduces to that of superconformal transformations that leave invariant one chiral component of the stress tensor supercurrent of a two-dimensional conformal field theory. This dynamics is governed by a supersymmetric extension of the de Alfaro-Fubini-Furlan model of conformal quantum mechanics. Finally, two-dimensional de Sitter gravity is also considered, and the dS₂ entropy is computed by counting CFT states.     

Holography at an extremal De Sitter horizon

Rotating maximal black holes in four-dimensional de Sitter space, for which the outer event horizon coincides with the cosmological horizon, have an infinite near-horizon region described by the rotating Nariai metric. We show that the asymptotic symmetry group at the spacelike future boundary of the near-horizon region contains a Virasoro algebra with a real, positive central charge. This is evidence that quantum gravity in a rotating Nariai background is dual to a two-dimensional Euclidean conformal field theory. These results are related to the Kerr/CFT correspondence for extremal black holes, but have two key differences: one of the black hole event horizons has been traded for the cosmological horizon, and the near-horizon geometry is a fiber over dS₂ rather than AdS₂.     

Thermodynamics in rotating anti-de Sitter black holes with massive scalar field in three dimensions

We investigated the tendency in the variations of CFT₂ when a rotating AdS₃ black hole changes because of the fluxes transferred by the scattering of a massive scalar field according to the anti-de Sitter (AdS)/conformal field theory (CFT) correspondence. The conserved quantities of the black hole are definitely constrained by the extremal condition. Moreover, the laws of thermodynamics provide a direction for the changes in the conserved quantities. Therefore, the black hole cannot be extremal under the scattering; this is naturally preferred. According to the relationship between the rotating AdS₃ black hole and dual CFT₂, we find that such changes in the black hole constrain the variations in the eigenstates of dual CFT₂. Furthermore, the tendency in the variations is closely related to the laws of thermodynamics.     

Type IIB string theory on AdS5×T

We study Kaluza-Klein spectrum of type IIB string theory compactified on AdS₅×T^nn′ in the context of AdS/CFT correspondence. We examine some of the modes of the complexified 2 form potential as an example and show that for the states at the bottom of the Kaluza-Klein tower the corresponding d=4 boundary field operators have rational conformal dimensions. The masses of some of the fermionic modes in the bottom of each tower as functions of the R charge in the boundary conformal theory are also rational. Furthermore the modes in the bottom of the towers originating from q forms on T¹¹ can be put in correspondence with the BRS cohomology classes of the c=1 non critical string theory with ghost number q.     

Spinor-vector duality in heterotic string vacua

Classification of the N=1 space–time supersymmetric fermionic Z₂×Z₂ heterotic-string vacua with symmetric internal shifts, revealed a novel spinor-vector duality symmetry over the entire space of vacua, where the S_t↔V duality interchanges the spinor plus anti-spinor representations with vector representations. In this paper we demonstrate that the spinor-vector duality exists also in fermionic Z₂ heterotic string models, which preserve N=2 space–time supersymmetry. In this case the interchange is between spinorial and vectorial representations of the unbroken SO(12) GUT symmetry. We provide a general algebraic proof for the existence of the S_t↔V duality map. We present a novel basis to generate the free fermionic models in which the ten-dimensional gauge degrees of freedom are grouped into four groups of four, each generating an SO(8) modular block. In the new basis the GUT symmetries are produced by generators arising from the trivial and non-trivial sectors, and due to the triality property of the SO(8) representations. Thus, while in the new basis the appearance of GUT symmetries is more cumbersome, it may be more instrumental in revealing the duality symmetries that underly the string vacua.     

Representations of (1,0) and (2,0) Superconformal Algebras in Six Dimensions: Massless and Short Superfields

We construct unitary representations of (1,0) and (2,0) superconformal algebras in six dimensions by using superfields defined on harmonic superspaces with coset manifolds USp(2n)/[U(1)]ⁿ, n=1, 2. In the spirit of the AdS₇/CFT₆ correspondence, massless conformal fields correspond to supersingletons in AdS₇. By tensoring them we produce all short representations corresponding to 1/2 and 1/4 BPS anti-de Sitter bulk states of which massless bulk representations are particular cases.     

