Conformal Anomaly for Dilaton Coupled Theories from AdS/CFT Correspondence

Trace anomaly for dilaton coupled conformal theories on curved background with non-zero dilaton is found from supergravity side as an IR effect using AdS/CFT correspondence. For $d=2$ it coincides with the conformal anomaly for dilaton coupled scalar (up to total derivative term which is known to be ambiguous). In four-dimensional case we get conformal anomaly for ${\cal N}=4$ super YM theory interacting with conformal supergravity. In the same way the calculation of dilaton dependent conformal anomaly in higher dimensions seems to be much easier than using standard QFT methods.Comment: LaTeX file 10 page

Quantum Annihilation of Anti- de Sitter Universe

We discuss the role of conformal matter quantum effects (using large $N$ anomaly induced effective action) to creation-annihilation of an Anti-de Sitter Universe. The arbitrary GUT with conformally invariant content of fields is considered. On a purely gravitational (supersymmetric) AdS background, the quantum effects act against an (already existing) AdS Universe. The annihilation of such a Universe occurs, what is common for any conformal matter theory. On a dilaton-gravitational background, where there is dilatonic contribution to the induced effective action, the quantum creation of an AdS Universe is possible assuming fine-tuning of the dilaton.Comment: 7 pages, LaTeX, no figures, minor modifications. Version to appear in Phys. Lett.

Wrapped branes as qubits

Recent work has established a correspondence between the tripartite entanglement measure of three qubits and the macroscopic entropy of the four-dimensional 8-charge STU black hole of supergravity. Here we consider the configurations of intersecting D3-branes, whose wrapping around the six compact dimensions T^6 provides the microscopic string-theoretic interpretation of the charges, and associate the three-qubit basis vectors |ABC>, (A,B,C=0 or 1) with the corresponding 8 wrapping cycles. In particular, we relate a well-known fact of quantum information theory, that the most general real three-qubit state can be parameterized by four real numbers and an angle, to a well-known fact of string theory, that the most general STU black hole can be described by four D3-branes intersecting at an angle.Comment: Version appearing in Phys. Rev. Lett, includes Type IIA description as well as Type II

Covariant perturbation theory and the Randall-Sundrum picture

The effective action for quantum fields on a $d$-dimensional spacetime can be computed using a non local expansion in powers of the curvature. We show explicitly that, for conformal fields and up to quadratic order in the curvature, the non local effective action is equivalent to the $d+1$ action for classical gravity in $AdS_{d+1}$ restricted to a $d-1$-brane. This generalizes previous results about quantum corrections to the Newtonian potential and provides an alternative method for making local a non-local effective action. The equivalence can be easily understood by comparing the Kallen-Lehmann decomposition of the classical propagator with the spectral representation of the non local form factors in the quantum effective action.Comment: 8 pages, Latex. Minor corrections. To appear in Phys. Lett.

Superqubits

We provide a supersymmetric generalization of n quantum bits by extending the local operations and classical communication entanglement equivalence group [SU(2)]^n to the supergroup [uOSp(1|2)]^n and the stochastic local operations and classical communication equivalence group [SL(2,C)]^n to the supergroup [OSp(1|2)]^n. We introduce the appropriate supersymmetric generalizations of the conventional entanglement measures for the cases of $n=2$ and $n=3$. In particular, super-Greenberger-Horne-Zeilinger states are characterized by a nonvanishing superhyperdeterminant.Comment: 16 pages, 4 figures, 4 tables, revtex; minor corrections, version appearing in Phys. Rev.

Generalized mirror symmetry and trace anomalies

We consider compactification of M-theory on X7 with betti numbers (b_0, b_1, b_2, b_3, b_3, b_2, b_1, b_0) and define a generalized mirror symmetry (b_0, b_1, b_2, b_3) goes to (b_0, b_1, b_2 -rho/2, b_3+rho/2)$ under which rho = 7b_0-5b_1+3b_2 -b_3 changes sign. Generalized self-mirror theories with rho=0 have massless sectors with vanishing trace anomaly (before dualization). Examples include pure supergravity with N \geq 4 and supergravity plus matter with N \leq 4.Comment: 19 pages late

