arXiv subjects
Publications and source records attributed to Shin'ichi Nojiri.
Holographic Renormalization Group (RG) in nine dimensions is considered. The d8 holographic conformal anomaly is found. It should correspond to d8 CFT in AdS_9/CFT_8 correspondence. The comparison of holographic and QFT anomalies in d8 de Sitter space is done. It may give the indication for rigorous AdS_9/CFT_8 correspondence proposal.
Using AdS/CFT correspondence we found the conformal anomaly from d3 and d5 gauged supergravity with single scalar (dilaton) and the arbitrary scalar potential on AdS-like scalar-gravitational background. Such dilatonic gravity action describes the special RG flows in extended gauged SG when scalars lie in one-dimensional submanifold of complete scalars space. This dilaton-dependent conformal anomaly corresponds to dual non-conformal (gauge) QFT (which is classically conformally invariant) with account of radiative corrections. Equations of motion in d5 gauged supergravity put some restrictions to the dilatonic potential on the conformal boundary. Using these restrictions we propose the candidate c-functions away from exact conformity. These c-functions are positively defined and monotonic, expressed in terms of dilatonic potential and have the fixed points in asymptotically AdS region.
5d dilatonic gravity (bosonic sector of gauged supergravity) with non-trivial bulk potential and with surface terms (boundary cosmological constant and trace anomaly induced effective action for brane quantum matter) is considered. For constant bulk potential and maximally SUSY Yang-Mills theory (CFT living on the brane) the inflationary brane-world is constructed. The bulk is singular asymptotically AdS space with non-constant dilaton and dilatonic de Sitter or hyperbolic brane is induced by quantum matter effects. At the same time, dilaton on the brane is determined dynamically. This all is natural realization of warped compactification in AdS/CFT correspondence. For fine-tuned toy example of non-constant bulk potential we found the non-singular dilatonic brane-world where bulk again represents asymptotically AdS space and de Sitter brane (inflationary phase of observable Universe) is induced exclusively by quantum effects. The radius of the brane and dilaton are determined dynamically. The analytically solvable example of exponential bulk potential leading to singular asymptotically AdS dilatonic bulk space with de Sitter (or hyperbolic) brane is also presented.In all cases under discussion the gravity on the brane is trapped via Randall-Sundrum scenario. It is shown that qualitatively the same types of brane-worlds occur when quantum brane matter is described by $N$ dilaton coupled spinors.
The role of conformal anomaly in AdS/CFT and related issues is clarified. The comparison of holographic and QFT conformal anomalies (with account of brane quantum gravity contribution) indicates on the possibility for brane quantum gravity to occur within AdS/CFT set-up. 3d quantum induced inflationary (or hyperbolic) brane-world is shown to be realized in frames of AdS3/CFT2 correspondence where the role of 2d brane cosmological constant is played by effective tension due to two-dimensional conformal anomaly. The dynamical equations to describe 4d FRW-Universe with account of quantum effects produced by conformal anomaly are obtained. The quantum corrected energy, pressure and entropy are found. Dynamical evolution of entropy bounds in inflationary Universe is estimated and its comparison with quantum corrected entropy is done. It is demonstrated that entropy bounds for quantum corrected entropy are getting the approximate ones and occur for some limited periods of evolution of inflationary Universe.
We consider the quantum effects of bulk matter (scalars, spinors) in the Randall-Sundrum AdS$_5$ brane-world at nonzero temperature. The thermodynamic energy (modulus potential) is evaluated at low and high temperatures. This potential has an extremum which could be a minimum in some cases (for example, for a single fermion). That suggests a new dynamical mechanism to stabilize the thermal AdS$_5$ brane-world. It is shown that the brane separation required to solve the hierarchy scale problem may occur at a quite low temperature. A natural generalization in terms of the AdS/CFT correspondence (through the supergravity thermal contribution) is also possible.
