Djordje Minic

Mass, entropy and holography in asymptotically de Sitter spaces

We propose a novel prescription for computing the boundary stress tensor and charges of asymptotically de Sitter (dS) spacetimes from data at early or late time infinity. If there is a holographic dual to dS spaces, defined analogously to the AdS/CFT correspondence, our methods compute the (Euclidean) stress tensor of the dual. We compute the masses of Schwarzschild-de Sitter black holes in four and five dimensions, and the masses and angular momenta of Kerr-de Sitter spaces in three dimensions. All these spaces are less massive than de Sitter, a fact which we use to qualitatively and quantitatively relate de Sitter entropy to the degeneracy of possible dual field theories. Our results in general dimension lead to a conjecture: Any asymptotically de Sitter spacetime with mass greater than de Sitter has a cosmological singularity. Finally, if a dual to de Sitter exists, the trace of our stress tensor computes the RG equation of the dual field theory. Cosmological time evolution corresponds to RG evolution in the dual. The RG evolution of the c function is then related to changes in accessible degrees of freedom in an expanding universe.

Probable values of the cosmological constant in a holographic theory

We point out that for a large class of universes, holography implies that the most probable value for the cosmological constant is zero. In four space-time dimensions, the probability distribution takes the Baum-Hawking form, dP approximately exp(cM(2)(p)/Lambda)dLambda.

On the quantization of Nambu brackets

We present several non-trivial examples of the three-dimensional quantum Nambu bracket which involve square matrices or three-index objects. Our examples satisfy two fundamental properties of the classical Nambu bracket: they are skew-symmetric and they obey the Fundamental Identity. We contrast our approach to the existing literature on the quantum deformations of Nambu mechanics. We also discuss possible applications of our results in M-theory.

Quantum gravity, torsion, parity violation, and all that

We discuss the issue of parity violation in quantum gravity. In particular, we study the coupling of fermionic degrees of freedom in the presence of torsion and the physical meaning of the Immirzi parameter from the viewpoint of effective field theory. We derive the low-energy effective lagrangian which turns out to involve two parameters, one measuring the non-minimal coupling of fermions in the presence of torsion, the other being the Immirzi parameter. In the case of non-minimal coupling the effective lagrangian contains an axial-vector interaction leading to parity violation. Alternatively, in the case of minimal coupling there is no parity violation and the effective lagrangian contains only the usual axial-axial interaction. In this situation the real values of the Immirzi parameter are not at all constrained. On the other hand, purely imaginary values of the Immirzi parameter lead to violations of unitarity for the case of non-minimal coupling. Finally, the effective lagrangian blows up for the positive and negative unit imaginary values of the Immirzi parameter.

Deconstructing de Sitter

Semiclassical gravity predicts that de Sitter space has a finite entropy. We suggest a picture for Euclidean de Sitter space in string theory, and use the AdS/CFT correspondence to argue that de Sitter entropy can be understood as the number of degrees of freedom in a quantum mechanical dual.

Exploring de Sitter space and holography

Abstract We explore aspects of the physics of de Sitter (dS) space that are relevant to holography with a positive cosmological constant. First we display a non-local map that commutes with the de Sitter isometries, transforms the bulk-boundary propagator and solutions of free wave equations in de Sitter onto the same quantities in Euclidean anti-de Sitter (EAdS), and takes the two boundaries of dS to the single EAdS boundary via an anti-podal identification. Second we compute the action of scalar fields on dS as a functional of boundary data. Third, we display a family of solutions to 3d gravity with a positive cosmological constant in which the equal time sections are arbitrary genus Riemann surfaces, and compute the action of these spaces as a functional of boundary data from the Einstein gravity and Chern–Simons gravity points of view. These studies suggest that if de Sitter space is dual to a Euclidean conformal field theory (CFT), this theory should involve two disjoint, but possibly entangled factors. We argue that these CFTs would be of a novel form, with unusual hermiticity conditions relating left movers and right movers. After exploring these conditions in a toy model, we combine our observations to propose that a holographic dual description of de Sitter space would involve a pure entangled state in a product of two of our unconventional CFTs associated with the de Sitter boundaries. This state can be constructed to preserve the de Sitter symmetries and and its decomposition in a basis appropriate to anti-podal inertial observers would lead to the thermal properties of static patch.

Robustness of topologically protected surface states in layering of Bi2Te3 thin films.