E_7 and the tripartite entanglement of seven qubits

In quantum information theory, it is well known that the tripartite entanglement of three qubits is described by the group [SL(2,C)]^3 and that the entanglement measure is given by Cayley's hyperdeterminant. This has provided an analogy with certain N=2 supersymmetric black holes in string theory, whose entropy is also given by the hyperdeterminant. In this paper, we extend the analogy to N=8. We propose that a particular tripartite entanglement of seven qubits, encoded in the Fano plane, is described by the exceptional group E_7(C) and that the entanglement measure is given by Cartan's quartic E_7 invariant.Comment: Minor improvements. 15 page late

Charged Particles and the Electro-Magnetic Field in Non-Inertial Frames of Minkowski Spacetime: I. Admissible 3+1 Splittings of Minkowski Spacetime and the Non-Inertial Rest Frames

By using the 3+1 point of view and parametrized Minkowski theories we develop the theory of {\it non-inertial} frames in Minkowski space-time. The transition from a non-inertial frame to another one is a gauge transformation connecting the respective notions of instantaneous 3-space (clock synchronization convention) and of the 3-coordinates inside them. As a particular case we get the extension of the inertial rest-frame instant form of dynamics to the non-inertial rest-frame one. We show that every isolated system can be described as an external decoupled non-covariant canonical center of mass (described by frozen Jacobi data) carrying a pole-dipole structure: the invariant mass and an effective spin. Moreover we identify the constraints eliminating the internal 3-center of mass inside the instantaneous 3-spaces. In the case of the isolated system of positive-energy scalar particles with Grassmann-valued electric charges plus the electro-magnetic field we obtain both Maxwell equations and their Hamiltonian description in non-inertial frames. Then by means of a non-covariant decomposition we define the non-inertial radiation gauge and we find the form of the non-covariant Coulomb potential. We identify the coordinate-dependent relativistic inertial potentials and we show that they have the correct Newtonian limit. In the second paper we will study properties of Maxwell equations in non-inertial frames like the wrap-up effect and the Faraday rotation in astrophysics. Also the 3+1 description without coordinate-singularities of the rotating disk and the Sagnac effect will be given, with added comments on pulsar magnetosphere and on a relativistic extension of the Earth-fixed coordinate system.Comment: This paper and the second one are an adaptation of arXiv 0812.3057 for publication on Int.J.Geom. Methods in Modern Phys. 77

Seeing social enterprise through the theoretical conceptualisation of ethical capital

Objectives: Current conceptualisations of social enterprise fail to fully satisfy an understanding of the movement. A focus on the economic implies a business model where deep tensions lie. A focus on social capital offers a different frame of reference, yet both these conceptualisations fail to fully identify the phenomena that is social enterprise. The objective of this paper seeks to fill that gap. Ethical capital is offered here as the missing conceptualisation in the field of social enterprise. Prior work: Pearce (2003) describes social enterprises as part of the third system, closer to the first system (private business), than the second system (public provision), yet primarily social and secondly a business. Social Enterprises are described as trading organisations in a market (Pearce 2003). A focus and operationalisation for social enterprises to be ‘business-like’ and ‘entrepreneurial’ is well documented (Leadbeater 1997; Dees 1998; Nicholls 2006b). Approach: Yet, if as part of the third sector, social enterprises are as Dart (2004) suggests; ‘blurring the boundaries between non-profit and profit’, but what blurs? What is compromised? What exactly is lost (or gained)? What challenges are there for social enterprises? And is a managerialist ideology taking precedence over the social? This paper provides a conceptual paper that seeks to outline the arguments on the table and develop an ethical capital conceptualisation of social enterprise. Results: This paper very much aims at starting the process of intellectual debate about the notion of ethical capital in social enterprises. The conclusions of this paper outline further research questions that need to be addressed in order to fully develop this concept. Implications: The current ideology of the neo-classical economic paradigm it is argued in the paper pursues interests towards the self and towards the erosion of the moral basis of association. The outcome leaves society with a problem of low ethical virtue - the implications of this paper are that social enterprises maximise ethical virtue beyond any other form of organisation and as such hold great value beyond their missions and values. Value: This paper offers great value in the understanding of social enterprise through fresh insight into the conceptualisation. A critical perspective to the current literature is taken and discussed but though the introduction of ethical capital this paper takes our understanding of the value of the sector into another light, providing practitioners, business support agencies and academics alike with a different level of conceptualisation that has not been explored before.</p