The role of bulk matter quantum effects (via the corresponding effective potential discussed on the example of conformal scalar) and of boundary matter quantum effects (via the conformal anomaly induced effective action) is considered in brane-world cosmology. Scenario is used where brane tension is not free parameter, and the initial bulk-brane classical action is defined by some considerations. The effective bulk-brane equations of motion are analyzed. The quantum creation of 4d de Sitter or Anti-de Sitter(AdS) brane Universe living in 5d AdS space is possible when quantum bulk and (or) brane matter is taken into account. The consideration of only conformal field theory (CFT) living on the brane admits the full analytical treatment. Then bulk gravitational Casimir effect leads to deformation of 5d AdS space shape as well as of shape of spherical or hyperbolic branes. The generalization of above picture for the dominant bulk quantum gravity naturally represents such scenario as self-consistent warped compactification within AdS/CFT set-up.
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 constants it coincides with multi-loop conformal anomaly which depends on regularization scheme in interacting dual QFT. Hence, scheme dependence of holographic conformal anomaly is consistent with dual QFT expectations.
We review (mainly) quantum effects in the theories where gravity sector is described by metric and dilaton. The one-loop effective action for dilatonic gravity in two and four dimensions is evaluated. Renormalization group equations are constructed. The conformal anomaly and induced effective action for 2d and 4d dilaton coupled theories are found. It is applied to study of quantum aspects of black hole thermodynamics, like calculation of Hawking radiation and quantum corrections to black hole parameters and investigation of quantum instability for such objects with multiple horizons. The use of above effective action in the construction of non-singular cosmological models in Einstein or Brans-Dicke (super)gravity and investigation of induced wormholes in supersymmetric Yang-Mills theory are given. 5d dilatonic gravity (bosonic sector of compactified IIB supergravity) is discussed in connection with bulk/boundary (or AdS/CFT) correspondence. Running gauge coupling and quark-antiquark potential for boundary gauge theory at zero or non-zero temperature are calculated from d=5 dilatonic Anti-de Sitter-like background solution which represents Anti-de Sitter black hole for periodic time.
The attempt to understand if AdS/CFT correspondence may be realized as the one between some AdS-like cosmological space and CFT living on the boundary is made. In order to obtain such cosmology we exchange the time and radial coordinates in d5 Schwarzschild-anti de Sitter (S-AdS) BH (with corresponding signature change). The test on proportionality of free energies from such d5 cosmological space (after AdS/CFT identification of parameters) and from ${\cal N}=4$ SU(N) super Yang-Mills quantum theory is successfully passed.
d3 and d5 maximally SUSY gauged supergravity is considered in the parametrization (flow) of full scalar coset where the kinetic term for scalars takes the standard field theory form and the bulk potential is an arbitrary one subject to consistent parametrization. From such SG duals we calculate d2 and d4 holographic conformal anomaly which depends on bulk scalars potential. AdS/CFT correspondence suggests that such SG side conformal anomaly should be identified with (non-perturbative) QFT conformal anomaly (taking account of radiative corrections) for the theory living on the boundary of AdS space. In the limit of constant bulk potential and single scalar, d4 result reproduces the known exact conformal anomaly corresponding to maximally SUSY super Yang-Mills theory coupled to ${\cal N}=4$ conformal supergravity.
The model of d5 higher derivative (HD) gravity admitting Schwarzschild--anti de Sitter Black Hole (S-AdS BH) as exact solution is considered. The surface counterterms are added to the complete action, they are fixed by the condition of finiteness of bulk AdS spacetime when brane goes to infinity. As a result the brane (observable Universe) is defined dynamically in terms of d5 theory parameters (brane tension is fixed). Brane radius is always bigger than horizon radius and the 4d Universe itself could be static or inflationary. Natural ganeralization of this model gives warped compactification (with dynamically generated brane) in the next-to-leading order of AdS/CFT correspondence.
Gauged supergravity (SG) with single scalar (dilaton) and arbitrary scalar potential is considered. Such dilatonic gravity describes special RG flows in extended SG where scalars lie in one-dimensional submanifold of total space. The surface counterterm and finite action for such gauged SG in three-, four- and five-dimensional asymptotically AdS space are derived. Using finite action and consistent gravitational stress tensor (local surface counterterm prescription) the regularized expressions for free energy, entropy and mass of d4 dilatonic AdS black hole are found. The same calculation is done within standard reference background subtraction. The dilaton-dependent conformal anomaly from d3 and d5 gauged SGs is calculated using AdS/CFT correspondence. Such anomaly should correspond to two- and four-dimensional dual quantum field theory which is classically (not exactly) conformally invariant, respectively. The candidate c-functions from d3 and d5 SGs are suggested. These c-functions which have fixed points in asymptoticaly AdS region are expressed in terms of dilatonic potential and they are positively defined and monotonic for number of potentials.