Generalised Chern–Simons actions for 3d gravity and κ-Poincaré symmetry

We consider Chern–Simons theories for the Poincaré, de Sitter and anti-de Sitter groups in three dimensions which generalise the Chern–Simons formulation of 3d gravity. We determine conditions under which κ-Poincaré symmetry and its de Sitter and anti-de Sitter analogues can be associated to these theories as quantised symmetries. Assuming the usual form of those symmetries, with a timelike vector as deformation parameter, we find that such an association is possible only in the de Sitter case, and that the associated Chern–Simons action is not the gravitational one. Although the resulting theory and 3d gravity have the same equations of motion for the gauge field, they are not equivalent, even classically, since they differ in their symplectic structure and the coupling to matter. We deduce that κ-Poincaré symmetry is not associated to either classical or quantum gravity in three dimensions. Starting from the (non-gravitational) Chern–Simons action we explain how to construct a multi-particle model which is invariant under the classical analogue of κ-de Sitter symmetry, and carry out the first steps in that construction.     

Hypothesis of friedmons as dark matter particles and hypothesis of initial cosmological constant decay

Hypothesis of friedmons as dark matter particles is proposed. Friedmons are stable particles with a mass of billion nucleon masses. These particles correspond to the not yet been discovered exact symmetry group dual to the SU(2) group: for the Standard model symmetries and dual symmetries, the roles of exact and broken symmetries and corresponding stable and unstable particles change places. The hypothesis of the decay of the primordial de Sitter vacuum of the Planck density to an asymptotic state of the expanding Universe with de Sitter vacuum of the observed critical density is proposed. The T -duality and S-duality hypotheses relating subgroups SU(3)×SU(2)×U(1) and dual subgroups S??(3)× S??(2) × ??(1) with decay of the primordial symmetry group E(8) × ??(8) are proposed. In particular, these dualities relate the minimum Planck length 10^?13 cm to the primordial curvature radius 10^?13 cmof theMetagalaxy of the Planck density and its modern curvature radius of 10²⁸ cm. That is, the probable relation of the Planck mass to the Metagalaxy mass of 10⁶¹ Planck masses is indicated.     

The Integral Form of D = 3 Chern‐Simons Theories Probing Singularities

We consider D=3 supersymmetric Chern Simons gauge theories both from the point of view of their formal structure and of their applications to the AdS₄/CFT₃ correspondence. From the structural view‐point, we use the new formalism of integral forms in superspace that utilizes the rheonomic Lagrangians and the Picture Changing Operators, as an algorithmic tool providing the connection between different approaches to supersymmetric theories. We provide here the generalization to an arbitrary Kähler manifold with arbitrary gauge group and arbitrary superpotential of the rheonomic lagrangian of D=3 matter coupled gauge theories constructed years ago. From the point of view of the AdS₄/CFT₃ correspondence and more generally of M2‐branes we emphasize the role of the Kähler quotient data in determining the field content and the interactions of the Cherns Simons gauge theory when the transverse space to the brane is a non‐compact Kähler quotient K ₄ of some flat variety with respect to a suitable group. The crepant resolutions of singularities fall in this category. In the present paper we anticipate the general scheme how the geometrical data are to be utilized in the construction of the D=3 Chern‐Simons Theory supposedly dual to the corresponding M2‐brane solution.     

Remarks on Positive Energy Vacua via Effective Potentials in String Theory

We study warped compactifications of string/M theory with the help of effective potentials, continuing previous work of the last two authors and Michael R. Douglas presented in (On the boundedness of effective potentials arising from string compactifications. Communications in Mathematical Physics 325(3):847–878, 2014). Under physically reasonable assumptions, we provide a mathematically rigorous proof of the existence of positive local minima of a large class of effective potentials. The dynamics of the conformal factor of the internal metric, which is responsible for instabilities in these constructions, is explored, and such instabilities are investigated in the context of de Sitter vacua. We prove existence results for the equations of motion in the case of a slowly varying warp factor, and the stability of such solutions is also addressed. These solutions are a family of meta-stable de Sitter vacua from type IIB string theory in a general non-supersymmetric setup.     

