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Ashoke Sen

Publications and source records attributed to Ashoke Sen.

At least 163 records · Page 9Linked to original sources
arXiv2007

Walls of Marginal Stability and Dyon Spectrum in N=4 Supersymmetric String Theories

The spectrum of quarter BPS dyons in N=4 supersymmetric string theories can change as the asymptotic moduli cross walls of marginal stability on which the dyon can break apart into a pair of half BPS states. In this paper we classify these marginal stability walls and examine this phenomenon in the context of exact dyon spectrum found in a class of N=4 supersymmetric string theories. We argue that the dyon partition functions in different domains separated by marginal stability walls are the same, but the choice of integration contour needed for extracting the degeneracies from the partition function differ in these different regions. We also find that in the limit of large charges the change in the degeneracy is exponentially suppressed compared to the leading contribution. This is consistent with the fact that in the computation of black hole entropy we do not encounter any change as the asymptotic moduli fields move across the walls of marginal stability. Finally we carry out some tests of S-duality invariance in the theory.

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arXiv2007

Geometric Tachyon to Universal Open String Tachyon

A system of k Neveu-Schwarz (NS) 5-branes of type II string theory with one transverse direction compactified on a circle admits various unstable D-brane systems, - some with geometric instability arising out of being placed at a point of unstable equilibrium in space and some with the usual open string tachyonic instability but no geometric instability. We discuss the effect of NS 5-branes on the descent relations among these branes and their physical interpretation in the T-dual ALF spaces. We argue that if the tachyon potential controlling these descent relations obeys certain conditions, then in certain region in the parameter space labelling the background the two types of unstable branes become identical via a second order phase transition, with the geometric tachyon in one system getting mapped to the open string tachyon of the other system. This would provide a geometric description of the tachyonic instability of the usual non-BPS Dp-brane in ten dimensional flat space-time.

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arXiv2006

Black Hole Microstates and Attractor Without Supersymmetry

Due to the attractor mechanism, the entropy of an extremal black hole does not vary continuously as we vary the asymptotic values of various moduli fields. Using this fact we argue that the entropy of an extremal black hole in string theory, calculated for a range of values of the asymptotic moduli for which the microscopic theory is strongly coupled, should match the statistical entropy of the same system calculated for a range of values of the asymptotic moduli for which the microscopic theory is weakly coupled. This argument does not rely on supersymmetry and applies equally well to nonsupersymmetric extremal black holes. We discuss several examples which support this argument and also several caveats which could invalidate this argument.

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arXiv2006

Spinning Strings as Small Black Rings

Certain supersymmetric elementary string states with spin can be viewed as small black rings whose horizon has the topology of S^1 \times S^{d-3} in a d-dimensional string theory. By analyzing the singular black ring solution in the supergravity approximation, and using various symmetries of the α' corrected effective action we argue that the Bekenstein-Hawking-Wald entropy of the black string solution in the full string theory agrees with the statistical entropy of the same system up to an overall normalization constant. While the normalization constant cannot be determined by the symmetry principles alone, it can be related to a similar normalization constant that appears in the expression for small black holes without angular momentum in one less dimension. Thus agreement between statistical and macroscopic entropy of (d-1)-dimensional non-rotating elementary string states would imply a similar agreement for a d-dimensional elementary string state with spin. Our analysis also determines the structure of the near horizon geometry and provides us with a geometric derivation of the Regge bound. These studies give further evidence that a ring-like horizon is formed when large angular momentum is added to a small black hole.

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arXiv2006

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.

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arXiv2006

Rotating Attractors

We prove that, in a general higher derivative theory of gravity coupled to abelian gauge fields and neutral scalar fields, the entropy and the near horizon background of a rotating extremal black hole is obtained by extremizing an entropy function which depends only on the parameters labeling the near horizon background and the electric and magnetic charges and angular momentum carried by the black hole. If the entropy function has a unique extremum then this extremum must be independent of the asymptotic values of the moduli scalar fields and the solution exhibits attractor behaviour. If the entropy function has flat directions then the near horizon background is not uniquely determined by the extremization equations and could depend on the asymptotic data on the moduli fields, but the value of the entropy is still independent of this asymptotic data. We illustrate these results in the context of two derivative theories of gravity in several examples. These include Kerr black hole, Kerr-Newman black hole, black holes in Kaluza-Klein theory, and black holes in toroidally compactified heterotic string theory.

