Galilean conformal algebra (GCA) is an Inönü-Wigner (IW) contraction of a conformal algebra, while Newton-Hooke string algebra is an IW contraction of an AdS algebra which is the isometry of an AdS space. It is shown that the GCA is a boundary realization of the Newton-Hooke string algebra in the bulk AdS. The string lies along the direction transverse to the boundary, and the worldsheet is AdS...

I review the dynamical symmetry breaking (DSB) approach to the Origin of Mass, which is traced back to the original (2008 Nobel prize) work of Nambu based on the BCS analogue of superconductor where mass of nucleon (then elementary particle) arises due to Cooper paring and pions are provided as massless Nambu-Goldstone (NG) bosons, being composite as in Fermi-Yang/Sakata model. In this talk I w...

Chiral gravity is three-dimensional asymptotically AdS3 gravity with an Einstein, cosmological, and Chern-Simons term at a critical value of the coupling denoted μl = 1. Ordinarily, excitations of AdS3 gravity are known to transform non-trivially under an asymptotic symmetry group consisting of both a left-moving and a right-moving conformal group. However it was recently conjectured [1] that a...

The conformal transformation in the Einstein Hilbert action leads to a new frame where an extra scalar degree of freedom is compensated by the local conformal-like symmetry. We write down a most general action resulting from such transformation and show that it covers both general relativity and conformally coupled to gravity scalar field as the particular cases. On quantum level the equivalenc...

In frames of dS/CFT correspondence suggested by Strominger we calculate holographic conformal anomaly for dual euclidean CFT. The holographic renormalization group method is used for this purpose. It is explicitly demonstrated that two-dimensional and four-dimensional conformal anomalies (or corresponding central charges) have the same form as those obtained in AdS/CFT duality. [email protected]...

For massless φ theory, we explicitly compute the lowest order non-local contributions to the one-loop effective action required for the determination of the trace anomaly. Imposing exact conformal invariance of the local part of the effective action, we argue that the issue of quadratic divergences does not arise in a theory where exact conformal symmetry is only broken by quantum effects. Conf...

We study the realization of conformal symmetry in the QHE as part of the W∞ algebra. Conformal symmetry can be realized already at the classical level and implies the complexification of coordinate space. Its quantum version is not unitary. Nevertheless, it can be rendered unitary by a suitable modification of its definition which amounts to taking proper care of the quantum measure. The conseq...

Definitions of non-relativistic conformal transformations are considered both in the Newton-Cartan and in the Kaluza-Klein-type Eisenhart/Bargmann geometrical frameworks. The symmetry groups that come into play are exemplified by the cosmological, and also the Newton-Hooke solutions of Newton’s gravitational field equations. It is shown, in particular, that the maximal symmetry group of the sta...

According to Schoen and Yau (1988), an extensive class of conformally flat manifolds is realized as Kleinian manifolds. Nayatani (1997) constructed a metric on a Kleinian manifold M which is compatible with the canonical flat conformal structure. He showed that this metric gN has a large symmetry if gN is a complete metric. Under certain assumptions including the completeness of gN , the isomet...

The six-dimensional exotic Galilean algebra in (2+1) dimensions with two central charges m and θ, is extended when m = 0, to a tendimensional Galilean conformal algebra with dilatation, expansion, two acceleration generators and the central charge θ. A realisation of such a symmetry is provided by a model with higher derivatives recently discussed in [1]. We consider also a realisation of the G...