Metrics with Galilean Conformal Isometry

The Galilean Conformal Algebra (GCA) arises in taking the non-relativistic limit of the symmetries of a relativistic Conformal Field Theory in any dimensions. It is known to be infinite-dimensional in all spacetime dimensions. In particular, the 2d GCA emerges out of a scaling limit of linear combinations of two copies of the Virasoro algebra. In this paper, we find metrics in dimensions greater than two which realize the finite 2d GCA (the global part of the infinite algebra) as their isometry by systematically looking at a construction in terms of cosets of this finite algebra. We list all possible sub-algebras consistent with some physical considerations motivated by earlier work in this direction and construct all possible higher dimensional non-degenerate metrics. We briefly study the properties of the metrics obtained. In the standard one higher dimensional "holographic" setting, we find that the only non-degenerate metric is Minkowskian. In four and five dimensions, we find families of non-trivial metrics with a rather exotic signature. A curious feature of these metrics is that all but one of them are Ricci-scalar flat.Comment: 20 page

Supersymmetric Extension of Galilean Conformal Algebras

The Galilean conformal algebra has recently been realised in the study of the non-relativistic limit of the AdS/CFT conjecture. This was obtained by a systematic parametric group contraction of the parent relativistic conformal field theory. In this paper, we extend the analysis to include supersymmetry. We work at the level of the co-ordinates in superspace to construct the N=1 Super Galilean conformal algebra. One of the interesting outcomes of the analysis is that one is able to naturally extend the finite algebra to an infinite one. This looks structurally similar to the N=1 superconformal algebra in two dimensions, but is different. We also comment on the extension of our construction to cases of higher $N$.Comment: 19 pages; v2: 20 pages, Appendix on OPEs added, other minor changes, references adde

Nash equilibrium mapping vs Hamiltonian dynamics vs Darwinian evolution for some social dilemma games in the thermodynamic limit

How cooperation evolves and manifests itself in the thermodynamic or infinite player limit of social dilemma games is a matter of intense speculation. Various analytical methods have been proposed to analyse the thermodynamic limit of social dilemmas. In a previous work [Chaos Solitons and fractals 135, 109762(2020)] involving one among us, two of those methods, Hamiltonian Dynamics(HD) and Nash equilibrium(NE) mapping were compared. The inconsistency and incorrectness of HD approach vis-a-vis NE mapping was brought to light. In this work we compare a third analytical method, i.e, Darwinian evolution(DE) with NE mapping and a numerical agent based approach. For completeness, we give results for HD approach as well. In contrast to HD which involves maximisation of payoffs of all individuals, in DE, payoff of a single player is maximised with respect to its nearest neighbour. While, HD utterly fails as compared to NE mapping, DE method gives a false positive for game magnetisation -- the net difference between the fraction of cooperators and defectors -- when payoffs obey the condition a+d=b+c, wherein a, d represent the diagonal elements and b, c the off diagonal elements in symmetric social dilemma games. When either a+d =/= b+c or, when one looks at average payoff per player, DE method fails much like the HD approach. NE mapping and numerical agent based method on the other hand agree really well for both game magnetisation as well as average payoff per player for the social dilemmas in question, i.e., Hawk-Dove game and Public goods game. This paper thus bring to light the inconsistency of the DE method vis-a-vis both NE mapping as well as a numerical agent based approach.Comment: 15 pages, 4 figures, 2 table

Determining the regimes of cold and warm inflation in the susy hybrid model

The SUSY hybrid inflation model is found to dissipate radiation during the inflationary period. Analysis is made of parameter regimes in which these dissipative effects are significant. The scalar spectral index, its running, and the tensor-scalar ratio are computed in the entire parameter range of the model. A clear prediction for strong dissipative warm inflation is found for n_S-1 \simeq 0.98 and a low tensor-scalar ratio much below 10^{-6}. The strong dissipative warm inflation regime also is found to have no \eta-problem and with the field amplitude much below the Planck scale. As will be discussed, this has important theoretical implications in permitting a much wider variety of SUGRA extensions to the basic model.Comment: paragraph added at the end of section V; references added; accepted for publication in Phys. Rev.

Singlet ground state in the alternating spin-1/21/2 chain compound NaVOAsO4_4

We present the synthesis and a detailed investigation of structural and magnetic properties of polycrystalline NaVOAsO$_4$ by means of x-ray diffraction, magnetization, electron spin resonance (ESR), and $^{75}$As nuclear magnetic resonance (NMR) measurements as well as density-functional band structure calculations. Temperature-dependent magnetic susceptibility, ESR intensity, and NMR line shift could be described well using an alternating spin-$1/2$ chain model with the exchange coupling $J/k_{\rm B}\simeq 52$ K and an alternation parameter $\alpha \simeq 0.65$. From the high-field magnetic isotherm measured at $T=1.5$ K, the critical field of the gap closing is found to be $H_{\rm c}\simeq 16$ T, which corresponds to the zero-field spin gap of $\Delta_0/k_{\rm B}\simeq 21.4$ K. Both NMR shift and spin-lattice relaxation rate show an activated behavior at low temperatures, further confirming the singlet ground state. The spin chains do not coincide with the structural chains, whereas the couplings between the spin chains are frustrated. Because of a relatively small spin gap, NaVOAsO$_4$ is a promising compound for further experimental studies under high magnetic fields.Comment: 14 pages, 10 figures, 2 table

Dynamics of Interacting Scalar Fields in Expanding Space-Time

The effective equation of motion is derived for a scalar field interacting with other fields in a Friedman-Robertson-Walker background space-time. The dissipative behavior reflected in this effective evolution equation is studied both in simplified approximations as well as numerically. The relevance of our results to inflation are considered both in terms of the evolution of the inflaton field as well as its fluctuation spectrum. A brief examination also is made of supersymmetric models that yield dissipative effects during inflation.Comment: 36 pages, 12 figures. Version published in the Physical Review

Sickness and death

This paper investigates the economic consequences of sickness and death and the manner in which poor urban households in Bangladesh respond to such events. Based on longitudinal data we assess the effects of morbidity and mortality episodes on household income, medical spending, labour supply and consumption. We find that despite maintaining household labour supply, a serious illness exerts a n