Abdus Salam and Quadratic Curvature Gravity: Classical Solutions

Stelle, K.S.

doi:10.1142/9789813144873_0011

Cited by 6 publications

(11 citation statements)

References 12 publications

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“…Then the cmc condition Spl = μ emerges as a consequence of Eqs. (38) and (40). So, we show that EOM (25) together with Eq.…”

Section: Cauchy Constraintssupporting

confidence: 54%

“…2 It means that action (4) with codim 1 encodes a particular case of ( p + 1)-dim. gravity theories quadratic in curvature [35][36][37][38]. So, the transition to new geometric variables uncovers the structure of non-linearities of fundamental branes with codim 1 and proves their similarity to non-linearities of f (R) theories of gravity.…”

Section: Introductionmentioning

confidence: 81%

“…So, we show that EOM (25) together with Eq. (8) provide conservation of IDC (38) and (40). The latter select a closed sector of the solutions descrbing constant mean curvature hyper-ws of codim 1.…”

Section: Cauchy Constraintsmentioning

confidence: 99%

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p-Branes with $$AdS_{p+1}$$ vacuum as models of $$R^2$$ gravity

Желтухин

2019

Eur. Phys. J. C

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Branes with constant mean curvature of their hyper-worldsheets of codimension 1 are treated as the Nambu-Goldstone fields of the broken Poincare symmetry. Mapping of their action into quadratic curvature gravity action with spontaneously generated gravity, is shown. Equation for the brane potential extremals and its solution describing hyper-ws of constant curvature are found. For membranes in R 1,3 this extremum is shown to be a saddle 3-dim. hypersurface which defines classically instable vacuum.633 Page 2 of 11 Eur. Phys. J. C (2019) 79 :633 p = 3, D = 6, 8; p = 4, D = 9 and p = 5, D = 10 corresponding to the embeddings of membranes and 3-, 4-, 5-branes into the mentioned higher-dimensional Minkowski spaces. The pair p = 5, D = 10 describes the heterotic 5-brane associated with the soliton solution of the heterotic string equations found in [10]. In M-theory the supermembrane and super 5-brane are called M2 and M5 branes. Mbranes together with superstrings are treated as fundamental constituents of supersymmetric 11-dimensional M-theory unifying gravity with other fundamental forces. Thus, both branes and strings play key roles in theoretical understanding of fundamental interactions, phenomenology of elementary particle physics, black holes, dark matter and AdS/CFT correspondence. A comprehensive review of these and other problems of contemporary physics in which branes play a vital role may be found in [11]. The breakthrough role of branes in attempts to reveal new physics sharpens the problem of their quantum consistency. Solution of this problem has to shed a new light on quantization of gravity. Until now quantization of extended objects remains an open problem even for the case of (super)membranes (p = 2) [12]. This uncertainty in the quantum status of the brane paradigma requires new tools for analyzing its viability. A weak progress in this matter is explained by a complicated non-linear character of brane equations and constraints. The non-linearity problem is typical of the theories unifying the Yang-Mills, gravitational and other fields covariant under diffeomorphisms, gauge and internal symmetries. To solve the problem, we need to deepen understanding of the structure of brane non-linearities.Here we assume that the non-linearities can be converted into the geometric structures known from gravity and gauge theories. For branes, the proof of this assumption allows to implement the BRST-BFV quantization and others methods used for general non-linear systems. We expect that the nonlinearities of ordinary p-branes can be described by a combination of scalars built from the curvature tensor of ( p + 1)dimensional hyper-worldsheets (h-ws). 1 It implies a map of non-linear terms into those known from ( p + 1)-dim. f (R) gravity which generalizes the Starobinsky 4-dim. model [13]. Construction of such a map will also give an additional motivation for the hypothesis that our world is a 3-brane embedded into higher-dimensional spaces [14][15][16][17].The inherent non-linearities prevent the use of string har...

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“…Then the cmc condition Spl = μ emerges as a consequence of Eqs. (38) and (40). So, we show that EOM (25) together with Eq.…”

Section: Cauchy Constraintssupporting

confidence: 54%

Section: Introductionmentioning

confidence: 81%

See 1 more Smart Citation

p-Branes with $$AdS_{p+1}$$ vacuum as models of $$R^2$$ gravity

Желтухин

2019

Eur. Phys. J. C

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“…Also, Refs. [98][99][100][101][102][103][104][105][106] found numerically and studied new black hole solutions (not present in Einstein gravity) and Ref. [107] identified a new class of static spherically symmetric solutions without horizon (called the 2-2-hole), which can, nevertheless, mimic the Schwarzschild solution outside the horizon, with interesting implications for the black hole information paradox.…”

Section: Black Holesmentioning

confidence: 99%

“…Ref. [103] pointed out that the Schwarzschild solution is stable for large horizon radius r h , but becomes unstable (see also [108]) when r h is taken below a critical value set basically by the inverse ghost mass ∼ 1/M 2 (see also [106]); the endpoint of the instability is conjectured to be another black hole solution, which is not present in Einstein gravity and may be stable when r h is small. Ref.…”

Section: Black Holesmentioning

confidence: 99%

Quadratic Gravity

2018

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Adding the terms quadratic in the curvature to the Einstein-Hilbert action renders gravity renormalizable. This property is preserved in the presence of the most general renormalizable couplings with (and of) a generic quantum field theory (QFT). The price to pay is a massive ghost, which is due to the higher derivatives that the terms quadratic in the curvature imply. In this paper, the quadratic gravity scenario is reviewed including the recent progress on the related stability problem of higher derivative theories. The renormalization of the theory is also reviewed and the final form of the full renormalization group equations in the presence of a generic renormalizable QFT is presented. The theory can be extrapolated up to infinite energy through the renormalization group if all matter couplings flow to a fixed point (either trivial or interacting). Moreover, besides reviewing the above-mentioned topics, are some further insight on the ghost issue and the infinite energy extrapolation are provided. There is hope that in the future, this scenario might provide a phenomenologically viable and UV complete relativistic field theory of all interactions.

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$p$-Branes with $AdS_{p+1}$ vacuum as models of $R^2$ gravity

Zheltukhin

2018

Preprint

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Abdus Salam and Quadratic Curvature Gravity: Classical Solutions

Cited by 6 publications

References 12 publications

p-Branes with $$AdS_{p+1}$$ vacuum as models of $$R^2$$ gravity

p-Branes with $$AdS_{p+1}$$ vacuum as models of $$R^2$$ gravity

Quadratic Gravity

$p$-Branes with $AdS_{p+1}$ vacuum as models of $R^2$ gravity

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