29,093 research outputs found
Entropy Function for Heterotic Black Holes
We use the entropy function formalism to study the effect of the Gauss-Bonnet
term on the entropy of spherically symmetric extremal black holes in heterotic
string theory in four dimensions. Surprisingly the resulting entropy and the
near horizon metric, gauge field strengths and the axion-dilaton field are
identical to those obtained by Cardoso et. al. for a supersymmetric version of
the theory that contains Weyl tensor squared term instead of the Gauss-Bonnet
term. We also study the effect of holomorphic anomaly on the entropy using our
formalism. Again the resulting attractor equations for the axion-dilaton field
and the black hole entropy agree with the corresponding equations for the
supersymmetric version of the theory. These results suggest that there might be
a simpler description of supergravity with curvature squared terms in which we
supersymmetrize the Gauss-Bonnet term instead of the Weyl tensor squared term.Comment: LaTeX file, 23 pages; v2: references added; v3: minor addition; v4:
minor change
Black Hole Entropy Function and the Attractor Mechanism in Higher Derivative Gravity
We study extremal black hole solutions in D dimensions with near horizon
geometry AdS_2\times S^{D-2} in higher derivative gravity coupled to other
scalar, vector and anti-symmetric tensor fields. We define an entropy function
by integrating the Lagrangian density over S^{D-2} for a general AdS_2\times
S^{D-2} background, taking the Legendre transform of the resulting function
with respect to the parameters labelling the electric fields, and multiplying
the result by a factor of 2\pi. We show that the values of the scalar fields at
the horizon as well as the sizes of AdS_2 and S^{D-2} are determined by
extremizing this entropy function with respect to the corresponding parameters,
and the entropy of the black hole is given by the value of the entropy function
at this extremum. Our analysis relies on the analysis of the equations of
motion and does not directly make use of supersymmetry or specific structure of
the higher derivative terms.Comment: LaTeX file, 12page
Spin-S Kitaev model: Classical Ground States, Order by Disorder and Exact Correlation Functions
In the first part of this paper, we study the spin-S Kitaev model using spin
wave theory. We discover a remarkable geometry of the minimum energy surface in
the N-spin space. The classical ground states, called Cartesian or CN-ground
states, whose number grows exponentially with the number of spins N, form a set
of points in the N-spin space. These points are connected by a network of flat
valleys in the N-spin space, giving rise to a continuous family of classical
ground states. Further, the CN-ground states have a correspondence with dimer
coverings and with self avoiding walks on a honeycomb lattice. The zero point
energy of our spin wave theory picks out a subset from a continuous family of
classically degenerate states as the quantum ground states; the number of these
states also grows exponentially with N. In the second part, we present some
exact results. For arbitrary spin-S, we show that localized Z_2 flux
excitations are present by constructing plaquette operators with eigenvalues
\pm 1 which commute with the Hamiltonian. This set of commuting plaquette
operators leads to an exact vanishing of the spin-spin correlation functions,
beyond nearest neighbor separation, found earlier for the spin-1/2 model [G.
Baskaran, S. Mandal and R. Shankar, Phys. Rev. Lett. 98, 247201 (2007)]. We
introduce a generalized Jordan-Wigner transformation for the case of general
spin-S, and find a complete set of commuting link operators, similar to the
spin-1/2 model, thereby making the Z_2 gauge structure more manifest. The
Jordan-Wigner construction also leads, in a natural fashion, to Majorana
fermion operators for half-integer spin cases and hard-core boson operators for
integer spin cases, strongly suggesting the presence of Majorana fermion and
boson excitations in the respective low energy sectors.Comment: 9 pages including 4 figures; added a section on an exactly solvable
higher spin version of the Kitaev model; this is the published versio
Geometry versus Entanglement in Resonating Valence Bond Liquids
We investigate the behavior of bipartite as well as genuine multipartite
entanglement of a resonating valence bond state on a ladder. We show that the
system possesses significant amounts of bipartite entanglement in the steps of
the ladder while no substantial bipartite entanglement is present in the rails.
