Samir D. Mathur

Correlation functions in the CFTd/AdSd+1 correspondence

Abstract Conformal techniques are applied to the calculation of integrals on AdS d +1 space which define correlators of composite operators in the superconformal field theory on the d -dimensional boundary. The 3-point amplitudes for scalar fields of arbitrary mass and gauge fields in the AdS supergravity are calculated explicitly. For three gauge fields we compare in detail with the known conformal structure of the SU (4) flavor current correlator 〈 J i a J j b J k c 〉 of the N = 4, d = 4 SU ( N ) SYM theory. Results agree with the free field approximation as would be expected from superconformal non-renormalization theorems. In studying the Ward identity relating 〈J i a O I O J 〉 to 〈 O I O J 〉 for (non-marginal) scalar composite operators O I , we find that there is a subtlety in obtaining the normalization of 〈 O I O J 〉 from the supergravity action integral.

AdS / CFT duality and the black hole information paradox

Abstract Near-extremal black holes are obtained by exciting the Ramond sector of the D1-D5 CFT, where the ground state is highly degenerate. We find that the dual geometries for these ground states have throats that end in a way that is characterized by the CFT state. Below the black hole threshold we find a detailed agreement between propagation in the throat and excitations of the CFT. We study the breakdown of the semiclassical approximation and relate the results to the proposal of gr-qc/0007011 for resolving the information paradox: semiclassical evolution breaks down if hypersurfaces stretch too much during an evolution. We find that a volume V stretches to a maximum throat depth of V /2G .

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 non-extremal system of 1-D- 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.

Metric of the multiply wound rotating string

Abstract We consider a string wrapped many times around a compact circle in space, and let this string carry a right-moving wave which imparts momentum and angular momentum to the string. The angular momentum causes the strands of the ‘multiwound’ string to separate and cover the surface of a torus. We compute the supergravity solution for this string configuration. We map this solution by dualities to the D1–D5 system with angular momentum that has been recently studied. We discuss how constructing this multiwound string solution may help us to relate the microscopic and macroscopic pictures of black hole absorption.

Graviton exchange and complete four point functions in the AdS / CFT correspondence

Abstract The graviton exchange diagram for the correlation function of arbitrary scalar operators is evaluated in anti-de Sitter space, AdS d +1 . This enables us to complete the computation of the four-point amplitudes of dilaton and axion fields in IIB supergravity on AdS 5 × S 5 . By the AdS/CFT correspondence, we obtain the four-point functions of the marginal operators Tr( F 2 +…) and Tr (F F +…) in N =4 , d =4 SU ( N ) SYM at large N , large g YM 2 N . The short distance asymptotics of the amplitudes are studied. We find that in the direct channel the leading power singularity agrees with the expected contribution of the stress-energy tensor in a double OPE expansion. Logarithmic singularities occur in the complete four-point functions at subleading orders.

Universality 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.

A comparison of the hard ASCA spectral slopes of broad- and narrow-line Seyfert 1 galaxies

The soft (\approx 0.1--2.0 keV) X-ray spectra of narrow-line Seyfert 1 galaxies are known to be generally steeper than those of Seyfert 1 galaxies with broader optical permitted lines. This has been attributed to the presence of strong soft X-ray excesses, over the hard X-ray power law, in many narrow-line Seyfert 1s. Here we use the currently available ASCA data to systematically compare the harder (\approx 2--10 keV) X-ray continua of soft ROSAT narrow-line Seyfert 1s with those of Seyfert 1s with larger H-beta FWHM. Our robust and nonparametric testing suggests, with high statistical significance, that soft ROSAT narrow-line Seyfert 1s have generally steeper intrinsic hard X-ray continua than Seyfert 1s with larger H-beta FWHM. The hard photon index trend appears similar to the previously known soft photon index trend, although with a reduced photon index spread. If the soft X-ray excesses of all Seyfert 1s are confined to below \approx 1 keV they cannot directly affect the \approx 2--10 keV spectra studied here. However, as suggested for the extreme narrow-line Seyfert 1 RE J 1034+393, a strong soft X-ray excess may affect the accretion disc corona which creates the underlying hard X-ray power law. If this is occurring, then more detailed study of this physical process could give clues about the formation of the underlying continua of all Seyferts. Other effects, such as intrinsic 2--10 keV continuum curvature, could also lead to the observed photon index trend and need further study.

Dual geometries for a set of 3-charge microstates

Abstract We construct a set of extremal D1–D5–P solutions, by taking appropriate limits in a known family of nonextremal 3-charge solutions. The extremal geometries turn out to be completely smooth, with no horizon and no singularity. The solutions have the right charges to be the duals of a family of CFT microstates which are obtained by spectral flow from the NS vacuum.

Glueball spectrum for QCD from AdS supergravity duality

Abstract We present the analysis of the complete glueball spectrum for the AdS 7 black hole supergravity dual of QCD 4 in strong coupling limit: g 2 N →∞ . The bosonic fields in the supergravity multiplet lead to 6 independent wave equations contributing to glueball states with J PC =2 ++ ,1 +− ,1 −− , 0 ++ and 0 −+ . We study the spectral splitting and degeneracy patterns for both QCD 4 and QCD 3 . Despite the expected limitations of a leading order strong coupling approximation, the pattern of spins, parities and mass inequalities bare a striking resemblance to the known QCD 4 glueball spectrum as determined by lattice simulations at weak coupling.

3-charge geometries and their CFT duals

Abstract We consider two families of D1–D5–P states and find their gravity duals. In each case the geometries are found to ‘cap off’ smoothly near r = 0 ; thus there are no horizons or closed timelike curves. These constructions support the general conjecture that the interior of black holes is nontrivial all the way up to the horizon.