189 research outputs found
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 .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- chain compound NaVOAsO
We present the synthesis and a detailed investigation of structural and
magnetic properties of polycrystalline NaVOAsO by means of x-ray
diffraction, magnetization, electron spin resonance (ESR), and 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- chain model with the exchange coupling K and
an alternation parameter . From the high-field magnetic
isotherm measured at K, the critical field of the gap closing is found
to be T, which corresponds to the zero-field spin gap of
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 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
- …