arXiv subjects

Sumit R. Das

Publications and source records attributed to Sumit R. Das.

At least 91 records · Page 5Linked to original sources

arXiv1998

Hawking Radiation from Four-dimensional Schwarzschild Black Holes in M-theory

Recently a method has been developed for relating four dimensional Schwarzschild black holes in M-theory to near-extremal black holes in string theory with four charges, using suitably defined ``boosts'' and T-dualities. We show that this method can be extended to obtain the emission rate of low energy massless scalars for the four dimensional Schwarzschild hole from the microscopic picture of radiation from the near extremal hole.

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arXiv1997

Boosts, Schwarzschild Black Holes and Absorption cross-sections in M theory

$D$ dimensional neutral black strings wrapped on a circle are related to $(D-1)$ dimensional charged black holes by boosts. We show that the boost has to be performed in the covering space and the boosted coordinate has to be compactified on a circle with a Lorentz contracted radius. Using this fact we show that the transition between Schwarzschild black holes to black p-branes observed recently in M theory is the well-known black hole- black string transition viewed in a boosted frame. In a similar way the correspondence point where an excited string state goes over to a neutral black hole is mapped exactly to the correspondence point for black p-branes. In terms of the $p$ brane quantities the equation of state for an excited string state becomes identical to that of a 3+1 dimensional massless gas for all $p$. Finally, we show how boosts can be used to relate Hawking radiation rates. Using the known microscopic derivation of absorption by extremal 3-branes and near-extremal 5D holes with three large charges we provide a microscopic derivation of absorption of 0-branes by seven and five dimensional Schwarzschild black holes in a certain regime.

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arXiv1997

D-brane decay and Hawking Radiation

Tree level decay amplitudes of near-BPS D-brane configurations are known to exactly reproduce Hawking radiation rates from corresponding black holes at low energies even though the brane configurations describe semiclassical black holes only when the open string couplings are large. We show that a large class of one (open string) loop corrections to emission processes from D-branes vanish at low energies and nonvanishing loop contributions have an energy dependence consistent with black hole answers, thus providing a justification for the agreement of the tree level results with semiclassical answers.

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arXiv1997

Emission from parallel p-brane Black Holes

The entropy of a near-extremal black hole made of parallel D-branes has been shown to agree, upto a numerical factor, with that of the gas of massless open string states on the brane worldvolume when the string coupling is chosen suitably. We investigate the process of emission or absorption of massless S-wave neutral scalars by these black holes. We show that with rather mild assumptions about the nature of the interactions between the scalar and open string states, the D-brane cross-section generally fails to reproduce the universal low energy black hole cross-section except for 1-branes and 3-branes.

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arXiv1997

The Effectiveness of D-branes in the Description of Near-Extremal Black Holes

It is known that weak coupling calculations of absorption or emission by slightly non-extremal D-brane configurations are in exact agreement with semiclassical results for the black holes they describe at strong couplings. We investigate one open string loop corrections to processes involving single and parallel D-branes and show that a class of relevant terms vanish, indicating that these processes are not renormalized. Our results have implications for five dimensional black holes and extremal 3-branes.

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arXiv1996

Comparing decay rates for black holes and D-branes

We compute the leading order (in coupling) rate of emission of low energy quanta from a slightly nonextremal system of 1 and 5 D-branes. We also compute the classical cross-section, and hence the Hawking emission rate, for low energy scalar quanta for the black hole geometry that corresponds to these branes (at sufficiently strong coupling). These rates are found to agree with each other.

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arXiv1996

Universailty of Low Energy Absorption Cross-sections for Black Holes

In this paper we compute the low energy absorption cross-section for minimally coupled massles scalars and spin-$1/2$ particles, into a general spherically symmetric black hole in arbitrary dimensions. The scalars have a cross section equal to the area of the black hole, while the spin-$1/2$ particles give the area measured in a flat spatial metric conformally related to the true metric.