A Stress Tensor for Anti-de Sitter Gravity

We propose a procedure for computing the boundary stress tensor associated with a gravitating system in asymptotically anti-de Sitter space. Our definition is free of ambiguities encountered by previous attempts, and correctly reproduces the masses and angular momenta of various spacetimes. Via the AdS/CFT correspondence, our classical result is interpretable as the expectation value of the stress tensor in a quantum conformal field theory. We demonstrate that the conformal anomalies in two and four dimensions are recovered. The two dimensional stress tensor transforms with a Schwarzian derivative and the expected central charge. We also find a nonzero ground state energy for global AdS₅, and show that it exactly matches the Casimir energy of the dual super Yang–Mills theory on S ³×R. Received: 20 April 1999 / Accepted: 8 July 1999     

Black holes,AdS, and CFTs

This brief conference proceeding attempts to explain the implications of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence for black hole entropy in a language accessible to relativists and other non-string theorists. The main conclusion is that the Bekenstein–Hawking entropy S _BH is the density of states associated with certain superselections sectors, defined by what may be called the algebra of boundary observables. Interestingly while there is a valid context in which this result can be restated as “S _BH counts all states inside the black hole,” there may also be another in which it may be restated as “S _BH does not count all states inside the black hole, but only those that are distinguishable from the outside.” The arguments and conclusions represent the author’s translation of the community’s collective wisdom, combined with a few recent results.     

Casimir Effect for Moving Branes in Static dS4+1 Bulk

In this paper we study the Casimir effect for conformally coupled massless scalar fields on background of Static dS₄₊₁ spacetime. We will consider the general plane–symmetric solutions of the gravitational field equations and boundary conditions of the Dirichlet type on the branes. Then we calculate the vacuum energy-momentum tensor in a configuration in which the boundary branes are moving by uniform proper acceleration in static de Sitter background. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentum tensor for conformally invariant field in static de Sitter space from the corresponding Rindler counterpart by the conformal transformation.     

High energy physics signatures from inflation and conformal symmetry of de Sitter

During inflation, the geometry of spacetime is described by a (quasi‐)de Sitter phase. Inflationary observables are determined by the underlying (softly broken) de Sitter isometry group which acts like a conformal group on : when the fluctuations are on super‐Hubble scales, the correlators of the scalar fields are constrained by conformal invariance. Heavy fields with mass m larger than the Hubble rate H correspond to operators with imaginary dimensions in the dual Euclidean three‐dimensional conformal field theory. By making use of the dS/CFT correspondence we show that, besides the Boltzmann suppression expected from the thermal properties of de Sitter space, the generic effect of heavy fields in the inflationary correlators of the light fields is to introduce power‐law suppressed corrections of the form . This can be seen, for instance, at the level of the four‐point correlator for which we provide the correction due to a massive scalar field exchange.     

〈 φ2 〉 REG in Schwarzschild-de Sitter spacetime

The regularized expectation values of the field fluctuation 〈 φ² 〉_REG of a conformal massless free scalar field in the spacetime of the Schwarzschild-de Sitter black hole in the Boulware, Unruh and Hartle-Hawking (left and right) vacua are evaluated. Their leading behaviour near the horizons is examined and Page's approximation is verified.     

Symmetry breaking in de Sitter spacetime by antipodal symmetric and antisymmetric fields

The symmetry behaviour of a ϵø⁴ model in the identified de Sitter space is considered. The different boundary conditions imposed on the quantum field correspond to antipodally symmetric and antisymmetric cases. For both cases, the variance of the quantum fluctuations around a constant background field is evaluated using a result on the conformal transformation of the effective action.     

Supersymmetry in the AdS/CFT correspondence

We study how local symmetry transformations of (p,q) anti de Sitter supergravities in three dimensions act on fields on the two-dimensional boundary. The boundary transformation laws are shown to be the same as those of two-dimensional (p,q) conformal supergravities for p,q≤2. Weyl and super Weyl transformations are generated from three-dimensional general coordinate and super transformations.