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arXiv2006

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.

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arXiv2006

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.

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arXiv2006

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.

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arXiv2006

Dyon Spectrum in CHL Models

We propose a formula for the degeneracy of quarter BPS dyons in a class of CHL models. The formula uses a modular form of a subgroup of the genus two modular group Sp(2,Z). Our proposal is S-duality invariant and reproduces correctly the entropy of a dyonic black hole to first non-leading order for large values of the charges.

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arXiv2006

BTZ Black Hole with Chern-Simons and Higher Derivative Terms

The entropy of a BTZ black hole in the presence of gravitational Chern-Simons terms has previously been analyzed using Euclidean action formalism. In this paper we treat the BTZ solution as a two dimensional black hole by regarding the angular coordinate as a compact direction, and use Wald's Noether charge method to calculate the entropy of this black hole in the presence of higher derivative and gravitational Chern-Simons terms. The parameters labelling the black hole solution can be determined by extremizing an entropy function whose value at the extremum gives the entropy of the black hole.

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arXiv2005

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.

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arXiv2005

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 2π. 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.

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arXiv2005

Stretching the Horizon of a Higher Dimensional Small Black Hole

There is a general scaling argument that shows that the entropy of a small black hole, representing a half-BPS excitation of an elementary heterotic string in any dimension, agrees with the statistical entropy up to an overall numerical factor. We propose that for suitable choice of field variables the near horizon geometry of the black hole in D space-time dimensions takes the form of AdS_2\times S^{D-2} and demonstrate how this ansatz can be used to calculate the numerical factor in the expression for the black hole entropy if we know the higher derivative corrections to the action. We illustrate this by computing the entropy of these black holes in a theory where we modify the supergravity action by adding the Gauss-Bonnet term. The black hole entropy computed this way is finite and has the right dependence on the charges in accordance with the general scaling argument, but the overall numerical factor does not agree with that computed from the statistical entropy except for D=4 and D=5. This is not surprising in view of the fact that we do not use a fully supersymmetric action in our analysis; however this analysis demonstrates that higher derivative corrections are capable of stretching the horizon of a small black hole in arbitrary dimensions.

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arXiv2005

Black Holes and the Spectrum of Half-BPS States in N=4 Supersymmetric String Theory

The entropy of a half-BPS black hole in N=4 supersymmetric heterotic string compactification is independent of the details of the charge vector and is a function only of the norm of the charge vector calculated using the appropriate Lorenzian metric. Thus in order for this to agree with the degeneracy of the elementary string states, the latter must also be a function of the same invariant norm. We show that this is true for generic CHL compactifications to all orders in a power series expansion in the inverse charges, but there are exponentially suppressed corrections which do depend on the details of the charge vector. This is consistent with the hypothesis that the black hole entropy reproduces the degeneracy of elementary string states to all orders in a power series expansion in the inverse charges, and helps us extend the earlier conjectured relation between black hole entropy and degeneracy of elementary string states to generic half-BPS electrically charged states in generic N=4 supersymmetric heterotic string compactification. Using this result we can also relate the black hole entropy to the statistical entropy calculated using an ensemble of elementary string states that contains all BPS states along a fixed null line in the lattice of electric charges.

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arXiv2004

Energy Momentum Tensor and Marginal Deformations in Open String Field Theory

Marginal boundary deformations in a two dimensional conformal field theory correspond to a family of classical solutions of the equations of motion of open string field theory. In this paper we develop a systematic method for relating the parameter labelling the marginal boundary deformation in the conformal field theory to the parameter labelling the classical solution in open string field theory. This is done by first constructing the energy-momentum tensor associated with the classical solution in open string field theory using Noether method, and then comparing this to the answer obtained in the conformal field theory by analysing the boundary state. We also use this method to demonstrate that in open string field theory the tachyon lump solution on a circle of radius larger than one has vanishing pressure along the circle direction, as is expected for a codimension one D-brane.

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arXiv2004

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.

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