The general model of higher derivative (HD) gravity is considered. The search of brane-world cosmology in such theory is presented when bulk is d5 AdS and boundary is spherical, hyperbolic or flat (single) brane. It is found the wide range of theory parameters where such cosmology may be realized. Special attention is paid to the version of HD theory representing SG dual of ${\cal N}=2$ $Sp(N)$ SCFT (in next-to-leading order of large $N$ expansion). In particular, it is shown that inflationary brane Universe does not occur for SG dual while hyperbolic brane occurs (which was not possible in leading order). The quantum effects of CFT living on the brane (via the corresponding conformal anomaly induced effective action) may qualitatively change the results of classical analysis. There appears inflationary (or hyperbolic) brane Universe induced by only quantum effects. In AdS/CFT correspondence (next-to-leading order) the addition of such CFT effective action (in some energy region) is naturally explained in terms of holographic renormalization group. It results in the possibility of quantum creation of inflationary brane Universe (with small rate) even for SG dual.
We consider brane-world universe where an arbitrary large $N$ quantum CFT is living on the domain wall. This corresponds to implementing of Randall-Sundrum compactification within the context of AdS/CFT correspondence. Using anomaly induced effective action for domain wall CFT the possibility of self-consistent quantum creation of 4d de Sitter wall Universe (inflation) is demonstrated. In case of maximally SUSY Yang-Mills theory the exact correspondence with radius and effective tension found by Hawking-Hertog-Reall is obtained. The hyperbolic wall Universe may be induced by quantum effects only for exotic matter (higher derivatives conformal scalar) which has unusual sign of central charge.
The family of brane-world solutions of d+1-dimensional dilatonic gravity is presented. It includes flat brane with small cosmological constant and (anti) de Sitter brane, dilatonic brane-world black holes (Schwarzschild-(anti-) de Sitter, Kerr, etc). Gravitational and dilatonic perturbations around such branes are found. It is shown that near dilatonic brane-world black hole the gravity may be localized in a standard form. The brane corrections to Newton law are estimated. The proposal to take into account the dilaton coupled brane matter quantum effects is made. The corresponding effective action changes the structure of 4d de Sitter wall. RG flow of four-dimensional Newton constant in IR and UV is briefly discussed.
Stability of dilatonic AdS spaces due to quantum effects of dilaton coupled conformal matter is considered. When such spaces do not exist on classical level, their dynamical generation occurs. Explicit examples corresponding to quantum creation of d4 dilatonic AdS Universe and of d2 dilatonic AdS Black Hole (BH) are presented. Motivated by holographic RG, in the similar approach the complete d5 effective action is discussed. The intermediate region where it is the sum of two parts: bulk (classical gravity) and boundary quantum action is investigated. The effective equations solution representing d5 AdS Universe with warp scale factor is found. Four-dimensional de Sitter or AdS world is generated on the boundary of such Universe as a result of quantum effects.
We generalize the local surface counterterm prescription suggested in Einstein gravity for higher derivative (HD) and Weyl gravities. Explicitly, the surface counterterm is found for three- and five-dimensional HD gravities. As a result, the gravitational action for asymptotically AdS spaces is finite and gravitational energy-momentum tensor is well-defined. The holographic trace anomaly for d2 and d4 boundary (gauge) QFT dual to above HD gravity is calculated from gravitational energy-momentum tensor. The calculation of AdS black hole mass in HD gravity is presented within above prescrition. The comparison with the standard prescription (using reference spacetime) is done.
We construct IIB supergravity (viewed as dilatonic gravity) background with non-trivial dilaton and with curved four-dimensional space. Such a background may describe another vacuum of maximally supersymmetric Yang-Mills theory or strong coupling regime of (non)-supersymmetric gauge theory with (power-like) running gauge coupling which depends on curvature. Curvature dependent quark-antiquark potential is calculated where the geometry type of hyperbolic (or de Sitter universe) shows (or not) the tendency of the confinement. Generalization of IIB supergravity background with non-constant axion is presented. Quark-antiquark potential being again curvature-dependent has a possibility to produce the standard area law for large separations.