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arXiv1996

Interactions involving D-branes

We investigate some aspects of the spectrum of D-branes and their interactions with closed strings. As argued earlier, a collection of many D-strings behaves, at large dilaton values, as a single multiply wound string. We use this result and T-duality transformations to show that a similar phenomenon occurs for effective strings produced by wrapping p-branes on a small (p-1)-dimensional torus, for suitable coupling. To understand the decay of an excited D-string at large dilaton values, we study the decay of an elementary string at small dilaton values. A long string, multiply wound on a circle, with a small excitation energy is found to predominantly decay into another string with the same winding number and an unwound closed string (rather than two wound strings). This decay amplitude agrees, under duality, with the decay amplitude computed using the Born-Infeld action for the D-string. We compute the absorption cross section for the D-brane model studied by Callan and Maldacena. The absorption cross section for the dilaton equals that for the scalars obtained by reduction of the graviton, and both agree with the cross section expected from a classical hole with the same charges.

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arXiv1996

Black Hole Entropy and String Theory

This is an expanded version of a talk given at ``{\em IInd Recontre du Vietnam}'' held at Ho Chi Minh City in October, 1995. We discuss several aspects of black hole entropy in string theory. We first explain why the geometric entropy in two dimensional noncritical string theory is nonperturbatively finite. We then explain the philosophy of regarding massive string states as black branes and how the Beckenstein-Hawking entropy for extremal BPS black holes may be understood as coming from degeneracy of string states. This is then discussed in the context of D-strings in Type IIB superstrings. We then describe non-BPS excitations of D-strings and their entropy and explore the possibility that their decay describes Hawking radiation. For these D-strings and other D-branes the entropy and temperature are consequences of the physical motion of stuck open strings along the D-brane and this leads to a simple space-time interpretation. Finally we speculate that the horizon may be itself regarded as a D-brane.

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arXiv1996

Quark Confinement and Dual Representation in 2+1 Dimensional Pure Yang-Mills Theory

We study the quark confinement problem in 2+1 dimensional pure Yang-Mills theory using euclidean instanton methods. The instantons are regularized and dressed Wu-Yang monopoles. The dressing of a monopole is due to the mean field of the rest of the monopoles. We argue that such configurations are stable to small perturbations unlike the case of singular, undressed monopoles. Using exact non-perturbative results for the 3-dim. Coulomb gas, where Debye screening holds for arbitrarily low temperatures, we show in a self-consistent way that a mass gap is dynamically generated in the gauge theory. The mass gap also determines the size of the monopoles. In a sense the pure Yang-Mills theory generates a dynamical Higgs effect. We also identify the disorder operator of the model in terms of the Sine-Gordon field of the Coulomb gas.

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arXiv1996

Excitations of D-strings, Entropy and Duality

We examine the BPS and low energy non-BPS excitations of the D-string, in terms of open strings that travel on the D-string. We use this to study the energy thresholds for exciting a long D-string, for arbitrary winding number. We also compute the leading correction to the entropy from non-BPS states for a long D-string, and observe the relation of all these quantities with the corresponding quantities for the elementary string.

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arXiv1995

Degrees of freedom in two dimensional string theory

We discuss two issues regarding the question of degrees of freedom in two dimensional string theory. The first issue relates to the classical limit of quantum string theory. In the classical theory one requires an infinite number of fields in addition to the collective field to describe ``folds'' on the fermi surface. We argue that in the quantum theory these are not additional degrees of freedom. Rather they represent quantum dispersions of the collective field which are {\em not} suppressed when $\hbar \rightarrow 0$ whenever a fold is present, thus leading to a nontrivial classical limit. The second issue relates to the ultraviolet properties of the geometric entropy. We argue that the geometric entropy is finite in the ultraviolet due to {\em nonperturbative} effects. This indicates that the true degrees of freedom of the two dimensional string at high energies is much smaller than what one naively expects. (Based on talks at Spring Workshop on String theory and Quantum Gravity, ICTP, Trieste, March 1995 and VIIth Regional Conference on Mathematical Physics, Bandar-Anzali, October 1995.)

