98 research outputs found
Background Independent Algebraic Structures in Closed String Field Theory
We construct a Batalin-Vilkovisky (BV) algebra on moduli spaces of Riemann
surfaces. This algebra is background independent in that it makes no reference
to a state space of a conformal field theory. Conformal theories define a
homomorphism of this algebra to the BV algebra of string functionals. The
construction begins with a graded-commutative free associative algebra \C
built from the vector space whose elements are orientable subspaces of moduli
spaces of punctured Riemann surfaces. The typical element here is a surface
with several connected components. The operation of sewing two
punctures with a full twist is shown to be an odd, second order derivation that
squares to zero. It follows that (\C, \Delta) is a Batalin-Vilkovisky
algebra. We introduce the odd operator , where
is the boundary operator. It is seen that , and that
consistent closed string vertices define a cohomology class of . This
cohomology class is used to construct a Lie algebra on a quotient space of
\C. This Lie algebra gives a manifestly background independent description of
a subalgebra of the closed string gauge algebra.Comment: phyzzx.tex, MIT-CTP-234
How Does a Fundamental String Stretch its Horizon?
It has recently been shown that if we take into account a class of higher
derivative corrections to the effective action of heterotic string theory, the
entropy of the black hole solution representing elementary string states
correctly reproduces the statistical entropy computed from the degeneracy of
elementary string states. So far the form of the solution has been analyzed at
distance scales large and small compared to the string scale. We analyze the
solution that interpolates between these two limits and point out a subtlety in
constructing such a solution due to the presence of higher derivative terms in
the effective action. We also study the T-duality transformation rules to
relate the moduli fields of the effective field theory to the physical
compactification radius in the presence of higher derivative corrections and
use these results to find the physical radius of compactification near the
horizon of the black hole. The radius approaches a finite value even though the
corresponding modulus field vanishes. Finally we discuss the non-leading
contribution to the black hole entropy due to space-time quantum corrections to
the effective action and the ambiguity involved in comparing this result to the
statistical entropy.Comment: LaTeX file, 38 pages; v2: minor changes and added reference
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
Dyon Spectrum in Generic N=4 Supersymmetric Z_N Orbifolds
We find the exact spectrum of a class of quarter BPS dyons in a generic N=4
supersymmetric Z_N orbifold of type IIA string theory on K3\times T^2 or T^6.
We also find the asymptotic expansion of the statistical entropy to first
non-leading order in inverse power of charges and show that it agrees with the
entropy of a black hole carrying same set of charges after taking into account
the effect of the four derivative Gauss-Bonnet term in the effective action of
the theory.Comment: LaTeX file, 39 pages; 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
Black Holes, Elementary Strings and Holomorphic Anomaly
In a previous paper we had proposed a specific route to relating the entropy
of two charge black holes to the degeneracy of elementary string states in N=4
supersymmetric heterotic string theory in four dimensions. For toroidal
compactification this proposal works correctly to all orders in a power series
expansion in inverse charges provided we take into account the corrections to
the black hole entropy formula due to holomorphic anomaly. In this paper we
demonstrate that similar agreement holds also for other N=4 supersymmetric
heterotic string compactifications.Comment: LaTeX file, 28 pages, reference added, minor changes in appendix
Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
We review and extend recent attempts to find a precise relation between
extremal black hole entropy and degeneracy of microstates using AdS_2/CFT_1
correspondence. Our analysis leads to a specific relation between degeneracy of
black hole microstates and an appropriately defined partition function of
string theory on the near horizon geometry, -- named the quantum entropy
function. In the classical limit this reduces to the usual relation between
statistical entropy and Wald entropy.Comment: LaTeX file, 27 pages, A modified and extended version of the talk
given at Strings 200
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
Higher Derivative Corrections to Non-supersymmetric Extremal Black Holes in N=2 Supergravity
Using the entropy function formalism we compute the entropy of extremal
supersymmetric and non-supersymmetric black holes in N=2 supergravity theories
in four dimensions with higher derivative corrections. For supersymmetric black
holes our results agree with all previous analysis. However in some examples
where the four dimensional theory is expected to arise from the dimensional
reduction of a five dimensional theory, there is an apparent disagreement
between our results for non-supersymmetric black holes and those obtained by
using the five dimensional description. This indicates that for these theories
supersymmetrization of the curvature squared term in four dimension does not
produce all the terms which would come from the dimensional reduction of a five
dimensional action with curvature squared terms.Comment: LaTeX file, 29 pages; v2: minor change
Rare Decay Modes of Quarter BPS Dyons
The degeneracy of quarter BPS dyons in N=4 supersymmetric string theories is
known to jump across walls of marginal stability on which a quarter BPS dyon
can decay into a pair of half BPS dyons. We show that as long as the electric
and magnetic charges of the original dyon are primitive elements of the charge
lattice, the subspaces of the moduli space on which a quarter BPS dyon becomes
marginally unstable against decay into a pair of quarter BPS dyons or a half
BPS dyon and a quarter BPS dyon are of codimension two or more. As a result any
pair of generic points in the moduli space can be connected by a path avoiding
these subspaces and there is no jump in the spectrum associated with these
subspaces.Comment: LaTeX file, 9 pages; v2: a minor logical error corrected with no
change in the result
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