Genuine multipartite entanglement present in the system is negligible. The
results are in stark contrast with the entanglement properties of the same
state on isotropic lattices in two and higher dimensions, indicating that the
geometry of the lattice can have important implications on the quality of
quantum information and other tasks that can be performed by using multiparty
states on that lattice.Comment: 6 pages, 8 figures, RevTeX
Discrete gravity and and its continuum limit
Recently Gambini and Pullin proposed a new consistent discrete approach to
quantum gravity and applied it to cosmological models. One remarkable result of
this approach is that the cosmological singularity can be avoided in a general
fashion. However, whether the continuum limit of such discretized theories
exists is model dependent. In the case of massless scalar field coupled to
gravity with , the continuum limit can only be achieved by fine
tuning the recurrence constant. We regard this failure as the implication that
cosmological constant should vary with time. For this reason we replace the
massless scalar field by Chaplygin gas which may contribute an effective
cosmological constant term with the evolution of the universe. It turns out
that the continuum limit can be reached in this case indeed.Comment: 16 pages,revised version published in MPL
CHL Dyons and Statistical Entropy Function from D1-D5 System
We give a proof of the recently proposed formula for the dyon spectrum in CHL
string theories by mapping it to a configuration of D1 and D5-branes and
Kaluza-Klein monopole. We also give a prescription for computing the degeneracy
as a systematic expansion in inverse powers of charges. The computation can be
formulated as a problem of extremizing a duality invariant statistical entropy
function whose value at the extremum gives the logarithm of the degeneracy.
During this analysis we also determine the locations of the zeroes and poles of
the Siegel modular forms whose inverse give the dyon partition function in the
CHL models.Comment: LaTeX file, 48 pages; v2: typos correcte
Dyon Spectrum in N=4 Supersymmetric Type II String Theories
We compute the spectrum of quarter BPS dyons in freely acting Z_2 and Z_3
orbifolds of type II string theory compactified on a six dimensional torus. For
large charges the result for statistical entropy computed from the degeneracy
formula agrees with the corresponding black hole entropy to first non-leading
order after taking into account corrections due to the curvature squared terms
in the effective action. The result is significant since in these theories the
entropy of a small black hole, computed using the curvature squared corrections
to the effective action, fails to reproduce the statistical entropy associated
with elementary string states.Comment: LaTeX file, 32 pages; v2:minor change
Dual quantum-correlation paradigms exhibit opposite statistical-mechanical properties
We report opposite statistical mechanical behaviors of the two major
paradigms in which quantum correlation measures are defined, viz., the
entanglement-separability paradigm and the information-theoretic one. We show
this by considering the ergodic properties of such quantum correlation measures
in transverse quantum XY spin-1/2 systems in low dimensions. While entanglement
measures are ergodic in such models, the quantum correlation measures defined
from an information-theoretic perspective can be nonergodic.Comment: 8 pages, 5 figures, REVTeX 4.1; v2: published version, 9 page
Symplectic Manifolds, Coherent States and Semiclassical Approximation
We describe the symplectic structure and Hamiltonian dynamics for a class of
Grassmannian manifolds. Using the two dimensional sphere () and disc
() as illustrative cases, we write their path integral representations
using coherent state techniques. These path integrals can be evaluated exactly
by semiclassical methods, thus providing examples of localisation formula.
Along the way, we also give a local coordinate description for a class of
Grassmannians.Comment: 17 pages, preprint TCD-4-93, UR-1324,ER40685-77
Magnetization plateaus and sublattice ordering in easy axis Kagome lattice antiferromagnets
We study kagome lattice antiferromagnets where the effects of easy axis
single-ion anisotropy () dominates over the Heisenberg exchange . For , virtual quantum fluctuations help lift the extensive classical
degeneracy. We demonstrate the presence of a one-third magnetization plateau
for a broad range of magnetic fields along the
easy axis. The fully equilibriated system at low temperature on this plateau
develops an unusual {\em nematic} order that breaks sublattice rotation
symmetry but not translation symmetry--however, extremely slow dynamics
associated with this ordering is expected to lead to glassy freezing of the
system on intermediate time-scales.Comment: published versio
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