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arXiv1995

Folds, Bosonization and non-triviality of the classical limit of 2D string theory

In the 1-dimensional matrix model one identifies the tachyon field in the asymptotic region with a nonlocal transform of the density of fermions. But there is a problem in relating the classical tachyon field with the surface profile of the fermi fluid if a fold forms in the fermi surface. Besides the collective field additional variables $w_j(x)$ are required to describe folds. In the quantum theory we show that the $w_j$ are the quantum dispersions of the collective field. These dispersions become $O(1)$ rather than $O(\hbar)$ precisely after fold formation, thus giving additional `classical' quantities and leading to a rather nontrivial classical limit. A coherent pulse reflecting from the potential wall turns into high energy incoherent quanta (if a fold forms), the frequency amplification being of the order of the square root of the number of quanta in the incident wave.

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arXiv1995

Geometric Entropy of Nonrelativistic Fermions and Two Dimensional Strings

We consider the geometric entropy of free nonrelativistic fermions in two dimensions and show that it is ultraviolet finite for finite fermi energies, but divergent in the infrared. In terms of the corresponding collective field theory this is a {\em nonperturbative} effect and is related to the soft behaviour of the usual thermodynamic entropy at high temperatures. We then show that thermodynamic entropy of the singlet sector of the one dimensional matrix model at high temperatures is governed by nonperturbative effects of the underlying string theory. In the high temperature limit the ``exact'' expression for the entropy is regular but leads to a negative specific heat, thus implying an instability. We speculate that in a properly defined two dimensional string theory, the thermodynamic entropy could approach a constant at high temperatures and lead to a geometric entropy which is finite in the ultraviolet.

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arXiv1994

Boundary Dynamics in Dilaton Gravity

We study the dynamics of the boundary dilaton gravity coupled to N massles scalars. We rederive the boundary conditions of [1] and [3] in a way which makes the requirement of reparametrization invariance and role of conformal anomaly explicit. We then study the semiclassical behaviour of the boundary in the N = 24 theory in the presence of an incoming matter wave with a constant energy flux spreaded over a finite interval. There is a critical value of the matter energy density below which the boundary is stable and all the matter is reflected back. For energy densities greater than this critical value there is a similar behaviour for small values of total energy thrown in. However, when the total energy exceeds another critical value, the boundary exibits a runaway behaviour and the spacetime devolopes singularities and horizons.

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arXiv1994

Black Hole Formation and Space-Time Fluctuations in Two Dimensional Dilaton Gravity and Complementarity

We study black hole formation in a model of two dimensional dilaton gravity and 24 massless scalar fields with a boundary. We find the most general boundary condition consistent with perfect reflection of matter and the constraints. We show that in the semiclassical approximation and for the generic value of the parameter which characterizes the boundary conditions, the boundary starts receeding to infinity at the speed of light whenever the total energy of the incoming matter flux exceeds a certain critical value. This is also the critical energy which marks the onset of black hole formation. We then compute the quantum fluctuations of the boundary and of the rescaled scalar curvature and show that as soon as the incoming energy exceeds this critical value, an asymptotic observer using normal time resolutions will always measure large fluctuations of space-time near the horizon, even though the freely falling observer does not. This is an aspect of black hole complementarity relating directly the quantum gravity effects.

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arXiv1993

Matrix Models and Nonperturbative String Propagation in Two-Dimensional Black Hole Backgrounds

We identify a quantity in the $c=1$ matrix model which describes the wavefunction for physical scattering of a tachyon from a black hole of the two dimensional critical string theory. At the semiclassical level this quantity corresponds to the usual picture of a wave coming in from infinity, part of which enters the black hole becoming singular at the singularity, while the rest is scattered back to infinity, with nothing emerging from the whitehole. We find, however, that the exact nonperturbative wavefunction is nonsingular at the singularity and appears to end up in the asymptotic region ``behind'' the singularity.

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arXiv1992

The One Dimensional Matrix Model and String Theory

We discuss the basic features of the double scaling limit of the one dimensional matrix model and its interpretation as a two dimensional string theory. Using the collective field theory formulation of the model we show how the fluctuations of the collective field can be interpreted as the massless "tachyon" of the two dimensional string in a linear dilaton background. We outline the basic physical properties of the theory and discuss the nature of the S-matrix. Finally we show that the theory admits of another interpretation in which a certain integral transform of the collective field behaves as the massless "tachyon" in the two dimensional string with a blackhole background. We show that both the classical background and the fluctuations are non-singular at the black hole singularity.

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