Exploring Lovelock theory moduli space for Schroedinger solutions

We look for Schroedinger solutions in Lovelock gravity in $D > 4$. We span the entire parameter space and determine parametric relations under which the Schroedinger solution exists. We find that in arbitrary dimensions pure Lovelock theories have Schroedinger solutions of arbitrary radius, on a co-dimension one locus in the Lovelock parameter space. This co-dimension one locus contains the subspace over which the Lovelock gravity can be written in the Chern-Simons form. Schroedinger solutions do not exist outside this locus and on this locus they exist for arbitrary dynamical exponent z. This freedom in z is due to the degeneracy in the configuration space. We show that this degeneracy survives certain deformation away from the Lovelock moduli space.Comment: 22 pages, Title changed, contents revised with focus on Schroedinger solutions, extra references added, to match with the version published in Nucl. Phys.

Yang-Baxter algebra and generation of quantum integrable models

An operator deformed quantum algebra is discovered exploiting the quantum Yang-Baxter equation with trigonometric R-matrix. This novel Hopf algebra along with its $q \to 1$ limit appear to be the most general Yang-Baxter algebra underlying quantum integrable systems. Three different directions of application of this algebra in integrable systems depending on different sets of values of deforming operators are identified. Fixed values on the whole lattice yield subalgebras linked to standard quantum integrable models, while the associated Lax operators generate and classify them in an unified way. Variable values construct a new series of quantum integrable inhomogeneous models. Fixed but different values at different lattice sites can produce a novel class of integrable hybrid models including integrable matter-radiation models and quantum field models with defects, in particular, a new quantum integrable sine-Gordon model with defect.Comment: 13 pages, revised and bit expanded with additional explanations, accepted for publication in Theor. Math. Phy

Constraints from Conformal Symmetry on the Three Point Scalar Correlator in Inflation

Using symmetry considerations, we derive Ward identities which relate the three point function of scalar perturbations produced during inflation to the scalar four point function, in a particular limit. The derivation assumes approximate conformal invariance, and the conditions for the slow roll approximation, but is otherwise model independent. The Ward identities allow us to deduce that the three point function must be suppressed in general, being of the same order of magnitude as in the slow roll model. They also fix the three point function in terms of the four point function, upto one constant which we argue is generically suppressed. Our approach is based on analyzing the wave function of the universe, and the Ward identities arise by imposing the requirements of spatial and time reparametrization invariance on it.Comment: 35 pages; Extra references and comments added, The version published in JHE

Ward Identities for Scale and Special Conformal Transformations in Inflation

We derive the general Ward identities for scale and special conformal transformations in theories of single field inflation. Our analysis is model independent and based on symmetry considerations alone. The identities we obtain are valid to all orders in the slow roll expansion. For special conformal transformations, the Ward identities include a term which is non-linear in the fields that arises due to a compensating spatial reparametrization. Some observational consequences are also discussed.Comment: 42 Pages. v3: Section on checks of the Ward identities added. The JHEP accepted versio

Economic Efficiency, Distributive Justice and Liability Rules

The main purpose of this paper is to show that the conflict between the considerations involving economic efficiency and those of distributive justice, in the context of assigning liability, is not as sharp as is generally believed to be the case. The condition of negligence liability which characterizes efficiency in the context of liability rules has an all-or-none character. Negligence liability requires that if one party is negligent and the other is not then the liability for the entire accident loss must fall on the negligent party. Thus within the framework of standard liability rules efficiency requirements preclude any non-efficiency considerations in cases where one party is negligent and the other is not. In this paper it is shown that a part of accident loss plays no part in providing appropriate incentives to the parties for taking due care and can therefore be apportioned on non-efficiency considerations. For a systematic analysis of efficiency requirements, a notion more general than that of a liability rule, namely, that of a decomposed liability rule is introduced. A complete characterization of efficient decomposed liability rules is provided in the paper. One important implication of the characterization theorems of this paper is that by decomposing accident loss in two parts, the scope for distributive considerations can be significantly broadened without sacrificing economic efficiency.Tort Law, Liability Rules, Decomposed liability Rules, Efficient Rules, Nash Equilibria, Negligence Liability, Distributive Justice