Bulk Bi2Te3 is known to be a topological insulator. We investigate surface states of Bi2Te3(111) thin films of one to six quintuple layers using density-functional theory including spin-orbit coupling. We construct a method to identify topologically protected surface states of thin film topological insulators. Applying this method to Bi2Te3 thin films, we find that the topological nature of the surface states remains robust with the film thickness and that the films of three or more quintuple layers have topologically nontrivial surface states, which agrees with experiments.

4D doubleton conformal theories, CPT and IIB strings on AdS5 × S5

We study the unitary supermultiplets of the N = 8 d = 5 anti-de Sitter (AdS) superalgebra SU(2, 2|4) which is the symmetry algebra of the IIB string theory on AdS5 × S5. We give a complete classification of the doubleton supermultiplets of SU(2, 2|4) which do not have a Poincare limit and correspond to d = 4 conformal field theories (CFT) living on the boundary of AdS5. The CPT self-conjugate irreducible doubleton supermultiplet corresponds to d = 4 N = 4 super Yang-Mills theory. The other irreducible doubleton supermultiplets come in CPT conjugate pairs. The maximum spin range of the general doubleton supermultiplets is 2. In particular, there exists a CPT conjugate pair of doubleton supermultiplets corresponding to the fields of N = 4 conformal supergravity in d = 4 which can be coupled to N = 4 super Yang-Mills theory in d = 4. We also study the “massless” supermultiplets of SU(2, 2|4) which can be obtained by tensoring two doubleton supermultiplets. The CPT self-conjugate “massless” supermultiplet is the N = 8 graviton supermultiplet in AdS5. The other “massless” supermultiplets generally come in conjugate pairs and can have maximum spin range of 4. We discuss the implications of our results for the conjectured CFT/AdS dualities.

Singletons, doubletons and M theory

Abstract We identify the two-dimensional AdS subsupergroup OSp( 16 2 , R ) of the M-theory supergroup OSp( 1 32 , R ) which captures the dynamics of n DO-branes in the large n limit of Matrix theory. The Sp(2, R ) factor in the even subgroup SO(16) x Sp(2, R ) of OSp( 16 2 , R ) corresponds to the AdS extension of the Poincare symmetry of the longitudinal directions. The infinite number of D0-branes with ever increasing and quantized values of longitudinal momenta are identified with the Fourier modes of the singleton supermultiplets of OSp( 16 2 , R ) , which consist of 128 bosons and 128 fermions. The large n limit of N = 16 U(n) Yang-Mills quantum mechanics which describes Matrix theory is a conformally invariant N = 16 singleton quantum mechanics living on the boundary of AdS2. We also review some of the earlier results on the spectra of Kaluza-Klein supergravity theories in relation to the recent conjecture of Maldacena relating the dynamics of n Dp-branes to certain AdS supergravity theories. We point out the remarkable parallel between the conjecture of Maldacena and the construction of the spectra of l 11d and type IIB supergravity theories compactified over various spheres in terms of singleton or doubleton supermultiplets of corresponding AdS supergroups.

Notes on de Sitter space and holography

We explore aspects of the physics of de Sitter (dS) space that are relevant to holography with a positive cosmological constant. First, we display a non-local map that commutes with the de Sitter isometries, transforms the bulk–boundary propagator and solutions of free wave equations in de Sitter onto the same quantities in Euclidean anti-de Sitter (EAdS) space, and takes the two boundaries of dS to the single EAdS boundary via an antipodal identification. Second, we compute the action of scalar fields on dS as a functional of boundary data. Third, we display a family of solutions to three-dimensional gravity with a positive cosmological constant in which the equal time sections are arbitrary genus Riemann surfaces, and compute the action of these spaces as a functional of boundary data. These studies suggest that if de Sitter space is dual to a Euclidean conformal field theory (CFT), this theory should involve two disjoint, but possibly entangled factors. We argue that these CFTs would be of a novel form, with unusual hermiticity conditions relating left movers and right movers. After exploring these conditions in a toy model, we combine our observations to propose that a holographic dual description of de Sitter space would involve a pure entangled state in a product of two of our unconventional CFTs associated with the de Sitter boundaries. This state can be constructed to preserve the de Sitter symmetries and its decomposition in a basis appropriate to antipodal inertial observers would lead to the thermal properties of a static patch. To conclude, we discuss the one-parameter family of de Sitter-invariant vacua for a massive free scalar field, and their thermodynamic properties. At the free field level, we find no obvious thermodynamic reason to favour one vacuum over the other.